Abstract:
Many applications in public health, medical and biomedical or other studies demand modelling of two or
more longitudinal outcomes jointly to get better insight into their joint evolution. In this regard, a jointmodel
for a longitudinal continuous and a count sequence, the latter possibly overdispersed and zero-inflated (ZI),
will be specified that assembles aspects coming from each one of them into one single model. Further, a
subject-specific random effect is included to account for the correlation in the continuous outcome. For
the count outcome, clustering and overdispersion are accommodated through two distinct sets of random
effects in a generalized linear model as proposed by Molenberghs et al. [A family of generalized linear
models for repeated measures with normal and conjugate random effects. Stat Sci. 2010;25:325–347];
one is normally distributed, the other conjugate to the outcome distribution. The association among the
two sequences is captured by correlating the normal random effects describing the continuous and count
outcome sequences, respectively. An excessive number of zero counts is often accounted for by using a
so-called ZI or hurdle model. ZI models combine either a Poisson or negative-binomial model with an
atom at zero as a mixture, while the hurdle model separately handles the zero observations and the positive
counts. This paper proposes a general joint modelling framework in which all these features can appear
together. We illustrate the proposed method with a case study and examine it further with simulations.
