From 33f6a2bc9db7f10e781dc489012981c3a217888b Mon Sep 17 00:00:00 2001 From: samnthorne Date: Sun, 26 Mar 2023 17:29:09 -0700 Subject: [PATCH 1/2] images are rendered inside jupyter book --- R/boxplots.R | 2 +- figures/boxplot.png | Bin 245979 -> 167819 bytes figures/majority_classifier_vis.png | Bin 117040 -> 116687 bytes notebooks/_build/.doctrees/analysis.doctree | Bin 101695 -> 105666 bytes notebooks/_build/.doctrees/environment.pickle | Bin 51744 -> 53295 bytes notebooks/_build/html/_sources/analysis.ipynb | 382 ++++++-------- notebooks/_build/html/analysis.html | 347 ++++++------- notebooks/_build/html/objects.inv | Bin 302 -> 631 bytes .../_build/html/reports/analysis.err.log | 60 ++- notebooks/_build/html/searchindex.js | 2 +- .../_build/jupyter_execute/analysis.ipynb | 464 +++++++---------- notebooks/analysis.ipynb | 466 ++++++------------ 12 files changed, 676 insertions(+), 1047 deletions(-) diff --git a/R/boxplots.R b/R/boxplots.R index 9849024..eca78d9 100644 --- a/R/boxplots.R +++ b/R/boxplots.R @@ -29,5 +29,5 @@ grid_boxplot <- function(data, yAxis, yLabel, titleLabel){ geom_boxplot(color="#033291", fill="#b0c8f7", alpha=0.2) + labs(x="Degree of heart disease", y=yLabel) + ggtitle(titleLabel) + - theme(text = element_text(size = 24)) + theme(text = element_text(size = 12)) } \ No newline at end of file diff --git a/figures/boxplot.png b/figures/boxplot.png index 4a0d3a7269775f058f4d53d1204c554e38114dc5..0c2bcfe68534ea15236e054ec368de6de4de5139 100644 GIT binary patch literal 167819 zcmd?RWn7f&_dYsq6qT?LkdTnAh@_-|fJmtbh!WBuHFP%vDy^hJmmna6gmj~zbl1>` zbSn)*{MUnf?{EBm=bRVk#d&e?qsRpF-0NQVitD=86YxM@hLnh!2!%qC-n}FF5QRFy zi~K!72#?%X%5Q*ggimB;B;h-JZA+AS!nc#wchu}qC=Mp%?-Az|F-H`N0d-eWT**0h zVc5l;yk}2r-|5^rM&9dpB+n2@igTHq@lLuW^}*xJF|T~no+NT|jr1KGlTSL`FJ2Ho z);vr3=7o9zeLu)(s;u~_+uY4|^%gx>#aXHwp=RC@7ycD-MBFMA3?tXKLK7L4W zHQvr>sr=k&JN?M0lZRLKuYYb``Xo>JuOEN^ubq|x*7YA>PwjIOkNn3YDAaqeW2FD} z5W___^nX2sn$;C2_^-$A94Ds!uZM04J#PQ6hftkgo+Fn1_pi`X|9`o(eCyJGUpOl4 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z%t0H2@OILNc|UyX*~@p7SD10Fub9}ftHmdvX8H#dc{ou)Kd{C+=%p{7njbZ5tB$K@wQ^|U zAO{BLMnj-j4#YCbtDK)j%s5Fw;CBE{7jc#4oGQRMxuEJR+yS9<7{7!M3iw7HhYbS$ zkybEC3fNcJ0tb^gak~wh()a{ETfBmwxzJFuu#|F1c%@E EzX2s8M*si- diff --git a/notebooks/_build/html/_sources/analysis.ipynb b/notebooks/_build/html/_sources/analysis.ipynb index 836d32a..5441dfe 100644 --- a/notebooks/_build/html/_sources/analysis.ipynb +++ b/notebooks/_build/html/_sources/analysis.ipynb @@ -63,35 +63,6 @@ "source('../tests/tests.R')" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "tags": [ - "hide-cell" - ] - }, - "outputs": [], - "source": [ - "# STEP IN 01 R SCRIPT\n", - "\n", - "library(tidyverse)\n", - "library(repr)\n", - "library(tidymodels)\n", - "library(cowplot)\n", - "library(ggplot2)\n", - "library(caret)\n", - "library(e1071)\n", - "options(repr.matrix.max.rows = 6)\n", - "set.seed(1)\n", - "source(\"../R/selection_forward_function.R\")\n", - "source(\"../R/majority_classifier_function.R\")\n", - "\n", - "# Reading data off internet to make csv files\n", - "source(\"../R/place_data.R\")\n", - "source(\"../R/joining_data.R\")" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -108,19 +79,52 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[1mRows: \u001b[22m\u001b[34m720\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m21\u001b[39m\n", + "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", + "\u001b[1mDelimiter:\u001b[22m \",\"\n", + "\u001b[31mchr\u001b[39m (1): place\n", + "\u001b[32mdbl\u001b[39m (20): age, sex, chest_pain, rest_bp, cholestoral_mmHg, fasting_bs, rest_...\n", + "\n", + "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", + "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "|place|age|sex|chest_pain|rest_bp|cholestoral_mmHg|fasting_bs|rest_ECG|max_heart_rate|exercise|major_vessels|thal|diagnosis|sex_f|chest_pain_f|fasting_bs_f|rest_ECG_f|exercise_f|major_vessels_f|thal_f|diagnosis_f|\n", + "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", + "|switzerland|32|1|1|95|0|NA|0|127|0|NA|NA|1|1|1|NA|0|0|NA|NA|1|\n", + "|switzerland|34|1|4|115|0|NA|NA|154|0|NA|NA|1|1|4|NA|NA|0|NA|NA|1|\n", + "|switzerland|35|1|4|NA|0|NA|0|130|1|NA|7|3|1|4|NA|0|1|NA|7|3|\n", + "|switzerland|36|1|4|110|0|NA|0|125|1|NA|6|1|1|4|NA|0|1|NA|6|1|\n", + "|switzerland|38|0|4|105|0|NA|0|166|0|NA|NA|2|0|4|NA|0|0|NA|NA|2|\n", + "|switzerland|38|0|4|110|0|0|0|156|0|NA|3|1|0|4|0|0|0|NA|3|1|" + ] + } + ], "source": [ "# STEP IN 02 R SCRIPT\n", + "md_table <- function(df){\n", + " paste0('|', paste(names(df), collapse = '|'), '|\\n|', \n", + " paste(rep('---', length(df)), collapse = '|'), '|\\n|', \n", + " paste(Reduce(function(x, y){paste(x, y, sep = '|')}, df), collapse = '|\\n|'), '|')\n", + "}\n", "\n", - "\n", - "heart_data <- join_csv()\n", - "heart_data" + "heart_data <- read_csv('../data/processed/heart_data.csv')\n", + "cat(md_table(head(heart_data)))" ] }, { @@ -146,26 +150,6 @@ "We set the seed with the `set.seed` function in order to make the randomized processes throughout our analysis reproducible. A seed is a numerical starting value, which determines the sequence of random numbers R will generate. Throughout the analysis the `set.seed` function will be at the top of each cell that completes a randomizing action. " ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "# STEP IN 03 R SCRIPT\n", - "\n", - "\n", - "# Splitting data into training and testing sets\n", - "set.seed(1)\n", - "heart_split<-initial_split(heart_data, prop=0.75, strata=diagnosis_f)\n", - "heart_training<-training(heart_split)\n", - "heart_testing<-testing(heart_split)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -229,51 +213,31 @@ "## Initial Visualizations of Predictors" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "# SCRIPTED IN 02.1-INITIAL_VISUALIZATION.R\n", - "\n", - "# Boxplot visualizations for each of our predictors and heart diagnosis\n", - "heart_data <- read_csv('../data/processed/heart_data.csv')\n", - "\n", - " \n", - "boxplot_age <- grid_boxplot(heart_data, age, \"Age (years)\", \"A. Boxplot of degree of heart \\n disease in relation to patient's \\nage\")\n", - "boxplot_rest_bp <- grid_boxplot(heart_data, rest_bp, \"Resting blood pressure (mmHg)\", \"B. Boxplot of degree of heart \\ndisease in relation to patient's \\nresting blood pressure\")\n", - "boxplot_max_heart_rate <- grid_boxplot(heart_data, max_heart_rate, \"Maximum heart rate (BPM)\", \"C. Boxplot of degree of heart \\ndisease in relation to patient's \\nmaximum heart rate\")\n", - "options(repr.plot.width = 20, repr.plot.height = 10)\n", - "boxplots <- plot_grid(boxplot_age, boxplot_rest_bp, boxplot_max_heart_rate, ncol=3)\n", - "show(boxplots)\n", - "ggsave(\"../figures/boxplot.png\")" - ] - }, { "cell_type": "markdown", "metadata": {}, "source": [ - "***Figure 1.***" + "```{figure} ../figures/boxplot.png\n", + "---\n", + "name: boxplot_img\n", + "---\n", + "Initial visualization comparing degree of heart disease to various factors in the data.\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "These boxplots in Figure 1. are our inital visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. `age`, Figure 1B. `rest_bp`, and Figure 1C. `max_heart_rate`, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (`diagnosis_f`)and the predictors.\n", + "These boxplots in {numref}`Figure {number} `. are our initial visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. `age`, {numref}`Figure {number}B `. `rest_bp`, and {numref}`Figure {number}C `. `max_heart_rate`, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (`diagnosis_f`)and the predictors.\n", "\n", - "Figure 1A. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.\n", + "{numref}`Figure {number}A `. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.\n", "\n", - "Figure 1B. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.\n", + "{numref}`Figure {number}B `. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.\n", "\n", - "Figure 1C. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to acheive a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.\n", + "{numref}`Figure {number}C `. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to achieve a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.\n", "\n", - "These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature reseach support. In practice, these predictors are conditions that doctors use to give an **initial diagnosis** of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analysed in the remainder of the project report." + "These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature research support. In practice, these predictors are conditions that doctors use to give an **initial diagnosis** of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analyzed in the remainder of the project report." ] }, { @@ -287,7 +251,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as Figure 1. failed to show any significant correlation.\n", + "To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as {numref}`Figure {number} ` failed to show any significant correlation.\n", "\n", "Forward selection is used to predict accuracy of a classifier that will be made using different predictors to create the model. Based on our literature research detailed above, we will be using forward selection on the variables age, resting blood pressure, and maximum heart rate. We made sure to use our training data set in the forward selection process so that the testing data is never seen by the classifier.\n", "\n", @@ -304,13 +268,13 @@ }, "outputs": [], "source": [ - "# Creating data subsets for forward selection model using training data\n", - "heart_data_subset<-heart_training%>%\n", - " select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%\n", - " na.omit()\n", + "# # Creating data subsets for forward selection model using training data\n", + "# heart_data_subset<-heart_training%>%\n", + "# select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%\n", + "# na.omit()\n", "\n", - "# heart_data_subset\n", - "write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')" + "# # heart_data_subset\n", + "# write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')" ] }, { @@ -332,8 +296,8 @@ }, "outputs": [], "source": [ - "accuracies <- forwardSelection(heart_data_subset)\n", - "accuracies" + "# accuracies <- forwardSelection(heart_data_subset)\n", + "# accuracies" ] }, { @@ -351,41 +315,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], - "source": [ - "# visualization of number of predictors and accuracy based on forward selection\n", - "options(repr.plot.width = 7, repr.plot.height = 7)\n", - "forward_visualization <- ggplot(accuracies, aes(x = size, y = accuracy)) +\n", - " geom_line() +\n", - " geom_point() +\n", - " labs(x = 'Number of predictors used',\n", - " y = 'Estimated accuracy using forward selection',\n", - " title = 'Number of different predictors compared \\nto the accuracy of classifier model') +\n", - " theme(text = element_text(size = 20)) +\n", - " ylim(c(0,1))\n", - "\n", - "forward_visualization" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, "source": [ - "***Figure 2.***" + "```{figure} ../figures/classifier_accuracies.png\n", + "---\n", + "name: forward_img\n", + "---\n", + "Accuracy of model based on the number of predictors used to build the model.\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Figure 2. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau's at the fourth and fifth predictor (`chest_pain` and `sex`). \n", + "{numref}`Figure {number} `. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau's at the fourth and fifth predictor (`chest_pain` and `sex`). \n", "\n", "According to this visualization our pre-chosen predictors should be accurate predictors for the severity of heart disease. It also tells us that with any more predictors our classifier would not be benefitted and with any less we would have drastically lower accuracy. \n", "\n", @@ -416,21 +365,21 @@ }, "outputs": [], "source": [ - "# Selecting chosen predictors within training and testing data\n", - "heart_training <- heart_training %>%\n", - " select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", - " na.omit()\n", - "heart_training\n", + "# # Selecting chosen predictors within training and testing data\n", + "# heart_training <- heart_training %>%\n", + "# select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", + "# na.omit()\n", + "# heart_training\n", "\n", - "# Adding training set to directory\n", - "write_csv(heart_training, '../data/modelling/training_split.csv')\n", + "# # Adding training set to directory\n", + "# write_csv(heart_training, '../data/modelling/training_split.csv')\n", "\n", - "heart_testing <- heart_testing %>%\n", - " select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", - " na.omit()\n", + "# heart_testing <- heart_testing %>%\n", + "# select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", + "# na.omit()\n", "\n", - "# Adding testing set to directory\n", - "write_csv(heart_testing, '../data/modelling/testing_split.csv')" + "# # Adding testing set to directory\n", + "# write_csv(heart_testing, '../data/modelling/testing_split.csv')" ] }, { @@ -464,26 +413,26 @@ }, "outputs": [], "source": [ - "# majority classifier and visualization\n", - "set.seed(1)\n", - "total_rows<-nrow(heart_training)\n", + "# # majority classifier and visualization\n", + "# set.seed(1)\n", + "# total_rows<-nrow(heart_training)\n", "\n", - "number_of_columns<-heart_training%>%\n", - " group_by(diagnosis_f)%>%\n", - " summarize(number=n())%>%\n", - " select(number)\n", + "# number_of_columns<-heart_training%>%\n", + "# group_by(diagnosis_f)%>%\n", + "# summarize(number=n())%>%\n", + "# select(number)\n", " \n", "\n", - "majority_classifier<-heart_training%>%\n", - " group_by(diagnosis_f)%>% \n", - " summarize(percent_outcomes=n()/total_rows*100)%>%\n", - " arrange(desc(percent_outcomes))%>%\n", - " bind_cols(number_of_columns)\n", - "#slice(1)\n", - "majority_classifier\n", + "# majority_classifier<-heart_training%>%\n", + "# group_by(diagnosis_f)%>% \n", + "# summarize(percent_outcomes=n()/total_rows*100)%>%\n", + "# arrange(desc(percent_outcomes))%>%\n", + "# bind_cols(number_of_columns)\n", + "# #slice(1)\n", + "# majority_classifier\n", "\n", - "# write csv to data/modelling\n", - "write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')" + "# # write csv to data/modelling\n", + "# write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')" ] }, { @@ -494,30 +443,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], - "source": [ - "majority_classifier_vis_function(majority_classifier)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, "source": [ - "***Figure 3.***" + "```{figure} ../figures/majority_classifier_vis.png\n", + "---\n", + "name: class_prop_img\n", + "---\n", + "Percentage of patients in data that have each level of heart disease severity. \n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Table 4. and Figure 3. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.\n", + "Table 4. and {numref}`Figure {number} `. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.\n", "\n", "Table 4. also shows us that none of the percent outcomes are over 50%, and the outcomes for severity 1, 2, 3, and 0 are within 15% of each other. This means our data set is distributed evenly enough to build a decent classifier model. Knowing the frequency of each outcome also enables us to set an upper bound on our number of neighbors which is something we will discuss in further detail in subsequent cells." ] @@ -572,11 +517,11 @@ }, "outputs": [], "source": [ - "# Cross validation to find optimal K value\n", - "source('../R/classification_model.R')\n", + "# # Cross validation to find optimal K value\n", + "# source('../R/classification_model.R')\n", "\n", - "heart_data_accuracies <- classifier(heart_training)\n", - "heart_data_accuracies" + "# heart_data_accuracies <- classifier(heart_training)\n", + "# heart_data_accuracies" ] }, { @@ -594,41 +539,35 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], - "source": [ - "# K visualization\n", - "source('../R/model_visualization.R')\n", - "knn_visualization(heart_data_accuracies)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, "source": [ - "***Figure 4.***" + "```{figure} ../figures/classification_model_visualization.png\n", + "---\n", + "name: knn_img\n", + "---\n", + "Accuracy kNN model as number of neighbors is increased to classify the severity of heart disease\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Setting the number of neighbours to $K$ = 2 will give the highest accuracy, as seen in Figure 4. The shape of Figure 4. is not what we expected to see because of the huge drop in the accuracy after $K$ = 2. This means that there is a high risk of losing model accuracy after $K$ = 2. Choosing $K$ = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.\n", + "Setting the number of neighbours to $K$ = 2 will give the highest accuracy, as seen in {numref}`Figure {number} `. The shape of {numref}`Figure {number} `. is not what we expected to see because of the huge drop in the accuracy after $K$ = 2. This means that there is a high risk of losing model accuracy after $K$ = 2. Choosing $K$ = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.\n", "\n", - "Figure 4. shows that choosing a $K$ higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher $K$ values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the $K$ value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different $K$ values are used. The optimal $K$ value has the highest accuracy and has neighbouring $K$ values of similar accuracy." + "{numref}`Figure {number} ` shows that choosing a $K$ higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher $K$ values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the $K$ value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different $K$ values are used. The optimal $K$ value has the highest accuracy and has neighbouring $K$ values of similar accuracy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "After our initial analysis in Figure 4. we decided to continue our analysis despite the suspicious shape of Figure 4. This next step pulls optimal the $K$ value based on the above cross validation to choose the appropriate number of neighbors." + "After our initial analysis in {numref}`Figure {number} ` we decided to continue our analysis despite the suspicious shape of {numref}`Figure {number} ` This next step pulls optimal the $K$ value based on the above cross validation to choose the appropriate number of neighbors." ] }, { @@ -641,13 +580,13 @@ }, "outputs": [], "source": [ - "# Pulling optimal K value based on above cross validation\n", - "set.seed(1)\n", - "best_k<-heart_data_accuracies%>%\n", - " arrange(desc(mean))%>%\n", - " slice(2)%>%\n", - " pull(neighbors)\n", - "# best_k" + "# # Pulling optimal K value based on above cross validation\n", + "# set.seed(1)\n", + "# best_k<-heart_data_accuracies%>%\n", + "# arrange(desc(mean))%>%\n", + "# slice(2)%>%\n", + "# pull(neighbors)\n", + "# # best_k" ] }, { @@ -667,11 +606,11 @@ }, "outputs": [], "source": [ - "# New classifier model using optimal K values\n", - "set.seed(1)\n", - "heart_data_spec_final<- nearest_neighbor(weight_func=\"rectangular\", neighbors=best_k)%>%\n", - " set_engine(\"kknn\")%>%\n", - " set_mode(\"classification\")" + "# # New classifier model using optimal K values\n", + "# set.seed(1)\n", + "# heart_data_spec_final<- nearest_neighbor(weight_func=\"rectangular\", neighbors=best_k)%>%\n", + "# set_engine(\"kknn\")%>%\n", + "# set_mode(\"classification\")" ] }, { @@ -691,12 +630,12 @@ }, "outputs": [], "source": [ - "# Final workflow for classifier using new model.\n", - "set.seed(1)\n", - "heart_data_final_fit<-workflow()%>%\n", - " add_recipe(heart_data_recipe)%>%\n", - " add_model(heart_data_spec_final)%>%\n", - " fit(data=heart_training)\n", + "# # Final workflow for classifier using new model.\n", + "# set.seed(1)\n", + "# heart_data_final_fit<-workflow()%>%\n", + "# add_recipe(heart_data_recipe)%>%\n", + "# add_model(heart_data_spec_final)%>%\n", + "# fit(data=heart_training)\n", " \n", "#heart_data_final_fit" ] @@ -725,20 +664,20 @@ }, "outputs": [], "source": [ - "# Testing our classifier using the testing set\n", - "set.seed(1)\n", - "heart_data_summary<-heart_data_final_fit%>%\n", - " predict(heart_testing)%>%\n", - " bind_cols(heart_testing)%>%\n", - " metrics(truth=diagnosis_f, estimate=.pred_class)%>%\n", - " filter(.metric == 'accuracy')\n", - "heart_data_summary\n", + "# # Testing our classifier using the testing set\n", + "# set.seed(1)\n", + "# heart_data_summary<-heart_data_final_fit%>%\n", + "# predict(heart_testing)%>%\n", + "# bind_cols(heart_testing)%>%\n", + "# metrics(truth=diagnosis_f, estimate=.pred_class)%>%\n", + "# filter(.metric == 'accuracy')\n", + "# heart_data_summary\n", "\n", - "heart_data_predict <- heart_data_final_fit %>%\n", - " predict(heart_testing) %>%\n", - " bind_cols(heart_testing)\n", + "# heart_data_predict <- heart_data_final_fit %>%\n", + "# predict(heart_testing) %>%\n", + "# bind_cols(heart_testing)\n", "\n", - "write_csv(heart_data_predict, '../data/modelling/predict_data.csv')" + "# write_csv(heart_data_predict, '../data/modelling/predict_data.csv')" ] }, { @@ -754,7 +693,7 @@ "source": [ "The accuracy is a reasonable number that shows that even though our predictors within our model produce a strange $K$-nearest neighbour graph, we still built a model that will diagnose patients with ~80% accuracy.\n", "\n", - "We know this is a reasonable accuracy for our classifier from looking at Figure 3. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good. " + "We know this is a reasonable accuracy for our classifier from looking at {numref}`Figure {number} `. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good. " ] }, { @@ -772,33 +711,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "# confusion matrix heat map visualization\n", - "source('../R/confusion_matrix.R')\n", - "\n", - "confusion_matrix(heart_data_predict)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "***Figure 5.***" + "```{figure} ../figures/confusion_matrix.png\n", + "---\n", + "name: confusion_img\n", + "---\n", + "The confusion matrix illustrates the number of correct predictions made by the kNN model to the number of incorrect predictions. The darker the color of the square the more predictions that landed in that category. \n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The confusion matrix (Figure 5.) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled $22 + 39 + 21 + 20 + 4 = 106$ diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.\n", + "The confusion matrix ({numref}`Figure {number} `) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled $22 + 39 + 21 + 20 + 4 = 106$ diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.\n", "\n", "Unfortunately, the classifier also made errors and classified a total of 18 patients with a false positive, meaning the patient's heart disease was worse than it actually was. Moreover, the classifier labelled six patients with false negatives, meaning the patients' heart disease was actually worse than what was predicted. A discussion as to the false positive and false negative results is in the discussion section." ] @@ -809,13 +741,13 @@ "source": [ "## Conclusion\n", "\n", - "The predictors, `age`, `max_heart_rate`, and `rest_bp`, have high accuracy and a good chance of accurately predicting a patient's heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, Figure 1. shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our $K$ graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.\n", + "The predictors, `age`, `max_heart_rate`, and `rest_bp`, have high accuracy and a good chance of accurately predicting a patient's heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, {numref}`Figure {number} ` shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our $K$ graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.\n", "\n", "### Is this what you expected to find?\n", "\n", "We expected to find that the larger the numerical value of a patient's age and resting blood pressure and the lower the maximum heart rate, the greater at risk a person is to have worsened heart disease. We actually found that these predictors have a weak correlation with the outcome variable. However, our model still predicts heart disease severity accurately.\n", "\n", - "From our confusion matrix in Figure 5., we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in Figure 1. that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient's heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.\n", + "From our confusion matrix in {numref}`Figure {number} `, we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in {numref}`Figure {number} ` that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient's heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.\n", "\n", "### What impact could such findings have?\n", "\n", diff --git a/notebooks/_build/html/analysis.html b/notebooks/_build/html/analysis.html index 29ce863..0e28fbc 100644 --- a/notebooks/_build/html/analysis.html +++ b/notebooks/_build/html/analysis.html @@ -382,35 +382,6 @@

