Nonparametric Bayesian functional two-part random effects model for analyzing longitudinal data with zero inflation

Abstract

This study proposes a nonparametric Bayesian method for the analysis of longitudinal data with zero inflation. In the first part of this study, we propose a nonparametric Bayesian functional two-part random effects model for analyzing the relationship between longitudinal semi-continuous outcome and functional/non-functional covariates and also identifying an underlying subgroup structure. In the second part, we propose a nonparametric Bayesian Poisson Hurdle random effect model that deals with longitudinal zero-inflated count data.

Longitudinal semi-continuous data, characterized by repeated measures of a large portion of zeros and continuous positive values, are frequently encountered in many applications including biomedical, epidemiological and social science studies. Two-part random effects models (TPREM) have been used to investigate the association between such longitudinal semi-continuous data and covariates accounting for the within-subject correlation. The existing TPREM is, however, limited to incorporate a functional covariate which is often available in a longitudinal study. Moreover, the existing TPREM typically assumes the normality of subject-specific random effects, which can be easily violated when there exists a subgroup structure. We propose a nonparametric Bayesian functional TPREM (NB-fTPREM) to assess the relationship between the longitudinal semi-continuous outcome and various types of covariates including a functional covariate. The proposed model also relaxes the normality assumption for the random effects through a Dirichlet process mixture of normals, which allows for identifying an underlying subgroup structure. The methodology is illustrated through an application to social insurance expenditure data collected by the Korean Welfare Panel Study and a simulation study.

Similarly, count data with zero inflation frequently encountered in many applications. Poisson hurdle random effects models (PHREM) have been proposed to investigate the association between such longitudinal zero-inflated count data and covariates. Since the two-part model and the hurdle model have a similar structure, the second level of NB-fTPREM can be combined with PHREM to handle the longitudinal zero-inflated count data. We propose a nonparametric Bayesian functional PHREM (NB-fPHREM) to assess the relationship between the longitudinal zero-inflated count outcome and various types of covariates. The methodology is illustrated through an application to suicide data of United states and a simulation study.