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

• Published in: Biometrics Vol. 78; no. 1; pp. 165 - 178
• Main Authors: Lee, Chun Yin, Wong, Kin Yau, Lam, K. F., Xu, Jinfeng
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishing Ltd 01.03.2022
• Subjects: clustered data; Computer Simulation; Dental materials; Estimators; Failure times; Frailty; Humans; Likelihood Functions; Linear functions; Linear Models; Maximum likelihood estimation; Models, Statistical; nonparametric estimation; Nonparametric statistics; partly linear model; random effects model; sieve maximum likelihood estimation; Transformations (mathematics); clustered data; random effects model; sieve maximum likelihood estimation; nonparametric estimation; partly linear model
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/biom.13399

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.