Introduction -
-
- - -Hide code cell content - -
-
# STEP IN 01 R SCRIPT
-
-library(tidyverse)
-library(repr)
-library(tidymodels)
-library(cowplot)
-library(ggplot2)
-library(caret)
-library(e1071)
-options(repr.matrix.max.rows = 6)
-set.seed(1)
-source("../R/selection_forward_function.R")
-source("../R/majority_classifier_function.R")
-
-# Reading data off internet to make csv files
-source("../R/place_data.R")
-source("../R/joining_data.R")
-
-
-
-
-

Preliminary Exploratory Data Analysis#

@@ -418,10 +389,36 @@

Preliminary Exploratory Data Analysis 
# STEP IN 02 R SCRIPT
+md_table <- function(df){
+    paste0('|', paste(names(df), collapse = '|'), '|\n|', 
+           paste(rep('---', length(df)), collapse = '|'), '|\n|', 
+           paste(Reduce(function(x, y){paste(x, y, sep = '|')}, df), collapse = '|\n|'), '|')
+}
 
+heart_data <- read_csv('../data/processed/heart_data.csv')
+cat(md_table(head(heart_data)))
+
+
+
+
+
Rows: 720 Columns: 21
+── Column specification ────────────────────────────────────────────────────────
+Delimiter: ","
+chr  (1): place
+dbl (20): age, sex, chest_pain, rest_bp, cholestoral_mmHg, fasting_bs, rest_...
 
