Statistical Modelling 21 (1-2) (2021), 72–94

Joint modelling of longitudinal and survival data in the presence of competing risks with applications to prostate cancer data

Md Tuhin Sheikh,
Department of Statistics, University of Connecticut,
Storrs, CT,
USA


Joseph G Ibrahim,
Department of Biostatistics,
University of North Carolina at Chapel Hill,
Chapel Hill, NC,
USA
e-mail: ibrahim@bios.unc.edu

Jonathan A Gelfond, Department of Epidemiology and Biostatistics,
University of Texas Health San Antonio,
San Antonio, TX,
USA


Wei Sun,
Biostatistics Program, Public Health Sciences Division,
Fred Hutchinson Cancer Research Center,
Seattle, WA,
USA


Abstract:

This research is motivated from the data from a large Selenium and Vitamin E Cancer Prevention Trial (SELECT). The prostate specific antigens (PSAs) were collected longitudinally, and the survival endpoint was the time to low-grade cancer or the time to high-grade cancer (competing risks). In this article, the goal is to model the longitudinal PSA data and the time-to-prostate cancer (PC) due to low- or high-grade. We consider the low-grade and high-grade as two competing causes of developing PC. A joint model for simultaneously analysing longitudinal and time-to-event data in the presence of multiple causes of failure (or competing risk) is proposed within the Bayesian framework. The proposed model allows for handling the missing causes of failure in the SELECT data and implementing an efficient Markov chain Monte Carlo sampling algorithm to sample from the posterior distribution via a novel reparameterization technique. Bayesian criteria, ⊿DICSurv, and ⊿WAICSurv, are introduced to quantify the gain in fit in the survival sub-model due to the inclusion of longitudinal data. A simulation study is conducted to examine the empirical performance of the posterior estimates as well as ⊿DICSurv and ⊿WAICSurv and a detailed analysis of the SELECT data is also carried out to further demonstrate the proposed methodology.

Keywords:

cause-specific competing risks model; DIC; mixed effects model; reparametrization; SELECT data; WAIC.

Downloads:

Supplementary material can be found here. The real SELECT dataset for this paper is proprietary and confidential. The authors do not have the permission to publish the raw data on any website or data hub. Computer code for this article was written for the FORTRAN 95 compiler and will be released once an R interface has been developed.
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