7 The Cox Proportional Hazards Model

The log-rank test says whether groups differ; it does not measure the difference, and it cannot handle several factors at once or continuous ones such as age. For that we need a regression model for survival data. The model proposed by Cox in 1972 is by far the most used: it relates the hazard to the covariates through a hazard ratio, leaves the shape of the hazard over time completely unspecified, and is estimated by a partial likelihood that does not need that shape at all. This section introduces the model, derives the partial likelihood, and shows how to interpret and test its coefficients.

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