chapter  3
26 Pages

Cox Regression

WithGöran Broström

The sole idea of the rewriting is to pave the way for the introduction of Cox’s regression model, which in its elementary form is a proportional hazards model. In discrete time, the hazard function is a set of probabilities, and so its range is restricted to the interval. Therefore, the definition of proportional hazards used for continuous time is unpractical; the multiplication of a probability by a constant may easily result in a quantity larger than one. The chapter discusses two-sample and k-sample cases, where the logrank test is introduced, to the general regression situation. There the logrank test is generalized to Cox regression. It describes the fundamental concept of proportional hazards. Explanatory variables, or covariates, may be of essentially two different types, continuous and discrete. Values taken by a continuous covariate are ordered. The effect on the response is by model definition ordered in the same or reverse order.