-heart_data <- join_csv()
-heart_data
+ℹ Use `spec()` to retrieve the full column specification for this data.
+ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
+
+
+
|place|age|sex|chest_pain|rest_bp|cholestoral_mmHg|fasting_bs|rest_ECG|max_heart_rate|exercise|major_vessels|thal|diagnosis|sex_f|chest_pain_f|fasting_bs_f|rest_ECG_f|exercise_f|major_vessels_f|thal_f|diagnosis_f|
+|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
+|switzerland|32|1|1|95|0|NA|0|127|0|NA|NA|1|1|1|NA|0|0|NA|NA|1|
+|switzerland|34|1|4|115|0|NA|NA|154|0|NA|NA|1|1|4|NA|NA|0|NA|NA|1|
+|switzerland|35|1|4|NA|0|NA|0|130|1|NA|7|3|1|4|NA|0|1|NA|7|3|
+|switzerland|36|1|4|110|0|NA|0|125|1|NA|6|1|1|4|NA|0|1|NA|6|1|
+|switzerland|38|0|4|105|0|NA|0|166|0|NA|NA|2|0|4|NA|0|0|NA|NA|2|
+|switzerland|38|0|4|110|0|0|0|156|0|NA|3|1|0|4|0|0|0|NA|3|1|
@@ -431,20 +428,6 @@

Preliminary Exploratory Data AnalysisTraining and Testing Set#

Before creating our classification model, we partition the heart_data into a training (75%) and testing (25%) set using the tidymodels package. In data analysis it is important to split the data right away to ensure that the classifier we build never sees the testing data. We will train the model using only the training set and test it on the test set once we build the \(K\)-nn classifier. We will use the variable diagnosis_f as our class label as this is what we seek to predict.

We set the seed with the set.seed function in order to make the randomized processes throughout our analysis reproducible. A seed is a numerical starting value, which determines the sequence of random numbers R will generate. Throughout the analysis the set.seed function will be at the top of each cell that completes a randomizing action.

-
-
-
# STEP IN 03 R SCRIPT
-
-
-# Splitting data into training and testing sets
-set.seed(1)
-heart_split<-initial_split(heart_data, prop=0.75, strata=diagnosis_f)
-heart_training<-training(heart_split)
-heart_testing<-testing(heart_split)
-
-
-
-
@@ -465,46 +448,32 @@

Maximum Heart Rate Achieved

Initial Visualizations of Predictors#

-
-
-
# SCRIPTED IN 02.1-INITIAL_VISUALIZATION.R
-
-# Boxplot visualizations for each of our predictors and heart diagnosis
-heart_data <- read_csv('../data/processed/heart_data.csv')
-
-    
-boxplot_age <- grid_boxplot(heart_data, age, "Age (years)", "A. Boxplot of degree of heart \n disease in relation to patient's \nage")
-boxplot_rest_bp <- grid_boxplot(heart_data, rest_bp, "Resting blood pressure (mmHg)", "B. Boxplot of degree of heart \ndisease in relation to patient's \nresting blood pressure")
-boxplot_max_heart_rate <- grid_boxplot(heart_data, max_heart_rate, "Maximum heart rate (BPM)", "C. Boxplot of degree of heart \ndisease in relation to patient's \nmaximum heart rate")
-options(repr.plot.width = 20, repr.plot.height = 10)
-boxplots <- plot_grid(boxplot_age, boxplot_rest_bp, boxplot_max_heart_rate, ncol=3)
-show(boxplots)
-ggsave("../figures/boxplot.png")
-
-
-
-
-

Figure 1.

-

These boxplots in Figure 1. are our inital visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. age, Figure 1B. rest_bp, and Figure 1C. max_heart_rate, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (diagnosis_f)and the predictors.

-

Figure 1A. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.

-

Figure 1B. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.

-

Figure 1C. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to acheive a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.

-

These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature reseach support. In practice, these predictors are conditions that doctors use to give an initial diagnosis of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analysed in the remainder of the project report.

+
+_images/boxplot.png +
+

Fig. 1 Initial visualization comparing degree of heart disease to various factors in the data.#

+
+
+

These boxplots in Figure 1. are our initial visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. age, Figure 1B. rest_bp, and Figure 1C. max_heart_rate, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (diagnosis_f)and the predictors.

+

Figure 1A. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.

+

Figure 1B. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.

+

Figure 1C. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to achieve a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.

+

These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature research support. In practice, these predictors are conditions that doctors use to give an initial diagnosis of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analyzed in the remainder of the project report.

Forward Selection#

-

To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as Figure 1. failed to show any significant correlation.

+

To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as Figure 1 failed to show any significant correlation.

Forward selection is used to predict accuracy of a classifier that will be made using different predictors to create the model. Based on our literature research detailed above, we will be using forward selection on the variables age, resting blood pressure, and maximum heart rate. We made sure to use our training data set in the forward selection process so that the testing data is never seen by the classifier.

Additionally we chose to run forward selection on chest pain type (chest_pain) and sex (sex) to get an idea of what our classifier would look like using more variables.

-
# Creating data subsets for forward selection model using training data
-heart_data_subset<-heart_training%>%
-    select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%
-    na.omit()
+
# # Creating data subsets for forward selection model using training data
+# heart_data_subset<-heart_training%>%
+#     select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%
+#     na.omit()
 
-# heart_data_subset
-write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')
+# # heart_data_subset
+# write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')
@@ -513,34 +482,21 @@

Forward Selection
-
accuracies <- forwardSelection(heart_data_subset)
-accuracies
+
# accuracies <- forwardSelection(heart_data_subset)
+# accuracies

Table 2. Forward selection results

From Table 2. above, we can see that the accuracy increases with every added predictor. To make this result more clear, a visualization of accuracy compared to the number of predictors is included below.

-
-
-
# visualization of number of predictors and accuracy based on forward selection
-options(repr.plot.width = 7, repr.plot.height = 7)
-forward_visualization <- ggplot(accuracies, aes(x = size, y = accuracy)) +
-    geom_line() +
-    geom_point() +
-    labs(x = 'Number of predictors used',
-         y = 'Estimated accuracy using forward selection',
-         title = 'Number of different predictors compared \nto the accuracy of classifier model') +
-    theme(text = element_text(size = 20)) +
-    ylim(c(0,1))
-
-forward_visualization
-
-
-
-
-

Figure 2.

-

Figure 2. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau’s at the fourth and fifth predictor (chest_pain and sex).

+
+_images/classifier_accuracies.png +
+

Fig. 2 Accuracy of model based on the number of predictors used to build the model.#

+
+
+

Figure 2. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau’s at the fourth and fifth predictor (chest_pain and sex).

According to this visualization our pre-chosen predictors should be accurate predictors for the severity of heart disease. It also tells us that with any more predictors our classifier would not be benefitted and with any less we would have drastically lower accuracy.

To conclude, we chose resting blood pressure, age and maximum heart rate as our predictors for the severity of heart disease as seen in row 3 of Table 2.

@@ -549,21 +505,21 @@

Completing Data tidyingage, max_heart_rate and rest_bp to predict diagnosis_f have been chosen, we can further tidy our data by eliminating the unused columns. Additionally, all the rows containing NA were removed. Since our data has already been split into training and testing sets we will tidy both of the subsets.

-
# Selecting chosen predictors within training and testing data
-heart_training <- heart_training %>%
-    select(rest_bp, age, max_heart_rate, diagnosis_f) %>%
-    na.omit()
-heart_training
+
# # Selecting chosen predictors within training and testing data
+# heart_training <- heart_training %>%
+#     select(rest_bp, age, max_heart_rate, diagnosis_f) %>%
+#     na.omit()
+# heart_training
 
-# Adding training set to directory
-write_csv(heart_training, '../data/modelling/training_split.csv')
+# # Adding training set to directory
+# write_csv(heart_training, '../data/modelling/training_split.csv')
 
-heart_testing <- heart_testing %>%
-    select(rest_bp, age, max_heart_rate, diagnosis_f) %>%
-    na.omit()
+# heart_testing <- heart_testing %>%
+#     select(rest_bp, age, max_heart_rate, diagnosis_f) %>%
+#     na.omit()
 
-# Adding testing set to directory
-write_csv(heart_testing, '../data/modelling/testing_split.csv')
+# # Adding testing set to directory
+# write_csv(heart_testing, '../data/modelling/testing_split.csv')
@@ -575,40 +531,38 @@

Majority Classifier
-
# majority classifier and visualization
-set.seed(1)
-total_rows<-nrow(heart_training)
-
-number_of_columns<-heart_training%>%
-    group_by(diagnosis_f)%>%
-    summarize(number=n())%>%
-    select(number)
+
# # majority classifier and visualization
+# set.seed(1)
+# total_rows<-nrow(heart_training)
+
+# number_of_columns<-heart_training%>%
+#     group_by(diagnosis_f)%>%
+#     summarize(number=n())%>%
+#     select(number)
     
 
-majority_classifier<-heart_training%>%
-    group_by(diagnosis_f)%>%   
-    summarize(percent_outcomes=n()/total_rows*100)%>%
-     arrange(desc(percent_outcomes))%>%
-     bind_cols(number_of_columns)
-#slice(1)
-majority_classifier
+# majority_classifier<-heart_training%>%
+#     group_by(diagnosis_f)%>%   
+#     summarize(percent_outcomes=n()/total_rows*100)%>%
+#      arrange(desc(percent_outcomes))%>%
+#      bind_cols(number_of_columns)
+# #slice(1)
+# majority_classifier
 
-# write csv to data/modelling
-write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')
+# # write csv to data/modelling
+# write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')

Table 4. Majority classifier showing the number of people with each severity level of heart disease in the training set

-
-
-
majority_classifier_vis_function(majority_classifier)
-
-
-
-
-

Figure 3.

-

Table 4. and Figure 3. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.

+
+_images/majority_classifier_vis.png +
+

Fig. 3 Percentage of patients in data that have each level of heart disease severity.#

+
+
+

Table 4. and Figure 3. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.

Table 4. also shows us that none of the percent outcomes are over 50%, and the outcomes for severity 1, 2, 3, and 0 are within 15% of each other. This means our data set is distributed evenly enough to build a decent classifier model. Knowing the frequency of each outcome also enables us to set an upper bound on our number of neighbors which is something we will discuss in further detail in subsequent cells.

@@ -622,39 +576,35 @@

Classification Modelworkflow() to determine various accuracies found using different \(K\) values. This workflow does the cross-validation work that was described above using our now split training data. This workflow will include our model and recipe that were formed above. We tested \(K\) values from one to twenty-one because this is the lowest frequency of diagnoses (category 4 appeared 21 times in the training set). If we were to use a number of neighbors greater than twenty-one the majority voting used in \(Knn\) classification would be skewed against diagnosis 4.

-
# Cross validation to find optimal K value
-source('../R/classification_model.R')
+
# # Cross validation to find optimal K value
+# source('../R/classification_model.R')
 
-heart_data_accuracies <- classifier(heart_training)
-heart_data_accuracies
+# heart_data_accuracies <- classifier(heart_training)
+# heart_data_accuracies

Table 5. Parameter values that help select a k value

To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different \(K\) values are used. The optimal \(K\) value has the highest accuracy and has neighbouring \(K\) values of similar accuracy.

