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Tests of Hypotheses in Frailty Models

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Modeling Survival Data Using Frailty Models

Part of the book series: Industrial and Applied Mathematics ((INAMA))

Abstract

In this chapter, we discuss some well-known tests for frailty which are used more often and they have a lot of applications. In frailty models, there is a clear need for inference on the heterogeneity parameter which measures the association between the survival outcomes in a specific cluster. The model specification of frailty models typically requires the heterogeneity parameter to be positive or, in case of homogeneity, to be zero. Therefore hypothesis testing problems for homogeneity against heterogeneity are described by a one-sided alternative hypothesis and, under the null hypothesis, the parameter is at the boundary of the parameter space which is \((0,\infty )\). Geerdens et al. (2013) constructed goodness-of-fit tests for gamma frailties. Mazroui et al. (2016) proposed joint frailty model for two types of recurrent events and a dependent terminal event to account for potential dependencies between events with potentially time-varying coefficients and applied this model to breast cancer data. They developed likelihood ratio tests to test time dependency and the association of covariates. In this chapter, three different test procedures are discussed. We first discuss tests for gamma frailty based on likelihood ratio and score tests and analyze diabetic retinopathy data. In Sect. 8.3, we discuss the logrank test for testing \(\beta =0\) in parametric and nonparametric setup for uncensored and censored data and we give some numerical examples. In the last section, we discuss a test for homogeneity, i.e., all frailties have common distribution and we analyze kidney infection data.

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Authors and Affiliations

  1. Symbiosis Statistical Institute, Symbiosis International University, Pune, Maharashtra, India

    David D. Hanagal

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  1. David D. Hanagal
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Correspondence to David D. Hanagal .

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Hanagal, D.D. (2019). Tests of Hypotheses in Frailty Models. In: Modeling Survival Data Using Frailty Models. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1181-3_8

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