A joint model for hierarchical continuous and zero-inflated overdispersed count data

Abstract

Many applications in public health, medical and biomedical or other studies demand modeling of two or more longitudinal outcomes jointly to get better insight in their joint evolution. In this regard, a joint model for a longitudinal continuous and a count sequence, the latter possibly overdispersed and zero-inflated, 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 (2010); 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 zero-inflated or hurdle model. Zero-inflated 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 modeling framework in which all these features can appear together.