A generalized F mixture model for cure rate estimation

Cure rate estimation is an important issue in clinical trials for diseases such as lymphoma and breast cancer and mixture models are the main statistical methods. In the last decade, mixture models under different distributions, such as exponential, Weibull, log-normal and Gompertz, have been discussed and used. However, these models involve stronger distributional assumptions than is desirable and inferences may not be robust to departures from these assumptions. In this paper, a mixture model is proposed using the generalized F distribution family. Although this family is seldom used because of computational difficulties, it has the advantage of being very flexible and including many commonly used distributions as special cases. The generalised F mixture model can relax the usual stronger distributional assumptions and allow the analyst to uncover structure in the data that might otherwise have been missed. This is illustrated by fitting the model to data from large-scale clinical trials with long follow-up of lymphoma patients. Computational problems with the model and model selection methods are discussed. Comparison of maximum likelihood estimates with those obtained from mixture models under other distributions are included.