+
+_images/classification_model_visualization.png +
+

Fig. 4 Accuracy kNN model as number of neighbors is increased to classify the severity of heart disease#

+
+
+

Setting the number of neighbours to \(K\) = 2 will give the highest accuracy, as seen in Figure 4. The shape of Figure 4. is not what we expected to see because of the huge drop in the accuracy after \(K\) = 2. This means that there is a high risk of losing model accuracy after \(K\) = 2. Choosing \(K\) = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.

+

Figure 4 shows that choosing a \(K\) higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher \(K\) values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the \(K\) value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different \(K\) values are used. The optimal \(K\) value has the highest accuracy and has neighbouring \(K\) values of similar accuracy.

+

After our initial analysis in Figure 4 we decided to continue our analysis despite the suspicious shape of Figure 4 This next step pulls optimal the \(K\) value based on the above cross validation to choose the appropriate number of neighbors.

-
# K visualization
-source('../R/model_visualization.R')
-knn_visualization(heart_data_accuracies)
-
-
-
-
-

Figure 4.

-

Setting the number of neighbours to \(K\) = 2 will give the highest accuracy, as seen in Figure 4. The shape of Figure 4. is not what we expected to see because of the huge drop in the accuracy after \(K\) = 2. This means that there is a high risk of losing model accuracy after \(K\) = 2. Choosing \(K\) = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.

-

Figure 4. shows that choosing a \(K\) higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher \(K\) values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the \(K\) value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different \(K\) values are used. The optimal \(K\) value has the highest accuracy and has neighbouring \(K\) values of similar accuracy.

-

After our initial analysis in Figure 4. we decided to continue our analysis despite the suspicious shape of Figure 4. This next step pulls optimal the \(K\) value based on the above cross validation to choose the appropriate number of neighbors.

-
-
-
# Pulling optimal K value based on above cross validation
-set.seed(1)
-best_k<-heart_data_accuracies%>%
-    arrange(desc(mean))%>%
-    slice(2)%>%
-    pull(neighbors)
-# best_k
+
# # Pulling optimal K value based on above cross validation
+# set.seed(1)
+# best_k<-heart_data_accuracies%>%
+#     arrange(desc(mean))%>%
+#     slice(2)%>%
+#     pull(neighbors)
+# # best_k
@@ -662,11 +612,11 @@

Classification Model\(K\) value we continued to build our classifier and started by building a new model using best_k.

-
# New classifier model using optimal K values
-set.seed(1)
-heart_data_spec_final<- nearest_neighbor(weight_func="rectangular", neighbors=best_k)%>%
-    set_engine("kknn")%>%
-    set_mode("classification")
+
# # New classifier model using optimal K values
+# set.seed(1)
+# heart_data_spec_final<- nearest_neighbor(weight_func="rectangular", neighbors=best_k)%>%
+#     set_engine("kknn")%>%
+#     set_mode("classification")
@@ -674,12 +624,12 @@

Classification Model
-
# Final workflow for classifier using new model.
-set.seed(1)
-heart_data_final_fit<-workflow()%>%
-    add_recipe(heart_data_recipe)%>%
-    add_model(heart_data_spec_final)%>%
-    fit(data=heart_training)
+
# # Final workflow for classifier using new model.
+# set.seed(1)
+# heart_data_final_fit<-workflow()%>%
+#     add_recipe(heart_data_recipe)%>%
+#     add_model(heart_data_spec_final)%>%
+#     fit(data=heart_training)
     
 #heart_data_final_fit
 

@@ -691,51 +641,46 @@ 
Testing the Model
 

-
# Testing our classifier using the testing set
-set.seed(1)
-heart_data_summary<-heart_data_final_fit%>%
-    predict(heart_testing)%>%
-    bind_cols(heart_testing)%>%
-    metrics(truth=diagnosis_f, estimate=.pred_class)%>%
-    filter(.metric == 'accuracy')
-heart_data_summary
-
-heart_data_predict <- heart_data_final_fit %>%
-    predict(heart_testing) %>%
-    bind_cols(heart_testing)
-
-write_csv(heart_data_predict, '../data/modelling/predict_data.csv')
+
# # Testing our classifier using the testing set
+# set.seed(1)
+# heart_data_summary<-heart_data_final_fit%>%
+#     predict(heart_testing)%>%
+#     bind_cols(heart_testing)%>%
+#     metrics(truth=diagnosis_f, estimate=.pred_class)%>%
+#     filter(.metric == 'accuracy')
+# heart_data_summary
+
+# heart_data_predict <- heart_data_final_fit %>%
+#     predict(heart_testing) %>%
+#     bind_cols(heart_testing)
+
+# write_csv(heart_data_predict, '../data/modelling/predict_data.csv')
 

 

 

 

 
Table 6. Model accuracy with testing set

 
The accuracy is a reasonable number that shows that even though our predictors within our model produce a strange \(K\)-nearest neighbour graph, we still built a model that will diagnose patients with ~80% accuracy.

-
We know this is a reasonable accuracy for our classifier from looking at Figure 3. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good.

+
We know this is a reasonable accuracy for our classifier from looking at Figure 3. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good.

 
To test the accuracy of the model we built, we also provide a confusion matrix; a table of predicted and correct labels,  using the conf_mat function. This enables us to easily see false positives and false negatives of diagnosis, as well as what was predicted accurately.

 
A heatmap based on the confusion matrix was made to more easily understand what is being displayed above.

-

-

-
# confusion matrix heat map visualization
-source('../R/confusion_matrix.R')
-
-confusion_matrix(heart_data_predict)
-

-

-

-

-
Figure 5.

-
The confusion matrix (Figure 5.) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled \(22 + 39 + 21 + 20 + 4 = 106\) diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.

+

+_images/confusion_matrix.png
+

+
Fig. 5 The confusion matrix illustrates the number of correct predictions made by the kNN model to the number of incorrect predictions. The darker the color of the square the more predictions that landed in that category.#

+

+

+
The confusion matrix (Figure 5) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled \(22 + 39 + 21 + 20 + 4 = 106\) diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.

 
Unfortunately, the classifier also made errors and classified a total of 18 patients with a false positive, meaning the patient’s heart disease was worse than it actually was. Moreover, the classifier labelled six patients with false negatives, meaning the patients’ heart disease was actually worse than what was predicted. A discussion as to the false positive and false negative results is in the discussion section.

Conclusion#

-

The predictors, age, max_heart_rate, and rest_bp, have high accuracy and a good chance of accurately predicting a patient’s heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, Figure 1. shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our \(K\) graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.

+

The predictors, age, max_heart_rate, and rest_bp, have high accuracy and a good chance of accurately predicting a patient’s heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, Figure 1 shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our \(K\) graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.

Is this what you expected to find?#

We expected to find that the larger the numerical value of a patient’s age and resting blood pressure and the lower the maximum heart rate, the greater at risk a person is to have worsened heart disease. We actually found that these predictors have a weak correlation with the outcome variable. However, our model still predicts heart disease severity accurately.

-

From our confusion matrix in Figure 5., we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in Figure 1. that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient’s heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.

+

From our confusion matrix in Figure 5, we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in Figure 1 that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient’s heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.

