Bayesian Change-Point Joint Models for Multivariate Longitudinal and Time-to-Event Data

Abstract

Joint modeling of longitudinal and survival data is an active area of statistical research that has received much attention recently. Although it is a common practice to analyze complex longitudinal data using nonlinear mixed-effects (NLME) or nonparametric mixed-effects (NPME) models in literature, the following issues may standout: (i) In practice, the profile of each subject’s longitudinal response may follow a “broken-stick” like trajectory, indicating multiple phases of increase and/or decline in response trajectory. Such multiple phases (with random change-points) may be an important indicator to help quantify treatment effect and clinical diagnosis of a disease. To estimate random change-points, NLME or NPME models become a challenge. (ii) Many studies are often to collect data of multivariate longitudinal variables which may be significantly correlated, ignoring their correlation may lead to biased estimate and reduce efficiency. Moreover, the time-to-event may be dependent of the multivariate longitudinal measures and it is of importance to explore their association. (iii) Missing observations in the longitudinal responses are often encountered. The missing data are likely to be informative (nonignorable) and ignoring this phenomenon may result in inaccurate statistical inference. In this article, under a Bayesian framework we consider a piecewise joint model for multivariate longitudinal and time-to-event data to accurately estimate change rates of longitudinal trajectory patterns and timing of change-point which may be critical indicators to quantify the effect of longitudinal profile on the risk of an event. The proposed models and method are applied to analyze a longitudinal dataset arising from a diabetes study. Simulation studies are conducted to assess the performance of the proposed models under various scenarios.