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Cox Regression Model

  1. Peter Sasieni

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a11013

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Sasieni, P. 2005. Cox Regression Model. Encyclopedia of Biostatistics. 2.

Author Information

  1. Cancer Research UK, London, UK

Publication History

  1. Published Online: 15 JUL 2005

Abstract

In 1972, D.R. Cox proposed the semiparametric model

  • equation image

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