Estimating the proportion of cured patients in a censored sample

There has been a recurring interest in modelling survival data which hypothesize subpopulations of individuals highly susceptible to some types of adverse events while other individuals are assumed to be at much less risk, like recurrence of breast cancer. A binary random effect is assumed in this article to model the susceptibility of each individual. We propose a simple multiple imputation algorithm for the analysis of censored data which combines a binary regression formulation for the probability of occurrence of an event, say recurrence of the breast cancer tumour, and a Cox's proportional hazards regression model for the time to occurrence of the event if it does. The model distinguishes the effects of the covariates on the probability of cure and on the time to recurrence of the disease. A SAS macro has been written to implement the proposed multiple imputation algorithm so that sophisticated programming effort can be rendered into a user-friendly application. Simulation results show that the estimates are reasonably efficient. The method is applied to analyse the breast cancer recurrence data. The proposed method can be modified easily to accommodate more general random effects other than the binary random effects so that the random effects not only affect the probability of occurrence of the event, but also the heterogeneity of the time to recurrence of the event among the uncured patients.