Cox Regression Model

In 1972, D.R. Cox proposed the semiparametric model for the hazard at time t for an individual with covariates z. Here, the hazard is the instantaneous conditional probability of failure at t given that failure has not happened before t. The Cox model has had enormous influence in the theory and practice of biostatistics, and this article surveys its definition, history, basic use, estimators and algorithms, asymptotic properties, use of time-dependent covariates, model checking, and alternatives and extensions. Keywords: survival analysis; hazard; proportional hazards model; time-dependent covariate; partial likelihood; semiparametric model; profile likelihood; goodness of fit; accelerated failure time; censoring; truncation