Mixed discrete and continuous Cox regression model.
The Cox (1972) regression model is extended to include discrete and mixed continuous/discrete failure time data by retaining the multiplicative hazard rate form of the absolutely continuous model. Application of martingale arguments to the regression parameter estimating function show the Breslow(1974) estimator to be consistent and asymptotically Gaussian under this model. A computationally convenient estimator of the variance of the score function can be developed, again using martingale arguments. This estimator reduces to the usual hypergeometric form in the special case of testing equality of several survival curves, and it leads more generally to a convenient consistent variance estimator for the regression parameter. A small simulation study is carried out to study the regression parameter estimator and its variance estimator under the discrete Cox model special case and an application to a bladder cancer recurrence dataset is provided.
Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, Seattle, WA 98109, USA. rprentic@fhcrc.org
Ross L
RL
Prentice
John D
JD
Kalbfleisch
D000704:Analysis of Variance; D006801:Humans; D009364:Neoplasm Recurrence, Local; D016016:Proportional Hazards Models; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D016019:Survival Analysis; D001749:Urinary Bladder Neoplasms / Q000188:drug therapy / Q000401:mortality / Q000503:physiopathology