A discrete time logistic regression model for analyzing censored survival data

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Abstract
Consideration is given to survival data analysis by modelling the hazard as a discrete function of time. This is done for each individual who is examined independently from the other individuals of the sample observed. Assuming time has been divided into intervals of the same length, the hazard associated with any specific time interval is taken to be of the form of a logistic function including a number of time‐dependent covariates which serve to characterize the individual under consideration. Asymptotic maximum likelihood results are given for the estimation of both the regression coefficients in the hazard function and the survivor function corresponding to a given profile, i.e. the successive values of the different covariates. The likelihood ratio statistic for testing the effects of the various covariates in order to compare several survival curves with respect to longevity is also derived. The process of model fitting is illustrated by two examples referring to clinical trails on leukaemia and advanced lung cancer patients, respectively.