Model Selection For Clustered Recurrent Event Data Using Nested Gamma Frailty Models

Correlated time-to-event data are commonly encounted in biomedical research, often as recurrent e v ent data or clustered data. To accommodate the correlation among survival times within the proportional hazards model framework, frailty m o d e l s h a ve beendeveloped. Clustered and recurrent event data may require two frailties, leading to a need for appropriate tests for frailty model selection. We focus here on nested frailties. This type of situation arises naturally for recurrent event data collected in a multi-center clinical trial: patients within a clinic share a common frailty, while multiple events for each p a t i e n t share another common frailty. A shared gamma frailty model (one level of frailty) and a multiplicative double gamma frailty m o d e l (t wo levels of frailty) can be tted to this type of data using EM-based algorithms. We carried out a simulation study to examine the performance of a likelihood ratio test (LRT) in choosing between the single and double frailty m o d e l. Simulation results show that when the single frailty is the correct model, the LRT statistic is approximately distributed as a 50:50 mixture of a 2 1 and 2 0. The power of the test to choose the correct model varies according to number of clinics, patients per clinic, and events per patient, as well as the strengths of the frailty eeects. Data from an AIDS clinical trial of prophylaxis for fungal infections (CPCRA 010) are used as an example to apply the LRT.