Title: Goodness-of-fit tests for the frailty distribution in proportional hazards models with shared frailty
Authors: Geerdens, Candida
Claeskens, Gerda
Janssen, Paul
Issue Date: Nov-2011
Publisher: K.U.Leuven - Faculty of Business and Economics
Series Title: FEB Research Report KBI_1131 pages:1-24
Abstract: Frailty models account for the clustering present in grouped event time data. A proportional hazards model with shared frailties expresses the hazard for each subject. Often a one-parameter gamma distribution is assumed for the frailties. The choice of a particular frailty
distribution is, most of the time, based on the availability of software, rather than on the way it fits the data. In this paper we construct formal goodness-of-fit tests to test for gamma frailties. We construct a new class of frailty models that extend the gamma frailty model by using certain polynomial expansions that are orthogonal with respect to the gamma density. For this extended family we obtain an explicit expression for the marginal likelihood of the data. The order selection test is based on finding the best fitting model in such a series of expanded models. A bootstrap is used to obtain p-values for
the tests. Simulations and data examples illustrate the test's performance.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Research Center for Operations Research and Business Statistics (ORSTAT), Leuven
Leuven Statistics Research Centre (LStat)

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