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A CLASS OF SURVIVAL MODELS FOR LIFETIME DATA WITH A SURVIVING FRACTION IN PRESENCE OF UNOBSERVED DEPENDENCE
Survivals models incorporating surviving fraction or cure rate are increasingly becoming very popular in analyzing time-to-event data in survival analysis. This is due to the fact that certain fraction of the population suffering a particular type of disease can obtain cured due to the advances in the medical treatments and health care system. In this paper, we propose a new class survival models for lifetime data in presence of surviving fractions and examine some of its properties. Its genesis is based on the extensions of promotion time cure model, where we add a parameter to control the heterogeneity or unobserved dependence of lifetimes. Besides we extend the model to regression model for evaluating the effect of covariates in the cure fraction. Several former cure survival models can be seen as particular cases of our modelling framework. We discuss inference aspects for the proposed model in a classical approach, where we exploit maximum likelihood tools. Besides, an expectation-maximization algorithm is then developed for determining the maximum likelihood estimates of the model parameters. Finally, the modelling is fully illustrated on a data set on colorectal cancer. From the practical point of view, besides having a more flexible modelling for fitting survival data in presence of cure fraction, questions of medical interesting can be answered. Particularly, treatment comparison can be made straightforwardly. Moreover, we can estimate the proportion of patients disease-free after a determined treatment.
Colorectal cancer; cured fraction; cure rate models; Likelihood function; survival models.
Análise de Sobrevivência
Gladys Dorotea Cacsire Barriga, Francisco Louzada, Vicente Garibay Cancho