A stochastic process applied to sequential parametric analysis of censored survival data

Abstract

A stochastic process that allows sequential parametric estimation of the hazard function is presented. The analysis of censored survival data is based on a discrete time definition of the hazard which is expressed as a logistic function of a number of time-dependent covariates. The method adequately handles large sets of data with many tied failure times and high rates of type I censored values. A procedure available to estimate the relative risk parameter characterizing two groups of individuals over a specific period of time is also given. Likelihood methods are used in estimating the parameters of the model and making inference about the survivor function, especially beyond the value of censoring. The method is illustrated by an example concerning the induction period between infection with the AIDS virus and the onset of clinical AIDS. The effects of censoring on the inference analysis of the survivor function corresponding to several groups of individuals are examined and discussed.