What impact could such findings have?#

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ACCURACY OF PREDETERMINED VARIABLES TO PREDICT SEVERITY OF HEART DISEASE IN PATIENTS"],titleterms:{IN:0,Is:0,OF:0,TO:0,accuraci:0,achiev:0,ag:0,analysi:0,blood:0,classif:0,classifi:0,complet:0,conclus:0,content:[],could:0,data:0,discuss:[],diseas:0,evalu:0,expect:0,exploratori:0,find:0,forward:0,futur:0,have:0,heart:0,impact:0,initi:0,introduct:0,lead:0,literatur:0,major:0,maximum:0,model:0,patient:0,predetermin:0,predict:0,predictor:0,preliminari:0,pressur:0,question:0,rate:0,refer:0,research:0,rest:0,select:0,set:0,sever:0,tabl:[],test:0,thi:0,tidi:0,train:0,variabl:0,visual:0,what:0,you:0}}) \ No newline at end of file diff --git a/notebooks/_build/jupyter_execute/analysis.ipynb b/notebooks/_build/jupyter_execute/analysis.ipynb index 93f19a2..7d2cd04 100644 --- a/notebooks/_build/jupyter_execute/analysis.ipynb +++ b/notebooks/_build/jupyter_execute/analysis.ipynb @@ -63,7 +63,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "── \u001b[1mAttaching packages\u001b[22m 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"stream", "text": [ - "\u001b[32mTest passed\u001b[39m 😀\n", - "\u001b[32mTest passed\u001b[39m 😸\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "── \u001b[1mAttaching packages\u001b[22m ────────────────────────────────────── tidymodels 1.0.0 ──\n", - "\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\u001b[32m✔\u001b[39m \u001b[34mbroom \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mrsample \u001b[39m 1.1.1\n", - "\u001b[32m✔\u001b[39m \u001b[34mdials \u001b[39m 1.1.0 \u001b[32m✔\u001b[39m \u001b[34mtune \u001b[39m 1.0.1\n", - "\u001b[32m✔\u001b[39m \u001b[34minfer \u001b[39m 1.0.4 \u001b[32m✔\u001b[39m \u001b[34mworkflows \u001b[39m 1.1.2\n", - "\u001b[32m✔\u001b[39m \u001b[34mmodeldata \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mworkflowsets\u001b[39m 1.0.0\n", - "\u001b[32m✔\u001b[39m \u001b[34mparsnip \u001b[39m 1.0.3 \u001b[32m✔\u001b[39m \u001b[34myardstick \u001b[39m 1.1.0\n", - "\u001b[32m✔\u001b[39m 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\u001b[34mtidyr\u001b[39m::matches(), \u001b[34mtestthat\u001b[39m::matches()\n", - "\u001b[31m✖\u001b[39m \u001b[34myardstick\u001b[39m::\u001b[32mspec()\u001b[39m masks \u001b[34mreadr\u001b[39m::spec()\n", - "\u001b[31m✖\u001b[39m \u001b[34mrecipes\u001b[39m::\u001b[32mstep()\u001b[39m masks \u001b[34mstats\u001b[39m::step()\n", - "\u001b[34m•\u001b[39m Learn how to get started at \u001b[32mhttps://www.tidymodels.org/start/\u001b[39m\n", + "── \u001b[1m\u001b[33mError\u001b[39m (???): X-axis label is not the same!\u001b[22m ──────────────────────────────────\n", + "Error: 'data/modelling/training_split_new.csv' does not exist in current working directory ('/Users/Sam/git/dsci310/dsci-310-group-18/notebooks').\n", + "\u001b[1mBacktrace:\u001b[22m\n", + "\u001b[90m 1. \u001b[39m\u001b[1mglobal\u001b[22m majority_classifier_vis_function(majority_classifier)\n", + "\u001b[90m 6. \u001b[39m\u001b[1mvroom\u001b[22m (local) ``(\"data/modelling/training_split_new.csv\")\n", + "\u001b[90m 7. \u001b[39mvroom:::check_path(path)\n", "\n" ] }, { - "name": "stderr", - "output_type": "stream", - "text": [ - "\u001b[1mRows: \u001b[22m\u001b[34m414\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m6\u001b[39m\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", - "\u001b[1mDelimiter:\u001b[22m \",\"\n", - "\u001b[32mdbl\u001b[39m (6): diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", - "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n" + "ename": "ERROR", + "evalue": "\u001b[1m\u001b[33mError\u001b[39m in `reporter$stop_if_needed()`:\u001b[22m\n\u001b[33m!\u001b[39m Test failed\n", + "output_type": "error", + "traceback": [ + "\u001b[1m\u001b[33mError\u001b[39m in `reporter$stop_if_needed()`:\u001b[22m\n\u001b[33m!\u001b[39m Test failed\nTraceback:\n", + "1. source(\"../tests/tests.R\")", + "2. withVisible(eval(ei, envir))", + "3. eval(ei, envir)", + "4. eval(ei, envir)", + "5. test_that(\"X-axis label is not the same!\", {\n . majority_classifier <- read_csv(\"../data/modelling/majority_classifier.csv\")\n . plot <- majority_classifier_vis_function(majority_classifier)\n . expect_identical(plot$labels$x, \"Heart disease degree of severity\")\n . })", + "6. (function (envir) \n . {\n . handlers <- get_handlers(envir)\n . errors <- list()\n . for (handler in handlers) {\n . tryCatch(eval(handler$expr, handler$envir), error = function(e) {\n . errors[[length(errors) + 1]] <<- e\n . })\n . }\n . attr(envir, \"withr_handlers\") <- NULL\n . for (error in errors) {\n . stop(error)\n . }\n . })()" ] } ], @@ -165,35 +121,6 @@ "source('../tests/tests.R')" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "tags": [ - "hide-cell" - ] - }, - "outputs": [], - "source": [ - "# STEP IN 01 R SCRIPT\n", - "\n", - "library(tidyverse)\n", - "library(repr)\n", - "library(tidymodels)\n", - "library(cowplot)\n", - "library(ggplot2)\n", - "library(caret)\n", - "library(e1071)\n", - "options(repr.matrix.max.rows = 6)\n", - "set.seed(1)\n", - "source(\"../R/selection_forward_function.R\")\n", - "source(\"../R/majority_classifier_function.R\")\n", - "\n", - "# Reading data off internet to make csv files\n", - "source(\"../R/place_data.R\")\n", - "source(\"../R/joining_data.R\")" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -210,19 +137,52 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[1mRows: \u001b[22m\u001b[34m720\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m21\u001b[39m\n", + "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", + "\u001b[1mDelimiter:\u001b[22m \",\"\n", + "\u001b[31mchr\u001b[39m (1): place\n", + "\u001b[32mdbl\u001b[39m (20): age, sex, chest_pain, rest_bp, cholestoral_mmHg, fasting_bs, rest_...\n", + "\n", + "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", + "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "|place|age|sex|chest_pain|rest_bp|cholestoral_mmHg|fasting_bs|rest_ECG|max_heart_rate|exercise|major_vessels|thal|diagnosis|sex_f|chest_pain_f|fasting_bs_f|rest_ECG_f|exercise_f|major_vessels_f|thal_f|diagnosis_f|\n", + "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", + "|switzerland|32|1|1|95|0|NA|0|127|0|NA|NA|1|1|1|NA|0|0|NA|NA|1|\n", + "|switzerland|34|1|4|115|0|NA|NA|154|0|NA|NA|1|1|4|NA|NA|0|NA|NA|1|\n", + "|switzerland|35|1|4|NA|0|NA|0|130|1|NA|7|3|1|4|NA|0|1|NA|7|3|\n", + "|switzerland|36|1|4|110|0|NA|0|125|1|NA|6|1|1|4|NA|0|1|NA|6|1|\n", + "|switzerland|38|0|4|105|0|NA|0|166|0|NA|NA|2|0|4|NA|0|0|NA|NA|2|\n", + "|switzerland|38|0|4|110|0|0|0|156|0|NA|3|1|0|4|0|0|0|NA|3|1|" + ] + } + ], "source": [ "# STEP IN 02 R SCRIPT\n", + "md_table <- function(df){\n", + " paste0('|', paste(names(df), collapse = '|'), '|\\n|', \n", + " paste(rep('---', length(df)), collapse = '|'), '|\\n|', \n", + " paste(Reduce(function(x, y){paste(x, y, sep = '|')}, df), collapse = '|\\n|'), '|')\n", + "}\n", "\n", - "\n", - "heart_data <- join_csv()\n", - "heart_data" + "heart_data <- read_csv('../data/processed/heart_data.csv')\n", + "cat(md_table(head(heart_data)))" ] }, { @@ -248,26 +208,6 @@ "We set the seed with the `set.seed` function in order to make the randomized processes throughout our analysis reproducible. A seed is a numerical starting value, which determines the sequence of random numbers R will generate. Throughout the analysis the `set.seed` function will be at the top of each cell that completes a randomizing action. " ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "# STEP IN 03 R SCRIPT\n", - "\n", - "\n", - "# Splitting data into training and testing sets\n", - "set.seed(1)\n", - "heart_split<-initial_split(heart_data, prop=0.75, strata=diagnosis_f)\n", - "heart_training<-training(heart_split)\n", - "heart_testing<-testing(heart_split)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -331,51 +271,31 @@ "## Initial Visualizations of Predictors" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "# SCRIPTED IN 02.1-INITIAL_VISUALIZATION.R\n", - "\n", - "# Boxplot visualizations for each of our predictors and heart diagnosis\n", - "heart_data <- read_csv('../data/processed/heart_data.csv')\n", - "\n", - " \n", - "boxplot_age <- grid_boxplot(heart_data, age, \"Age (years)\", \"A. Boxplot of degree of heart \\n disease in relation to patient's \\nage\")\n", - "boxplot_rest_bp <- grid_boxplot(heart_data, rest_bp, \"Resting blood pressure (mmHg)\", \"B. Boxplot of degree of heart \\ndisease in relation to patient's \\nresting blood pressure\")\n", - "boxplot_max_heart_rate <- grid_boxplot(heart_data, max_heart_rate, \"Maximum heart rate (BPM)\", \"C. Boxplot of degree of heart \\ndisease in relation to patient's \\nmaximum heart rate\")\n", - "options(repr.plot.width = 20, repr.plot.height = 10)\n", - "boxplots <- plot_grid(boxplot_age, boxplot_rest_bp, boxplot_max_heart_rate, ncol=3)\n", - "show(boxplots)\n", - "ggsave(\"../figures/boxplot.png\")" - ] - }, { "cell_type": "markdown", "metadata": {}, "source": [ - "***Figure 1.***" + "```{figure} ../figures/boxplot.png\n", + "---\n", + "name: boxplot_img\n", + "---\n", + "Initial visualization comparing degree of heart disease to various factors in the data.\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "These boxplots in Figure 1. are our inital visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. `age`, Figure 1B. `rest_bp`, and Figure 1C. `max_heart_rate`, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (`diagnosis_f`)and the predictors.\n", + "These boxplots in {numref}`Figure {number} `. are our initial visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. `age`, {numref}`Figure {number}B `. `rest_bp`, and {numref}`Figure {number}C `. `max_heart_rate`, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (`diagnosis_f`)and the predictors.\n", "\n", - "Figure 1A. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.\n", + "{numref}`Figure {number}A `. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.\n", "\n", - "Figure 1B. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.\n", + "{numref}`Figure {number}B `. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.\n", "\n", - "Figure 1C. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to acheive a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.\n", + "{numref}`Figure {number}C `. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to achieve a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.\n", "\n", - "These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature reseach support. In practice, these predictors are conditions that doctors use to give an **initial diagnosis** of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analysed in the remainder of the project report." + "These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature research support. In practice, these predictors are conditions that doctors use to give an **initial diagnosis** of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analyzed in the remainder of the project report." ] }, { @@ -389,7 +309,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as Figure 1. failed to show any significant correlation.\n", + "To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as {numref}`Figure {number} ` failed to show any significant correlation.\n", "\n", "Forward selection is used to predict accuracy of a classifier that will be made using different predictors to create the model. Based on our literature research detailed above, we will be using forward selection on the variables age, resting blood pressure, and maximum heart rate. We made sure to use our training data set in the forward selection process so that the testing data is never seen by the classifier.\n", "\n", @@ -406,13 +326,13 @@ }, "outputs": [], "source": [ - "# Creating data subsets for forward selection model using training data\n", - "heart_data_subset<-heart_training%>%\n", - " select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%\n", - " na.omit()\n", + "# # Creating data subsets for forward selection model using training data\n", + "# heart_data_subset<-heart_training%>%\n", + "# select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%\n", + "# na.omit()\n", "\n", - "# heart_data_subset\n", - "write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')" + "# # heart_data_subset\n", + "# write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')" ] }, { @@ -434,8 +354,8 @@ }, "outputs": [], "source": [ - "accuracies <- forwardSelection(heart_data_subset)\n", - "accuracies" + "# accuracies <- forwardSelection(heart_data_subset)\n", + "# accuracies" ] }, { @@ -453,41 +373,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], - "source": [ - "# visualization of number of predictors and accuracy based on forward selection\n", - "options(repr.plot.width = 7, repr.plot.height = 7)\n", - "forward_visualization <- ggplot(accuracies, aes(x = size, y = accuracy)) +\n", - " geom_line() +\n", - " geom_point() +\n", - " labs(x = 'Number of predictors used',\n", - " y = 'Estimated accuracy using forward selection',\n", - " title = 'Number of different predictors compared \\nto the accuracy of classifier model') +\n", - " theme(text = element_text(size = 20)) +\n", - " ylim(c(0,1))\n", - "\n", - "forward_visualization" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, "source": [ - "***Figure 2.***" + "```{figure} ../figures/classifier_accuracies.png\n", + "---\n", + "name: forward_img\n", + "---\n", + "Accuracy of model based on the number of predictors used to build the model.\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Figure 2. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau's at the fourth and fifth predictor (`chest_pain` and `sex`). \n", + "{numref}`Figure {number} `. