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Bayesian Regression Analysis of Data with Random Effects Covariates from Nonlinear Longitudinal Measurements

Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to asses association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. The most common joint model in this framework is based on a linear mixed model for the longitudinal data. However, for complex datasets the linearity assumption may be too restrictive. Some works have considered generalizing this setting with the use of a nonlinear mixed-effects model for the longitudinal trajectories but the proposed estimation procedures based on likelihood approximations have been shown De la Cruz et al. (2011) to exhibit some computational efficiency problems. In this article we propose an MCMC-based estimation procedure in the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to asses the importance of modelling correlated errors and quantify the consequences of model misspecification.