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Laplace’s approximation for relative risk frailty models. (English) Zbl 1282.62216

Summary: Relative risk frailty models are used extensively in analyzing clustered and/or recurrent time-to-event data. In this paper, Laplace’s approximation for integrals is applied to marginal distributions of data arising from parametric relative risk frailty models. Under regularity conditions, the approximate maximum likelihood estimators (MLE) are consistent with a rate of convergence that depends on both the number of subjects and number of members per subject. We compare the approximate MLE against alternative estimators using limited simulation and demonstrate the utility of Laplace’s approximation approach by analyzing U.S. patient waiting time to deceased kidney transplant data.

MSC:

62N02 Estimation in survival analysis and censored data
62P10 Applications of statistics to biology and medical sciences; meta analysis
62G05 Nonparametric estimation
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