2018/11/30_Dolores M. Miranda, Universidad de Granada

Goodness-of-fit tests in proportional hazards models with random effects

2018/11/30- 13:00 h | Dolores M. Miranda, Universidad de Granada

Abstract

In survival analysis the Cox hazard model is without any doubt the most used and well known semiparametric model to study the relationship between a survival time and a set of covariates. The popularity of this model can, among others, be explained by its easy interpretation and the fact that the nonparametric baseline hazard function cancels out in the likelihood, making the estimation of the parametric components as simple as in a purely parametric model. An appealing extension of the Cox model consists of adding random effects. This provides a powerful tool in a wide variety of applications, where the data have a natural clustered structure. The model can reflect then the fact that some of the regression parameters are cluster-dependent and they may be treated as random.

The assumption of linear covariate effects in the Cox model with random effects is quite strong in practice. Nevertheless, linearity is often assumed without any formal verification. This paper deals with testing the functional form of the covariate effects in a Cox model with random effects. The estimation of the model under the null (parametric covariate effect) and the alternative (non-parametric effect) is performed using full marginal likelihood. Under the alternative, the non-parametric effects are estimated using orthogonal expansions. The test statistic is the likelihood ratio statistic, and its distribution is approximated using bootstrap. The performance of the testing procedure is evaluated through simulations. The method is also applied on real survival data.