Goodness-of-fit tests in proportional hazards models with random effects |
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Authors: | Wenceslao González-Manteiga María Dolores Martínez-Miranda Ingrid Van Keilegom |
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Affiliation: | 1. Department of Statistics, Mathematical Analysis and Operational Research, University of Santiago de Compostela, Santiago de Compostela, Spain;2. Department of Statistics and Operations Research, University of Granada, Granada, Spain;3. ORSTAT, KU Leuven, Leuven, Belgium |
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Abstract: | This paper deals with testing the functional form of the covariate effects in a Cox proportional hazards model with random effects. 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 (nonparametric effect) is performed using the full marginal likelihood. Under the alternative, the nonparametric 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 two real data sets one from biomedical research and one from veterinary medicine. |
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Keywords: | Cox regression frailty orthogonal polynomials proportional hazards random effects |
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