A Bayesian approach of analysing semi-continuous longitudinal data with monotone missingness

There is a rich literature on the analysis of longitudinal data with missing values. However, the analysis becomes complex for semi-continuous (zero-inflated) longitudinal response with missingness. In this article, we propose a partially varying coefficients regression model for analysing such data. We use a two-part model, where in the first part we propose a latent dynamic model for accounting a `zero' or a `non-zero' response, and in the second part we use another dynamic model for estimating the mean trajectories of non-zero responses. Two dynamic models are linked through subject-specific random effects. The missing covariates are imputed repeatedly based on their respective posterior predictive distributions and the missing responses are imputed using the working model under different identifying restrictions. We analyse data from the Health and Retirement Study (HRS) for aged individuals and develop a dynamic model for predicting out-of-pocket medical expenditures (OOPME) containing excess zeros. The operating characteristics of the proposed model are investigated through extensive simulation studies.