Analysis of clustered interval‐censored data using a class of semiparametric partly linear frailty transformation models

Abstract

Abstract A flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval‐censored data, which arise naturally in complex diseases and dental research. This class of models features two nonparametric components, resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate. The dependence among failure times within a cluster is induced by a shared, unobserved frailty term. A sieve maximum likelihood estimation method based on piecewise linear functions is proposed. The proposed estimators of the regression, dependence, and transformation parameters are shown to be strongly consistent and asymptotically normal, whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence. An extensive simulation study is conducted to study the finite‐sample performance of the proposed estimators. We provide an application to a dental study for illustration.