Two-Part Pattern-Mixture Model for Longitudinal Incomplete Semi-Continuous Toenail Data

Abstract

Longitudinal data with true zero values, known as longitudinal semi-continuous data, frequently occur in medical, environmental and biological studies. To model longitudinal semi-continuous data, two-part modelling approaches have been widely used in literature. In the first part of the two-part model, binary logistic regression is commonly used after converting the semi-continuous responses to binary responses. In the second part, the semi-continuous data are converted to positive continuous data after removing the true zero values from the responses. Although positive continuous or non-zero values tend to show a positively skewed distribution pattern, in the literature the normal distribution is commonly used to model them. Also, in longitudinal studies, data often suffer individual dropouts as they are collected overtime. In this paper, we propose a two-part pattern-mixture model to analyze longitudinal semi-continuous data with dropouts. In the proposed approach, we use pattern-mixture binary mixed models for the first part and positively continuous pattern-mixture gamma mixed models for the second part. Our approach can accommodate both subject- and time-specific correlation as well as dropout pattern. We also incorporate a computationally efficient estimation method for our models using a penalize quasi-likelihood approach. The proposed method is illustrated with an application to the longitudinal incomplete toenail data