  Joint models have proven to be an effective approach for uncovering
potentially hidden connections between various types of outcomes, mainly
continuous, time-to-event, and binary. Typically, longitudinal continuous
outcomes are characterized by linear mixed-effects models, survival outcomes
are described by proportional hazards models, and the link between outcomes are
captured by shared random effects. Other modeling variations include
generalized linear mixed-effects models for longitudinal data and logistic
regression when a binary outcome is present, rather than time until an event of
interest. However, in a clinical research setting, one might be interested in
modeling the physician's chosen treatment based on the patient's medical
history in order to identify prognostic factors. In this situation, there are
often multiple treatment options, requiring the use of a multiclass
classification approach. Inspired by this context, we develop a Bayesian joint
model for longitudinal and categorical data. In particular, our motivation
comes from a multiple myeloma study, in which biomarkers display nonlinear
trajectories that are well captured through bi-exponential submodels, where
patient-level information is shared with the categorical submodel. We also
present a variable importance strategy for ranking prognostic factors. We apply
our proposal and a competing model to the multiple myeloma data, compare the
variable importance and inferential results for both models, and illustrate
patient-level interpretations using our joint model.
