Classification of “cured” individuals in survival analysis: the mixture approach to the diagnostic–prognostic problem

Abstract

Various mixture survival models have been presented in the literature since 1982 (Farewell, Biometrics 38 (1982) 1041). Such models have been widely applied in different frameworks due to their flexibility in mirroring complex situations, even though a general theory has not been fully developed yet. In the present contribution, a general ‘coherent’ setting is outlined for survival models dealing with non-homogeneous populations, with special focus on cure-rate models and some exploratory and diagnostic tools are studied. The class of cure-rate models proposed here is a generalization of the previous one presented in Schinaia and Rossi (Biometrical J. 42(5) (2000) 583) to address the diagnostic–prognostic problem, now allowing for unknown prior probability of long survivorship. The classification (diagnostic) problem is developed using the Bayesian paradigm. The parameter estimation procedure is based on the development of a class of GEM algorithms, in the framework of the MLE approach. The model diagnostic is based on the asymptotic properties of the survival and risk functions and of the censoring process and on the generalization and application of the theory of log-odds residuals (Nardi and Schemper, Biometrics 55 (1999) 523). The results of an extended experimentation by means of simulated data is also reported in order to present the main features of the model, the methods and the procedures proposed.