Semiparametric transformation joint models for longitudinal covariates and interval-censored failure time

In many clinical trials and epidemiology research, subjects are followed-up repeatedly, and repeated measurements on longitudinal covariates as well as an observation on a possibly censored time-to-event are collected on each subject. The longitudinal covariates are often measured intermittently with measurement errors, and the measurement process is terminated by a correlated event process, leading to informative missing data. Methods for joint modelling of longitudinal and time to-event data have received much attention in the statistics literature in recent years. Most research has focused on right-censoring mechanism for the event time. In practice, the event time is often examined at the pre-scheduled times, at which the longitudinal covariates are also measured, resulting in interval-censored survival data. To take the interval censoring into account and to provide a more general framework for studying the effects of covariates on survival time, a new class of joint models is proposed. The joint model comprises a linear mixed-effects model for the longitudinal biomarkers and a class of semiparametric transformation models for the failure time, which incorporates the underlying longitudinal biomarkers as time-dependent covariates. The likelihood approach and an EM algorithm for obtaining the semiparametric maximum likelihood estimator (SPMLE) are developed. In M-step, a hybrid algorithm combining the Newton-Raphson and self-consistency algorithms is used to compute the finite-dimensional and infinite-dimensional parameters. The existence and consistency of the SPMLE are established. The proposed method is investigated through simulation studies and illustrated using a real dataset from a Taiwanese HIV/AIDS cohort study.