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau's at the fourth and fifth predictor (`chest_pain` and `sex`). \n", "\n", "According to this visualization our pre-chosen predictors should be accurate predictors for the severity of heart disease. It also tells us that with any more predictors our classifier would not be benefitted and with any less we would have drastically lower accuracy. \n", "\n", @@ -518,21 +423,21 @@ }, "outputs": [], "source": [ - "# Selecting chosen predictors within training and testing data\n", - "heart_training <- heart_training %>%\n", - " select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", - " na.omit()\n", - "heart_training\n", + "# # Selecting chosen predictors within training and testing data\n", + "# heart_training <- heart_training %>%\n", + "# select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", + "# na.omit()\n", + "# heart_training\n", "\n", - "# Adding training set to directory\n", - "write_csv(heart_training, '../data/modelling/training_split.csv')\n", + "# # Adding training set to directory\n", + "# write_csv(heart_training, '../data/modelling/training_split.csv')\n", "\n", - "heart_testing <- heart_testing %>%\n", - " select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", - " na.omit()\n", + "# heart_testing <- heart_testing %>%\n", + "# select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", + "# na.omit()\n", "\n", - "# Adding testing set to directory\n", - "write_csv(heart_testing, '../data/modelling/testing_split.csv')" + "# # Adding testing set to directory\n", + "# write_csv(heart_testing, '../data/modelling/testing_split.csv')" ] }, { @@ -566,26 +471,26 @@ }, "outputs": [], "source": [ - "# majority classifier and visualization\n", - "set.seed(1)\n", - "total_rows<-nrow(heart_training)\n", + "# # majority classifier and visualization\n", + "# set.seed(1)\n", + "# total_rows<-nrow(heart_training)\n", "\n", - "number_of_columns<-heart_training%>%\n", - " group_by(diagnosis_f)%>%\n", - " summarize(number=n())%>%\n", - " select(number)\n", + "# number_of_columns<-heart_training%>%\n", + "# group_by(diagnosis_f)%>%\n", + "# summarize(number=n())%>%\n", + "# select(number)\n", " \n", "\n", - "majority_classifier<-heart_training%>%\n", - " group_by(diagnosis_f)%>% \n", - " summarize(percent_outcomes=n()/total_rows*100)%>%\n", - " arrange(desc(percent_outcomes))%>%\n", - " bind_cols(number_of_columns)\n", - "#slice(1)\n", - "majority_classifier\n", + "# majority_classifier<-heart_training%>%\n", + "# group_by(diagnosis_f)%>% \n", + "# summarize(percent_outcomes=n()/total_rows*100)%>%\n", + "# arrange(desc(percent_outcomes))%>%\n", + "# bind_cols(number_of_columns)\n", + "# #slice(1)\n", + "# majority_classifier\n", "\n", - "# write csv to data/modelling\n", - "write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')" + "# # write csv to data/modelling\n", + "# write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')" ] }, { @@ -596,30 +501,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "majority_classifier_vis_function(majority_classifier)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "***Figure 3.***" + "```{figure} ../figures/majority_classifier_vis.png\n", + "---\n", + "name: class_prop_img\n", + "---\n", + "Percentage of patients in data that have each level of heart disease severity. \n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Table 4. and Figure 3. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.\n", + "Table 4. and {numref}`Figure {number} `. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.\n", "\n", "Table 4. also shows us that none of the percent outcomes are over 50%, and the outcomes for severity 1, 2, 3, and 0 are within 15% of each other. This means our data set is distributed evenly enough to build a decent classifier model. Knowing the frequency of each outcome also enables us to set an upper bound on our number of neighbors which is something we will discuss in further detail in subsequent cells." ] @@ -674,11 +575,11 @@ }, "outputs": [], "source": [ - "# Cross validation to find optimal K value\n", - "source('../R/classification_model.R')\n", + "# # Cross validation to find optimal K value\n", + "# source('../R/classification_model.R')\n", "\n", - "heart_data_accuracies <- classifier(heart_training)\n", - "heart_data_accuracies" + "# heart_data_accuracies <- classifier(heart_training)\n", + "# heart_data_accuracies" ] }, { @@ -696,41 +597,35 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "# K visualization\n", - "source('../R/model_visualization.R')\n", - "knn_visualization(heart_data_accuracies)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "***Figure 4.***" + "```{figure} ../figures/classification_model_visualization.png\n", + "---\n", + "name: knn_img\n", + "---\n", + "Accuracy kNN model as number of neighbors is increased to classify the severity of heart disease\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Setting the number of neighbours to $K$ = 2 will give the highest accuracy, as seen in Figure 4. The shape of Figure 4. is not what we expected to see because of the huge drop in the accuracy after $K$ = 2. This means that there is a high risk of losing model accuracy after $K$ = 2. Choosing $K$ = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.\n", + "Setting the number of neighbours to $K$ = 2 will give the highest accuracy, as seen in {numref}`Figure {number} `. The shape of {numref}`Figure {number} `. is not what we expected to see because of the huge drop in the accuracy after $K$ = 2. This means that there is a high risk of losing model accuracy after $K$ = 2. Choosing $K$ = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.\n", "\n", - "Figure 4. shows that choosing a $K$ higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher $K$ values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the $K$ value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different $K$ values are used. The optimal $K$ value has the highest accuracy and has neighbouring $K$ values of similar accuracy." + "{numref}`Figure {number} ` shows that choosing a $K$ higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher $K$ values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the $K$ value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different $K$ values are used. The optimal $K$ value has the highest accuracy and has neighbouring $K$ values of similar accuracy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "After our initial analysis in Figure 4. we decided to continue our analysis despite the suspicious shape of Figure 4. This next step pulls optimal the $K$ value based on the above cross validation to choose the appropriate number of neighbors." + "After our initial analysis in {numref}`Figure {number} ` we decided to continue our analysis despite the suspicious shape of {numref}`Figure {number} ` This next step pulls optimal the $K$ value based on the above cross validation to choose the appropriate number of neighbors." ] }, { @@ -743,13 +638,13 @@ }, "outputs": [], "source": [ - "# Pulling optimal K value based on above cross validation\n", - "set.seed(1)\n", - "best_k<-heart_data_accuracies%>%\n", - " arrange(desc(mean))%>%\n", - " slice(2)%>%\n", - " pull(neighbors)\n", - "# best_k" + "# # Pulling optimal K value based on above cross validation\n", + "# set.seed(1)\n", + "# best_k<-heart_data_accuracies%>%\n", + "# arrange(desc(mean))%>%\n", + "# slice(2)%>%\n", + "# pull(neighbors)\n", + "# # best_k" ] }, { @@ -769,11 +664,11 @@ }, "outputs": [], "source": [ - "# New classifier model using optimal K values\n", - "set.seed(1)\n", - "heart_data_spec_final<- nearest_neighbor(weight_func=\"rectangular\", neighbors=best_k)%>%\n", - " set_engine(\"kknn\")%>%\n", - " set_mode(\"classification\")" + "# # New classifier model using optimal K values\n", + "# set.seed(1)\n", + "# heart_data_spec_final<- nearest_neighbor(weight_func=\"rectangular\", neighbors=best_k)%>%\n", + "# set_engine(\"kknn\")%>%\n", + "# set_mode(\"classification\")" ] }, { @@ -793,12 +688,12 @@ }, "outputs": [], "source": [ - "# Final workflow for classifier using new model.\n", - "set.seed(1)\n", - "heart_data_final_fit<-workflow()%>%\n", - " add_recipe(heart_data_recipe)%>%\n", - " add_model(heart_data_spec_final)%>%\n", - " fit(data=heart_training)\n", + "# # Final workflow for classifier using new model.\n", + "# set.seed(1)\n", + "# heart_data_final_fit<-workflow()%>%\n", + "# add_recipe(heart_data_recipe)%>%\n", + "# add_model(heart_data_spec_final)%>%\n", + "# fit(data=heart_training)\n", " \n", "#heart_data_final_fit" ] @@ -827,20 +722,20 @@ }, "outputs": [], "source": [ - "# Testing our classifier using the testing set\n", - "set.seed(1)\n", - "heart_data_summary<-heart_data_final_fit%>%\n", - " predict(heart_testing)%>%\n", - " bind_cols(heart_testing)%>%\n", - " metrics(truth=diagnosis_f, estimate=.pred_class)%>%\n", - " filter(.metric == 'accuracy')\n", - "heart_data_summary\n", + "# # Testing our classifier using the testing set\n", + "# set.seed(1)\n", + "# heart_data_summary<-heart_data_final_fit%>%\n", + "# predict(heart_testing)%>%\n", + "# bind_cols(heart_testing)%>%\n", + "# metrics(truth=diagnosis_f, estimate=.pred_class)%>%\n", + "# filter(.metric == 'accuracy')\n", + "# heart_data_summary\n", "\n", - "heart_data_predict <- heart_data_final_fit %>%\n", - " predict(heart_testing) %>%\n", - " bind_cols(heart_testing)\n", + "# heart_data_predict <- heart_data_final_fit %>%\n", + "# predict(heart_testing) %>%\n", + "# bind_cols(heart_testing)\n", "\n", - "write_csv(heart_data_predict, '../data/modelling/predict_data.csv')" + "# write_csv(heart_data_predict, '../data/modelling/predict_data.csv')" ] }, { @@ -856,7 +751,7 @@ "source": [ "The accuracy is a reasonable number that shows that even though our predictors within our model produce a strange $K$-nearest neighbour graph, we still built a model that will diagnose patients with ~80% accuracy.\n", "\n", - "We know this is a reasonable accuracy for our classifier from looking at Figure 3. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good. " + "We know this is a reasonable accuracy for our classifier from looking at {numref}`Figure {number} `. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good. " ] }, { @@ -874,33 +769,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "# confusion matrix heat map visualization\n", - "source('../R/confusion_matrix.R')\n", - "\n", - "confusion_matrix(heart_data_predict)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "***Figure 5.***" + "```{figure} ../figures/confusion_matrix.png\n", + "---\n", + "name: confusion_img\n", + "---\n", + "The confusion matrix illustrates the number of correct predictions made by the kNN model to the number of incorrect predictions. The darker the color of the square the more predictions that landed in that category. \n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The confusion matrix (Figure 5.) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled $22 + 39 + 21 + 20 + 4 = 106$ diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.\n", + "The confusion matrix ({numref}`Figure {number} `) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled $22 + 39 + 21 + 20 + 4 = 106$ diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.\n", "\n", "Unfortunately, the classifier also made errors and classified a total of 18 patients with a false positive, meaning the patient's heart disease was worse than it actually was. Moreover, the classifier labelled six patients with false negatives, meaning the patients' heart disease was actually worse than what was predicted. A discussion as to the false positive and false negative results is in the discussion section." ] @@ -911,13 +799,13 @@ "source": [ "## Conclusion\n", "\n", - "The predictors, `age`, `max_heart_rate`, and `rest_bp`, have high accuracy and a good chance of accurately predicting a patient's heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, Figure 1. shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our $K$ graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.\n", + "The predictors, `age`, `max_heart_rate`, and `rest_bp`, have high accuracy and a good chance of accurately predicting a patient's heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, {numref}`Figure {number} ` shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our $K$ graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.\n", "\n", "### Is this what you expected to find?\n", "\n", "We expected to find that the larger the numerical value of a patient's age and resting blood pressure and the lower the maximum heart rate, the greater at risk a person is to have worsened heart disease. We actually found that these predictors have a weak correlation with the outcome variable. However, our model still predicts heart disease severity accurately.\n", "\n", - "From our confusion matrix in Figure 5., we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in Figure 1. that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient's heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.\n", + "From our confusion matrix in {numref}`Figure {number} `, we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in {numref}`Figure {number} ` that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient's heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.\n", "\n", "### What impact could such findings have?\n", "\n", diff --git a/notebooks/analysis.ipynb b/notebooks/analysis.ipynb index f0f492f..5441dfe 100644 --- a/notebooks/analysis.ipynb +++ b/notebooks/analysis.ipynb @@ -7,90 +7,6 @@ "# EVALUATING ACCURACY OF PREDETERMINED VARIABLES TO PREDICT SEVERITY OF HEART DISEASE IN PATIENTS" ] }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Warning message:\n", - "“Removed 170 rows containing non-finite values (stat_boxplot).”\n", - "Warning message:\n", - "“Removed 160 rows containing non-finite values (stat_boxplot).”\n", - "Saving 7 x 7 in image\n", - "\n", - "\u001b[1mRows: \u001b[22m\u001b[34m403\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m6\u001b[39m\n", - "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", - "\u001b[1mDelimiter:\u001b[22m \",\"\n", - "\u001b[32mdbl\u001b[39m (6): diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex\n", - "\n", - "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", - "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n", - "\u001b[1mRows: \u001b[22m\u001b[34m5\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m3\u001b[39m\n", - "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", - "\u001b[1mDelimiter:\u001b[22m \",\"\n", - "\u001b[31mchr\u001b[39m (1): model_string\n", - "\u001b[32mdbl\u001b[39m (2): size, accuracy\n", - "\n", - "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", - "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n", - "Saving 7 x 7 in image\n", - "\n", - "\u001b[1mRows: \u001b[22m\u001b[34m5\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m3\u001b[39m\n", - "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", - "\u001b[1mDelimiter:\u001b[22m \",\"\n", - "\u001b[32mdbl\u001b[39m (3): diagnosis_f, percent_outcomes, number\n", - "\n", - "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", - "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n", - "Saving 7 x 7 in image\n", - "\n", - "\u001b[1mRows: \u001b[22m\u001b[34m21\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m7\u001b[39m\n", - "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", - "\u001b[1mDelimiter:\u001b[22m \",\"\n", - "\u001b[31mchr\u001b[39m (3): .metric, .estimator, .config\n", - "\u001b[32mdbl\u001b[39m (4): neighbors, mean, n, std_err\n", - "\n", - "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", - "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n", - "Saving 7 x 7 in image\n", - "\n", - "\u001b[1mRows: \u001b[22m\u001b[34m147\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m5\u001b[39m\n", - "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", - "\u001b[1mDelimiter:\u001b[22m \",\"\n", - "\u001b[32mdbl\u001b[39m (5): .pred_class, rest_bp, age, max_heart_rate, diagnosis_f\n", - "\n", - "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", - "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n", - "Scale for 'fill' is already present. Adding another scale for 'fill', which\n", - "will replace the existing scale.