2. Department of Statistics, College of Science, Wuhan University of Technology, Wuhan 430070, P.R.China.
3. Amgen, 1 Amgen Center Dr, Thousand Oaks, CA 91320, USA.
Methodological development and applications of joint models for longitudinal and survival data have mostly coupled a single longitudinal outcome-based mixed-effects model with normal distribution and Cox proportional hazards model. In practice, however, (i) normality of model error in longitudinal sub-models is a routine assumption, but it may be unrealistically violating data features of subject variations. (ii) The data collected are often featured by multivariate longitudinal outcomes which are significantly correlated, ignoring their correlation may lead to biased estimation. Additionally, a parametric specification may be inflexible to capture the complicated longitudinal pattern of biomarkers. (iii) It is of importance to investigate how multivariate longitudinal outcomes are associated with an event time of interest. Multilevel item response theory (MLIRT) models have been increasingly used to analyze the multivariate longitudinal data of mixed types (e.g., continuous and categorical) in clinical studies. In this article, we develop a multivariate joint model that consists of an extended MLIRT model for the mixed types of multivariate longitudinal data and a Cox proportional hazards model, linked through random-effects. The proposed models and method are applied to analyze longitudinalsurvival data arising from a primary biliary cirrhosis study. Simulation studies are conducted to evaluate the performance of the proposed models and method.
Keywords: Bayesian inference; latent variable; longitudinal-survival data; multivariate joint model; multilevel item response theory; skew-normal distribution