A mixture of hierarchical joint models for longitudinal data with heterogeneity, non-normality, missingness, and covariate measurement error.

Longitudinal data arise frequently in medical studies and it is a common practice to analyze such complex data with nonlinear mixed-effects (NLME) models. However, the following four issues may be critical in longitudinal data analysis. (i) A homogeneous population assumption for models may be unrealistically obscuring important features of between-subject and within-subject variations; (ii) normality assumption for model errors may not always give robust and reliable results, in particular, if the data exhibit skewness; (iii) the responses may be missing and the missingness may be nonignorable; and (iv) some covariates of interest may often be measured with substantial errors. When carrying out statistical inference in such settings, it is important to account for the effects of these data features; otherwise, erroneous or even misleading results may be produced. Inferential procedures can be complicated dramatically when these four data features arise. In this article, the Bayesian joint modeling approach based on a finite mixture of NLME joint models with skew distributions is developed to study simultaneous impact of these four data features, allowing estimates of both model parameters and class membership probabilities at population and individual levels. A real data example is analyzed to demonstrate the proposed methodologies, and to compare various scenarios-based potential models with different specifications of distributions.