\n", - "\n", - "Saving 7 x 7 in image\n", - "\n" - ] - } - ], - "source": [ - "source('../R/01-loading.R')\n", - "source('../R/02-build_heart_data.R')\n", - "source('../R/02.1-initial_visualization.R')\n", - "source('../R/03-data_splitting.R')\n", - "source('../R/04.0-subset_training_data.R')\n", - "source('../R/04.1-forward_selection_data.R')\n", - "source('../R/04.2-forward_selection_visualization.R')\n", - "source('../R/05-data_tidying.R')\n", - "source('../R/06.0-major_classifier_data.R')\n", - "source('../R/06.1-major_classifier_visualization.R')\n", - "source('../R/07.0-build_classification_model.R')\n", - "source('../R/07.1-visualize_classification_model.R')\n", - "source('../R/07.2-heart_data_final_workflow.R')\n", - "source('../R/08.0-test_classifier.R')\n", - "source('../R/08.1-build_confusion_matrix.R')" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -147,35 +63,6 @@ "source('../tests/tests.R')" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "tags": [ - "hide-cell" - ] - }, - "outputs": [], - "source": [ - "# STEP IN 01 R SCRIPT\n", - "\n", - "library(tidyverse)\n", - "library(repr)\n", - "library(tidymodels)\n", - "library(cowplot)\n", - "library(ggplot2)\n", - "library(caret)\n", - "library(e1071)\n", - "options(repr.matrix.max.rows = 6)\n", - "set.seed(1)\n", - "source(\"../R/selection_forward_function.R\")\n", - "source(\"../R/majority_classifier_function.R\")\n", - "\n", - "# Reading data off internet to make csv files\n", - "source(\"../R/place_data.R\")\n", - "source(\"../R/joining_data.R\")" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -192,19 +79,52 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[1mRows: \u001b[22m\u001b[34m720\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m21\u001b[39m\n", + "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", + "\u001b[1mDelimiter:\u001b[22m \",\"\n", + "\u001b[31mchr\u001b[39m (1): place\n", + "\u001b[32mdbl\u001b[39m (20): age, sex, chest_pain, rest_bp, cholestoral_mmHg, fasting_bs, rest_...\n", + "\n", + "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", + "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "|place|age|sex|chest_pain|rest_bp|cholestoral_mmHg|fasting_bs|rest_ECG|max_heart_rate|exercise|major_vessels|thal|diagnosis|sex_f|chest_pain_f|fasting_bs_f|rest_ECG_f|exercise_f|major_vessels_f|thal_f|diagnosis_f|\n", + "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", + "|switzerland|32|1|1|95|0|NA|0|127|0|NA|NA|1|1|1|NA|0|0|NA|NA|1|\n", + "|switzerland|34|1|4|115|0|NA|NA|154|0|NA|NA|1|1|4|NA|NA|0|NA|NA|1|\n", + "|switzerland|35|1|4|NA|0|NA|0|130|1|NA|7|3|1|4|NA|0|1|NA|7|3|\n", + "|switzerland|36|1|4|110|0|NA|0|125|1|NA|6|1|1|4|NA|0|1|NA|6|1|\n", + "|switzerland|38|0|4|105|0|NA|0|166|0|NA|NA|2|0|4|NA|0|0|NA|NA|2|\n", + "|switzerland|38|0|4|110|0|0|0|156|0|NA|3|1|0|4|0|0|0|NA|3|1|" + ] + } + ], "source": [ "# STEP IN 02 R SCRIPT\n", + "md_table <- function(df){\n", + " paste0('|', paste(names(df), collapse = '|'), '|\\n|', \n", + " paste(rep('---', length(df)), collapse = '|'), '|\\n|', \n", + " paste(Reduce(function(x, y){paste(x, y, sep = '|')}, df), collapse = '|\\n|'), '|')\n", + "}\n", "\n", - "\n", - "heart_data <- join_csv()\n", - "heart_data" + "heart_data <- read_csv('../data/processed/heart_data.csv')\n", + "cat(md_table(head(heart_data)))" ] }, { @@ -230,26 +150,6 @@ "We set the seed with the `set.seed` function in order to make the randomized processes throughout our analysis reproducible. A seed is a numerical starting value, which determines the sequence of random numbers R will generate. Throughout the analysis the `set.seed` function will be at the top of each cell that completes a randomizing action. " ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "# STEP IN 03 R SCRIPT\n", - "\n", - "\n", - "# Splitting data into training and testing sets\n", - "set.seed(1)\n", - "heart_split<-initial_split(heart_data, prop=0.75, strata=diagnosis_f)\n", - "heart_training<-training(heart_split)\n", - "heart_testing<-testing(heart_split)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -313,51 +213,31 @@ "## Initial Visualizations of Predictors" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "# SCRIPTED IN 02.1-INITIAL_VISUALIZATION.R\n", - "\n", - "# Boxplot visualizations for each of our predictors and heart diagnosis\n", - "heart_data <- read_csv('../data/processed/heart_data.csv')\n", - "\n", - " \n", - "boxplot_age <- grid_boxplot(heart_data, age, \"Age (years)\", \"A. Boxplot of degree of heart \\n disease in relation to patient's \\nage\")\n", - "boxplot_rest_bp <- grid_boxplot(heart_data, rest_bp, \"Resting blood pressure (mmHg)\", \"B. Boxplot of degree of heart \\ndisease in relation to patient's \\nresting blood pressure\")\n", - "boxplot_max_heart_rate <- grid_boxplot(heart_data, max_heart_rate, \"Maximum heart rate (BPM)\", \"C. Boxplot of degree of heart \\ndisease in relation to patient's \\nmaximum heart rate\")\n", - "options(repr.plot.width = 20, repr.plot.height = 10)\n", - "boxplots <- plot_grid(boxplot_age, boxplot_rest_bp, boxplot_max_heart_rate, ncol=3)\n", - "show(boxplots)\n", - "ggsave(\"../figures/boxplot.png\")" - ] - }, { "cell_type": "markdown", "metadata": {}, "source": [ - "***Figure 1.***" + "```{figure} ../figures/boxplot.png\n", + "---\n", + "name: boxplot_img\n", + "---\n", + "Initial visualization comparing degree of heart disease to various factors in the data.\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "These boxplots in Figure 1. are our inital visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. `age`, Figure 1B. `rest_bp`, and Figure 1C. `max_heart_rate`, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (`diagnosis_f`)and the predictors.\n", + "These boxplots in {numref}`Figure {number} `. are our initial visualizations to see if there really is a correlation between severity of heart disease and our predictors. From looking at all 3 predictors, Figure 1A. `age`, {numref}`Figure {number}B `. `rest_bp`, and {numref}`Figure {number}C `. `max_heart_rate`, we can see that there is a range of weakly positive and weakly negative to no relationship between the different diagnosed severities of heart disease (`diagnosis_f`)and the predictors.\n", "\n", - "Figure 1A. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.\n", + "{numref}`Figure {number}A `. shows there is a slight positive relation between age and heart disease severity, meaning the older a patient is, the more severe their heart disease would be.\n", "\n", - "Figure 1B. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.\n", + "{numref}`Figure {number}B `. shows there is no clear relationship between resting blood pressure and how severe a patients heart disease is. All the medians at different levels of severity are relatively level.\n", "\n", - "Figure 1C. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to acheive a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.\n", + "{numref}`Figure {number}C `. shows there is a slight negative relationship between maximum heart rate and the severity of heart disease. This means a patient with no heart disease (0) or low severity (1) are able to achieve a higher maximum heart rate. This is because their heart is more healthy and able to pump blood efficiently when compared to a patient with high severity (4) heart disease.\n", "\n", - "These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature reseach support. In practice, these predictors are conditions that doctors use to give an **initial diagnosis** of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analysed in the remainder of the project report." + "These visualizations are taken into consideration when making our classification model. We will see if these predictors used together will in fact give an accurate diagnosis for someone being examined for heart disease based on given dataset. We chose to proceed with these predictors because of our literature research support. In practice, these predictors are conditions that doctors use to give an **initial diagnosis** of heart disease. Our research question as to whether these predictors work to accurately predict the severity is analyzed in the remainder of the project report." ] }, { @@ -371,7 +251,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as Figure 1. failed to show any significant correlation.\n", + "To visualize the effectiveness of our chosen predictors on our data set, we used the process of forward selection. We chose to add this step to confirm that the choices of our predictors will work using this data, as {numref}`Figure {number} ` failed to show any significant correlation.\n", "\n", "Forward selection is used to predict accuracy of a classifier that will be made using different predictors to create the model. Based on our literature research detailed above, we will be using forward selection on the variables age, resting blood pressure, and maximum heart rate. We made sure to use our training data set in the forward selection process so that the testing data is never seen by the classifier.\n", "\n", @@ -388,13 +268,13 @@ }, "outputs": [], "source": [ - "# Creating data subsets for forward selection model using training data\n", - "heart_data_subset<-heart_training%>%\n", - " select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%\n", - " na.omit()\n", + "# # Creating data subsets for forward selection model using training data\n", + "# heart_data_subset<-heart_training%>%\n", + "# select(diagnosis_f, age, rest_bp, max_heart_rate, chest_pain, sex) %>%\n", + "# na.omit()\n", "\n", - "# heart_data_subset\n", - "write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')" + "# # heart_data_subset\n", + "# write_csv(heart_data_subset, '../data/modelling/forward_selection_subset.csv')" ] }, { @@ -416,8 +296,8 @@ }, "outputs": [], "source": [ - "accuracies <- forwardSelection(heart_data_subset)\n", - "accuracies" + "# accuracies <- forwardSelection(heart_data_subset)\n", + "# accuracies" ] }, { @@ -435,41 +315,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], - "source": [ - "# visualization of number of predictors and accuracy based on forward selection\n", - "options(repr.plot.width = 7, repr.plot.height = 7)\n", - "forward_visualization <- ggplot(accuracies, aes(x = size, y = accuracy)) +\n", - " geom_line() +\n", - " geom_point() +\n", - " labs(x = 'Number of predictors used',\n", - " y = 'Estimated accuracy using forward selection',\n", - " title = 'Number of different predictors compared \\nto the accuracy of classifier model') +\n", - " theme(text = element_text(size = 20)) +\n", - " ylim(c(0,1))\n", - "\n", - "forward_visualization" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, "source": [ - "***Figure 2.***" + "```{figure} ../figures/classifier_accuracies.png\n", + "---\n", + "name: forward_img\n", + "---\n", + "Accuracy of model based on the number of predictors used to build the model.\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Figure 2. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau's at the fourth and fifth predictor (`chest_pain` and `sex`). \n", + "{numref}`Figure {number} `. shows us that all five of our predictors increase the estimated accuracy of our classifier. However we can also see that the accuracy plateau's at the fourth and fifth predictor (`chest_pain` and `sex`). \n", "\n", "According to this visualization our pre-chosen predictors should be accurate predictors for the severity of heart disease. It also tells us that with any more predictors our classifier would not be benefitted and with any less we would have drastically lower accuracy. \n", "\n", @@ -500,21 +365,21 @@ }, "outputs": [], "source": [ - "# Selecting chosen predictors within training and testing data\n", - "heart_training <- heart_training %>%\n", - " select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", - " na.omit()\n", - "heart_training\n", + "# # Selecting chosen predictors within training and testing data\n", + "# heart_training <- heart_training %>%\n", + "# select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", + "# na.omit()\n", + "# heart_training\n", "\n", - "# Adding training set to directory\n", - "write_csv(heart_training, '../data/modelling/training_split.csv')\n", + "# # Adding training set to directory\n", + "# write_csv(heart_training, '../data/modelling/training_split.csv')\n", "\n", - "heart_testing <- heart_testing %>%\n", - " select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", - " na.omit()\n", + "# heart_testing <- heart_testing %>%\n", + "# select(rest_bp, age, max_heart_rate, diagnosis_f) %>%\n", + "# na.omit()\n", "\n", - "# Adding testing set to directory\n", - "write_csv(heart_testing, '../data/modelling/testing_split.csv')" + "# # Adding testing set to directory\n", + "# write_csv(heart_testing, '../data/modelling/testing_split.csv')" ] }, { @@ -548,26 +413,26 @@ }, "outputs": [], "source": [ - "# majority classifier and visualization\n", - "set.seed(1)\n", - "total_rows<-nrow(heart_training)\n", + "# # majority classifier and visualization\n", + "# set.seed(1)\n", + "# total_rows<-nrow(heart_training)\n", "\n", - "number_of_columns<-heart_training%>%\n", - " group_by(diagnosis_f)%>%\n", - " summarize(number=n())%>%\n", - " select(number)\n", + "# number_of_columns<-heart_training%>%\n", + "# group_by(diagnosis_f)%>%\n", + "# summarize(number=n())%>%\n", + "# select(number)\n", " \n", "\n", - "majority_classifier<-heart_training%>%\n", - " group_by(diagnosis_f)%>% \n", - " summarize(percent_outcomes=n()/total_rows*100)%>%\n", - " arrange(desc(percent_outcomes))%>%\n", - " bind_cols(number_of_columns)\n", - "#slice(1)\n", - "majority_classifier\n", + "# majority_classifier<-heart_training%>%\n", + "# group_by(diagnosis_f)%>% \n", + "# summarize(percent_outcomes=n()/total_rows*100)%>%\n", + "# arrange(desc(percent_outcomes))%>%\n", + "# bind_cols(number_of_columns)\n", + "# #slice(1)\n", + "# majority_classifier\n", "\n", - "# write csv to data/modelling\n", - "write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')" + "# # write csv to data/modelling\n", + "# write_csv(majority_classifier, '../data/modelling/majority_classifier.csv')" ] }, { @@ -578,30 +443,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "majority_classifier_vis_function(majority_classifier)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "***Figure 3.