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 specic cluster. The model specication 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 is described by a onesided alternative hypothesis and, under the null hypothesis, the parameter is at the boundary of the parameter space which is (0;1). In this chapter, three dierent test procedures are discussed. We rst discuss tests for gamma frailty based on likelihood ratio and score tests and analyze diabetic retinopathy data. In Section 8.3, we discuss the logrank test for testing = 0 in parametric and nonparametric setup for uncensored and censored data and we give some numerical examples. In the last section, we discuss test for homogeneity, i.e., all frailties have common distribution and we analyze kidney infection data.
