  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.
