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Joint models for a wide class of response variables and longitudinalmeasurements consist on a mixed-effects model to fit longitudinal trajectorieswhose random effects enter as covariates in a generalized linear model for theprimary response. They provide a useful way to asses association between thesetwo kinds of data, which in clinical studies are often collected jointly on aseries of individuals and may help understanding, for instance, the mechanismsof recovery of a certain disease or the efficacy of a given therapy. The mostcommon joint model in this framework is based on a linear mixed model for thelongitudinal data. However, for complex datasets the linearity assumption maybe too restrictive. Some works have considered generalizing this setting withthe use of a nonlinear mixed-effects model for the longitudinal trajectoriesbut the proposed estimation procedures based on likelihood approximations havebeen shown De la Cruz et al. (2011) to exhibit some computational efficiencyproblems. In this article we propose an MCMC-based estimation procedure in thejoint model with a nonlinear mixed-effects model for the longitudinal data anda generalized linear model for the primary response. Moreover, we consider thatthe errors in the longitudinal model may be correlated. We apply our method tothe analysis of hormone levels measured at the early stages of pregnancy thatcan be used to predict normal versus abnormal pregnancy outcomes. We alsoconduct a simulation study to asses the importance of modelling correlatederrors and quantify the consequences of model misspecification.

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