# A monotone data augmentation algorithm for longitudinal data analysis via multivariate skew-t, skew-normal or t distributions

## TL;DR

This paper introduces a robust extension of the mixed effects model for repeated measures (MMRM) using multivariate skew-t, skew-normal, or t distributions, enhancing analysis of skewed and heavy-tailed longitudinal data.

## Contribution

It develops a new monotone data augmentation algorithm for the multivariate skew-t distribution, enabling more reliable longitudinal data analysis with non-normal data.

## Key findings

- Effective handling of skewed and heavy-tailed data.
- Application to real clinical trial data.
- Provides SAS programs for implementation.

## Abstract

The mixed effects model for repeated measures (MMRM) has been widely used for the analysis of longitudinal clinical data collected at a number of fixed time points. We propose a robust extension of the MMRM for skewed and heavy-tailed data on basis of the multivariate skew-t distribution, and it includes the multivariate normal, t, and skew-normal distributions as special cases. An efficient Markov chain Monte Carlo algorithm is developed using the monotone data augmentation and parameter expansion techniques. We employ the algorithm to perform controlled pattern imputations for sensitivity analyses of longitudinal clinical trials with nonignorable dropouts. The proposed methods are illustrated by real data analyses. Sample SAS programs for the analyses are provided in the online supplementary material.