Modelos de sobrevivência com fração de cura via partição bayesiana

Abstract

In general, models for survival data with a cure fraction relate the cure fraction with the covariates using different link functions, for example, the logit link function and do not consider the problem of selection of covariates that have an effect on the cure fraction. So, in this work we propose a model that considers a partition of the predictor space in which the cure fraction depends locally of covariates. In this context, it adopts a orthogonal hyperplane tessellation to the axes to obtain a partition of the predictor space with the advantage that the proposed model selects the covariates that have an effect on the cure fraction. The developed modeling extends the Bayesian partition model proposed by Hoggart & Griffin (2001) to include information for qualitative variables with more than two categories and therefore a new computational strategy is considered. This extension allows to capture the effects of covariates on a local structure in which it is considered that the number of competing causes follows a power series distribution. This distribution is flexible because it includes special cases such as the binomial, Poisson, negative binomial and logarithmic distributions. To demonstrate the potential of the methodology, we used two set of data relating with cancer studies.