Fifty Years of the Cox Model

The Cox model is now 50 years old. seminal paper of Sir David has had an immeasurable impact on the analysis censored survival data, with applications in many different disciplines. This work also stimulated much additional research diverse areas and led to important theoretical practical advances. These include semiparametric models, nonparametric efficiency, partial likelihood. In addition quickly becoming go-to method for estimating covariate effects, regression been extended a vast number complex data structures, all which central idea sampling from set individuals at risk time t can be applied. this article, we review evolution ideas surrounding it. We then highlight its extensions competing risks, attention models based cause-specific hazards, hazards associated subdistribution or cumulative incidence function. discuss their relative merits domains application. recurrent events another major topic discussion, including introduction martingales complete intensity as well more marginal rate models. several worked examples illustrate main ideas.