From f5601583a8abf8f40bf6f92a70eed4a1b73b48d8 Mon Sep 17 00:00:00 2001 From: Matthias Schmidtblaicher Date: Tue, 5 Nov 2024 18:43:33 +0100 Subject: [PATCH] add clarifying sentence --- docs/tutorials/cox_model/cox_model.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/cox_model/cox_model.ipynb b/docs/tutorials/cox_model/cox_model.ipynb index 4b5260dc..cb9c1cc2 100644 --- a/docs/tutorials/cox_model/cox_model.ipynb +++ b/docs/tutorials/cox_model/cox_model.ipynb @@ -33,7 +33,7 @@ "$$\n", "\\sum_{\\text{event times}}\\log\\left(\\frac{y_{i,t}\\exp(\\eta_{i})}{\\sum_{i \\in \\mathcal{R}_t} \\exp(\\eta_i)} \\right) - 1,\n", "$$\n", - "which is the same as the partial likelihood in the Cox model, apart from the -1 which drops out when taking derivatives. In short, the Cox partial log likelihood is equivalent to a Poisson log likelihood with the estimate for time period effects fed back in (\"profiled out\"). This means that, to estimate the parameters of the Cox model, one can simply run a Poisson regression with time fixed effects $\\alpha_t$.\n", + "which is the same as the partial likelihood in the Cox model, apart from the -1 which drops out when taking derivatives. In short, the Cox partial log likelihood is equivalent to a Poisson log likelihood with the estimate for time period effects fed back in (\"profiled out\"). This means that, to estimate the parameters of the Cox model, one can simply run a Poisson regression with time fixed effects $\\alpha_t$. The data structures for the two objectives are different: the Cox partial log-likelihood operates on data with one row per observed individual, while the Poisson log-likelihood uses one row per individual and time period.\n", "\n", "## 2. Estimating a Cox Model in Glum\n", "\n",