Two-Part Mixed Effects Mixture Model for Zero-Inflated Longitudinal Compositional Data

Abstract

Compositional data (CD) is mostly analyzed using ratios of components and log-ratio transformations to apply known multivariable statistical methods. Therefore, CD where some components equal zero represents a problem. Furthermore, when the data is measured longitudinally, and appear to come from different sub-populations, the analysis becomes highly complex. Our objective is to build a statistical model addressing structural zeros in longitudinal CD and apply it to the analysis of radiation-induced lung damage (RILD) over time. We propose a two-part mixed-effects model extended to the case where the non-zero components of the vector might come from a two-component mixture population. Maximum likelihood estimates for fixed effects and variance components were calculated by an approximate Fisher scoring procedure base on sixth-order Laplace approximation. The expectation-maximization (EM) algorithm estimates the mixture model’s probability. This model was used to analyze the radiation therapy effect on tissue change in one patient with non-small cell lung cancer (NSCLC), utilizing five CT scans over 24 months. Instead of using voxel-level data, voxels were grouped into larger subvolumes called patches. Each patch’s data is a CD vector showing proportions of dense, hazy, or normal tissue. Proposed method performed reasonably for estimation of the fixed effects, and their variability. However, the model produced biased estimates of the nuisance parameters in the model.