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Title: Goodness-of-fit tests in proportional hazards models with random effects Authors:  Ingrid Van Keilegom - KU Leuven (Belgium) [presenting]
Wenceslao Gonzalez-Manteiga - University of Santiago de Compostela (Spain)
Maria-Dolores Martinez-Miranda - Universidad de Granada (Spain)
Abstract: The aim is to test the functional form of the covariate effects in a Cox proportional hazards model with random effects, like for instance a shared frailty model. We assume that the responses are clustered and incomplete due to right censoring. The estimation of the model under the null (parametric covariate effect) and the alternative (non-parametric effect) is performed using the full marginal likelihood. Under the alternative, the non-parametric covariate effects are estimated using orthogonal expansions. The test statistic is the likelihood ratio statistic, and its distribution is approximated using a bootstrap method. The performance of the proposed testing procedure is studied through simulations. The method is also applied on real data coming from a study on the chronic granulotomous disease.