Joint modeling of zero-inflated longitudinal measurements and time-to-event outcomes with applications to dynamic prediction

In this article, we present a joint modeling approach for zero-inflated longitudinal count measurements and time-to-event outcomes. For the longitudinal sub-model, a mixed effects Hurdle model is utilized, incorporating various distributional assumptions such as zero-inflated Poisson, zero-inflated negative binomial, or zero-inflated generalized Poisson. For the time-to-event sub-model, a Cox proportional hazard model is applied. For the functional form linking the longitudinal outcome history to the hazard of the event, a linear combination is used. This combination is derived from the current values of the linear predictors of Hurdle mixed effects. Some other forms are also considered, including a linear combination of the current slopes of the linear predictors of Hurdle mixed effects as well as the shared random effects. A Markov chain Monte Carlo method is implemented for Bayesian parameter estimation. Dynamic prediction using joint modeling is highly valuable in personalized medicine, as discussed here for joint modeling of zero-inflated longitudinal count measurements and time-to-event outcomes. We assess and demonstrate the effectiveness of the proposed joint models through extensive simulation studies, with a specific emphasis on parameter estimation and dynamic predictions for both over-dispersed and under-dispersed data. We finally apply the joint model to longitudinal microbiome pregnancy and HIV data sets.