A Bayesian Shared Parameter Model for Incomplete Semicontinuous longitudinal Data: An Application To Toenail Dermatophyte Onychomycosis Study

Abstract

Most of statistical analysis for longitudinal data are based on normality assumption for the continuous response of interest which might be violated in some practical areas due to skewed data which possibly contain excess zeros. Some authors have proposed frequentist and Bayesian approaches to model semicontinuous data using a zero-inflated log-normal model which do not consider the problem of incomplete responses which is an almost inevitable complication in drawing inferences for follow up studies. In this article, we will propose a Mixed effect zero inflated log-normal model along with a possibly non-ignorable dropout mechanism by utilizing a practical Bayesian approach for parameter estimation. To account for the possibility of non-ignorable dropout we will use a shared-parameter framework where the outcome and the missingness models are connected by means of common latent variables or random effects. The approach will be illustrated by analyzing a real data set from a longitudinal study for the comparison of two oral treatments for toenail dermatophyte onychomycosis in which the outcome of interest present a typical example of log-normal data with excess zeros. These data have been analyzed by many researchers with the normality assumption for the continuous response of interest which cannot be justified based on the descriptive aspects of the data at hand and the zero-inflated log-normal assumption leads to the better goodness of fit results

Keywords

• Longitudinal Studies; Semicontinuous Responses; Non-random Dropout; Bayesian Approach