Multivariate piecewise joint models with random change-points for skewed-longitudinal and survival data.

Methodological development and application of joint models for longitudinal and time-to-event data have mostly coupled a single longitudinal outcome-based linear mixed-effects model with normal distribution and Cox proportional hazards model. In practice, however, (i) profile of subject's longitudinal response may follow a `broken-stick nonlinear' (piecewise) trajectory. Such multiple phases are an important indicator to help quantify treatment effect, disease diagnosis and clinical decision-making. (ii) Normality in longitudinal models is a routine assumption, but it may be unrealistically obscuring important features of subject variations. (iii) Data collected are often featured by multivariate longitudinal outcomes which are significantly correlated, ignoring their correlation may lead to biased estimation. (iv) It is of importance to investigate how multivariate longitudinal outcomes are associated with event time of interest. In the article, driven by a motivating example, we propose Bayesian multivariate piecewise joint models with a skewed distribution and random change-points for longitudinal measures with an attempt to cope with correlated multivariate longitudinal data, adjust departures from normality, mediate accuracy from longitudinal trajectories with random change-point and tailor linkage in specifying a time-to-event process. A real example is analyzed to demonstrate methodology and simulation studies are conducted to evaluate performance of the proposed models and method.