A shared parameter model of longitudinal measurements and survival time with heterogeneous random-effects distribution
Taban Baghfalaki, Mojtaba Ganjali, Geert N. Verbeke · Journal of Applied Statistics · 2016
Taban Baghfalakiad*, Mojtaba Ganjalibd & Geert Verbekeca Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iranb Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iranc Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Katholieke Universiteit Leuven, Leuven, Belgiumd School of Biological Science, Institute for Research in Fundamental Sciences (IPM), Tehran, IranCONTACT Taban Baghfalaki [email protected] joint modeling of longitudinal measurements and time to event data assumes that two models share a common set of random effects with a normal distribution assumption. But, sometimes the underlying population that the sample is extracted from is a heterogeneous population and detecting homogeneous subsamples of it is an important scientific question. In this paper, a finite mixture of normal distributions for the shared random effects is proposed for considering the heterogeneity in the population. For detecting whether the unobserved heterogeneity exits or not, we use a simple graphical exploratory diagnostic tool proposed by Verbeke and Molenberghs [34] to assess whether the traditional normality assumption for the random effects in the mixed model is adequate. In the joint modeling setting, in the case of evidence against normality (homogeneity), a finite mixture of normals is used for the shared random-effects distribution. A Bayesian MCMC procedure is developed for parameter estimation and inference. The methodology is illustrated using some simulation studies. Also, the proposed approach is used for analyzing a real HIV data set, using the heterogeneous joint model for this data set, the individuals are classified into two groups: a group with high risk and a group with moderate risk.