Application of the theory of finite mixtures for the estimation of ‘cure’ rates of treated cancer patients

Abstract

I assume the survival function of treated cancer patients to be a mixture of two subpopulations, with c equal to the proportion who will die of other causes, and 1 — c the proportion who will die of their disease. Using census data, I estimate the parameters of the survival distribution of those patients dying of other causes, and then use follow-up data to determine the maximum likelihood estimates of the proportion constant c and the parameters of the survival function of those dying of their disease. I illustrate the methodology using data from a prospective clinical trial in breast cancer.