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Clustered survival data frequently arise in biomedical applications, where event times of interest are clustered into groups such as families. In this article we consider an accelerated failure time frailty model for clustered survival data and develop nonparametric maximum likelihood estimation for it via a kernel smoother aided EM algorithm. We show that the proposed estimator for the regression coefficients is consistent, asymptotically normal and semiparametric efficient when the kernel bandwidth is properly chosen. An EM-aided numerical differentiation method is derived for estimating its variance. Simulation studies evaluate the finite sample performance of the estimator, and it is applied to the Diabetic Retinopathy data set.

Kernel smoothed profile likelihood estimation in the accelerated failure time frailty model for clustered survival data