***" + "```{figure} ../figures/majority_classifier_vis.png\n", + "---\n", + "name: class_prop_img\n", + "---\n", + "Percentage of patients in data that have each level of heart disease severity. \n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Table 4. and Figure 3. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.\n", + "Table 4. and {numref}`Figure {number} `. give insight into the proportion of patients from the training set with each level of heart disease. The most common diagnosis in our data set is severity 1 with 31%. This value sets a baseline accuracy that our model should exceed to be deemed an acceptable classifier. In other words, if our model can predict more accurately than simply picking the most likely outcome every time, then we are on the right track in terms of accuracy.\n", "\n", "Table 4. also shows us that none of the percent outcomes are over 50%, and the outcomes for severity 1, 2, 3, and 0 are within 15% of each other. This means our data set is distributed evenly enough to build a decent classifier model. Knowing the frequency of each outcome also enables us to set an upper bound on our number of neighbors which is something we will discuss in further detail in subsequent cells." ] @@ -656,11 +517,11 @@ }, "outputs": [], "source": [ - "# Cross validation to find optimal K value\n", - "source('../R/classification_model.R')\n", + "# # Cross validation to find optimal K value\n", + "# source('../R/classification_model.R')\n", "\n", - "heart_data_accuracies <- classifier(heart_training)\n", - "heart_data_accuracies" + "# heart_data_accuracies <- classifier(heart_training)\n", + "# heart_data_accuracies" ] }, { @@ -678,41 +539,35 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "# K visualization\n", - "source('../R/model_visualization.R')\n", - "knn_visualization(heart_data_accuracies)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "***Figure 4.***" + "```{figure} ../figures/classification_model_visualization.png\n", + "---\n", + "name: knn_img\n", + "---\n", + "Accuracy kNN model as number of neighbors is increased to classify the severity of heart disease\n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Setting the number of neighbours to $K$ = 2 will give the highest accuracy, as seen in Figure 4. The shape of Figure 4. is not what we expected to see because of the huge drop in the accuracy after $K$ = 2. This means that there is a high risk of losing model accuracy after $K$ = 2. Choosing $K$ = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.\n", + "Setting the number of neighbours to $K$ = 2 will give the highest accuracy, as seen in {numref}`Figure {number} `. The shape of {numref}`Figure {number} `. is not what we expected to see because of the huge drop in the accuracy after $K$ = 2. This means that there is a high risk of losing model accuracy after $K$ = 2. Choosing $K$ = 1 would also work considering the accuracy; however, it is a small number and it could lead to overfitting our classifier.\n", "\n", - "Figure 4. shows that choosing a $K$ higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher $K$ values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the $K$ value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different $K$ values are used. The optimal $K$ value has the highest accuracy and has neighbouring $K$ values of similar accuracy." + "{numref}`Figure {number} ` shows that choosing a $K$ higher than two results in a drastically lower estimated accuracy. We experimented with testing the accuracy of models with higher $K$ values, but they decreased the accuracy even further. For example, when we used three neighbours instead of two, the accuracy decreased by about 15%, and it continued to decrease the higher the $K$ value we used. We also checked for spikes at much higher K values, but the accuracy continued to level off around 0.40. To make this table easier to understand, we made a visualization of the mean column and the number of neighbours. The mean represents an accuracy estimate of the model when different $K$ values are used. The optimal $K$ value has the highest accuracy and has neighbouring $K$ values of similar accuracy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "After our initial analysis in Figure 4. we decided to continue our analysis despite the suspicious shape of Figure 4. This next step pulls optimal the $K$ value based on the above cross validation to choose the appropriate number of neighbors." + "After our initial analysis in {numref}`Figure {number} ` we decided to continue our analysis despite the suspicious shape of {numref}`Figure {number} ` This next step pulls optimal the $K$ value based on the above cross validation to choose the appropriate number of neighbors." ] }, { @@ -725,13 +580,13 @@ }, "outputs": [], "source": [ - "# Pulling optimal K value based on above cross validation\n", - "set.seed(1)\n", - "best_k<-heart_data_accuracies%>%\n", - " arrange(desc(mean))%>%\n", - " slice(2)%>%\n", - " pull(neighbors)\n", - "# best_k" + "# # Pulling optimal K value based on above cross validation\n", + "# set.seed(1)\n", + "# best_k<-heart_data_accuracies%>%\n", + "# arrange(desc(mean))%>%\n", + "# slice(2)%>%\n", + "# pull(neighbors)\n", + "# # best_k" ] }, { @@ -751,11 +606,11 @@ }, "outputs": [], "source": [ - "# New classifier model using optimal K values\n", - "set.seed(1)\n", - "heart_data_spec_final<- nearest_neighbor(weight_func=\"rectangular\", neighbors=best_k)%>%\n", - " set_engine(\"kknn\")%>%\n", - " set_mode(\"classification\")" + "# # New classifier model using optimal K values\n", + "# set.seed(1)\n", + "# heart_data_spec_final<- nearest_neighbor(weight_func=\"rectangular\", neighbors=best_k)%>%\n", + "# set_engine(\"kknn\")%>%\n", + "# set_mode(\"classification\")" ] }, { @@ -775,12 +630,12 @@ }, "outputs": [], "source": [ - "# Final workflow for classifier using new model.\n", - "set.seed(1)\n", - "heart_data_final_fit<-workflow()%>%\n", - " add_recipe(heart_data_recipe)%>%\n", - " add_model(heart_data_spec_final)%>%\n", - " fit(data=heart_training)\n", + "# # Final workflow for classifier using new model.\n", + "# set.seed(1)\n", + "# heart_data_final_fit<-workflow()%>%\n", + "# add_recipe(heart_data_recipe)%>%\n", + "# add_model(heart_data_spec_final)%>%\n", + "# fit(data=heart_training)\n", " \n", "#heart_data_final_fit" ] @@ -809,20 +664,20 @@ }, "outputs": [], "source": [ - "# Testing our classifier using the testing set\n", - "set.seed(1)\n", - "heart_data_summary<-heart_data_final_fit%>%\n", - " predict(heart_testing)%>%\n", - " bind_cols(heart_testing)%>%\n", - " metrics(truth=diagnosis_f, estimate=.pred_class)%>%\n", - " filter(.metric == 'accuracy')\n", - "heart_data_summary\n", + "# # Testing our classifier using the testing set\n", + "# set.seed(1)\n", + "# heart_data_summary<-heart_data_final_fit%>%\n", + "# predict(heart_testing)%>%\n", + "# bind_cols(heart_testing)%>%\n", + "# metrics(truth=diagnosis_f, estimate=.pred_class)%>%\n", + "# filter(.metric == 'accuracy')\n", + "# heart_data_summary\n", "\n", - "heart_data_predict <- heart_data_final_fit %>%\n", - " predict(heart_testing) %>%\n", - " bind_cols(heart_testing)\n", + "# heart_data_predict <- heart_data_final_fit %>%\n", + "# predict(heart_testing) %>%\n", + "# bind_cols(heart_testing)\n", "\n", - "write_csv(heart_data_predict, '../data/modelling/predict_data.csv')" + "# write_csv(heart_data_predict, '../data/modelling/predict_data.csv')" ] }, { @@ -838,7 +693,7 @@ "source": [ "The accuracy is a reasonable number that shows that even though our predictors within our model produce a strange $K$-nearest neighbour graph, we still built a model that will diagnose patients with ~80% accuracy.\n", "\n", - "We know this is a reasonable accuracy for our classifier from looking at Figure 3. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good. " + "We know this is a reasonable accuracy for our classifier from looking at {numref}`Figure {number} `. As discussed in the preceding paragraph, we are looking for a classifier with higher accuracy than that of the majority classifier. In our case, the majority label made up ~30% of our dataset, so the accuracy of ~80% is more than double that of our majority label. Therefore, our classifier is reasonably good. " ] }, { @@ -856,33 +711,26 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "# confusion matrix heat map visualization\n", - "source('../R/confusion_matrix.R')\n", - "\n", - "confusion_matrix(heart_data_predict)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "***Figure 5.***" + "```{figure} ../figures/confusion_matrix.png\n", + "---\n", + "name: confusion_img\n", + "---\n", + "The confusion matrix illustrates the number of correct predictions made by the kNN model to the number of incorrect predictions. The darker the color of the square the more predictions that landed in that category. \n", + "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The confusion matrix (Figure 5.) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled $22 + 39 + 21 + 20 + 4 = 106$ diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.\n", + "The confusion matrix ({numref}`Figure {number} `) shows that 22 individuals were correctly diagnosed with no presence of heart disease, 39 were correctly diagnosed with low severity of heart disease, 22 were correctly diagnosed with medium severity of heart disease, 20 were correctly diagnosed with high severity of heart disease, and 4 were correctly diagnosed with extreme severity of heart disease. Therefore, the classifier labeled $22 + 39 + 21 + 20 + 4 = 106$ diagnoses correctly. This is a rather good result as the proportions of each heart disease class diagnosed correctly mirror the proportions seen in the dataset. Our classifier is therefore not favouring one diagnosis over the other.\n", "\n", "Unfortunately, the classifier also made errors and classified a total of 18 patients with a false positive, meaning the patient's heart disease was worse than it actually was. Moreover, the classifier labelled six patients with false negatives, meaning the patients' heart disease was actually worse than what was predicted. A discussion as to the false positive and false negative results is in the discussion section." ] @@ -893,13 +741,13 @@ "source": [ "## Conclusion\n", "\n", - "The predictors, `age`, `max_heart_rate`, and `rest_bp`, have high accuracy and a good chance of accurately predicting a patient's heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, Figure 1. shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our $K$ graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.\n", + "The predictors, `age`, `max_heart_rate`, and `rest_bp`, have high accuracy and a good chance of accurately predicting a patient's heart disease severity. However, some results indicate that these predictors may not be the best in actual practice. For instance, {numref}`Figure {number} ` shows that these predictors do not have significant correlations with a diagnosis of severity of heart disease. Additionally, there was a significant drop-off after two neighbours in our $K$ graph, proposing that our accuracy results could be due to luck. However, our confusion matrix reveals promising results.\n", "\n", "### Is this what you expected to find?\n", "\n", "We expected to find that the larger the numerical value of a patient's age and resting blood pressure and the lower the maximum heart rate, the greater at risk a person is to have worsened heart disease. We actually found that these predictors have a weak correlation with the outcome variable. However, our model still predicts heart disease severity accurately.\n", "\n", - "From our confusion matrix in Figure 5., we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in Figure 1. that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient's heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.\n", + "From our confusion matrix in {numref}`Figure {number} `, we were more likely to predict a false positive than a false negative. This is good because, with a health condition like heart disease that generates ranging severity, it is better to be given a false positive and be treated as if the disease were worse than be given a false negative and not be treated at all or to a lower care level than what is needed. A reason we see 18 false positives could be because of the predictors we chose to use in our model. We saw in {numref}`Figure {number} ` that these predictors are not ideal because of the weak relationships they show with the severities of heart disease. This can also be said as to why we have 6 false negatives. However, considering that the accuracy of our model is good, this is a reasonable number of false negatives. These values for the false positives and false negatives also relate to our research question and conclusion that our selected predictors are primarily good at predicting the preliminary severity of a patient's heart disease. However, a diagnosis cannot be concluded off these factors alone. Unfortunately, false negatives and false positives are given in medicine in the real world, but from actual research and examples like we were able to display in our classification, it is more likely that a patient will have a proper diagnosis than a false positive or negative.\n", "\n", "### What impact could such findings have?\n", "\n", From ab4ffe2d614b357e55231eacc71d8d887b1b71b8 Mon Sep 17 00:00:00 2001 From: samnthorne Date: Sun, 26 Mar 2023 17:30:51 -0700 Subject: [PATCH 2/2] changed gitignore to ignore notebook/_build --- .gitignore | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.gitignore b/.gitignore index 3571917..a1ddc34 100644 --- a/.gitignore +++ b/.gitignore @@ -71,4 +71,4 @@ Footer navigation .virtual_documents # ignore _build -*/_build/* \ No newline at end of file +notebooks/_build/* \ No newline at end of file