A Robust Approach to Longitudinal Data Analysis Using the t Linear Mixed Model with AR(1) Serial Correlation

Abstract

The most popular analytic tool for longitudinal data with continuous outcomes is the linear mixed model proposed by Laird and Ware (1982, Biometrics). The model assumes that both random effects and error terms are normally distributed for its mathematical convenience and nice statistical properties. In many applied problems, however, such normalities are violated and the inference could be misleading since some of real data may involve atypical observations, which might seriously affect the estimates of fixed effects and variance components in the normal linear mixed model being fitted. In this talk, I will discuss a robust extension of linear mixed model based on multivariate t distributions. Since longitudinal data are collected over time and hence tend to be serially correlated, we employ a parsimonious first- order autoregressive (AR(1)) dependence structure for the within-subject errors. For parameter estimation, we present a hybrid ECME/scoring algorithm that combines the stability and rapid convergence with standard errors as a by- product. Moreover, we offer a score test statistic for testing the existence of autocorrelation in the within-subject errors. The techniques for estimating random effects and predicting future responses of a subject are also investigated. Numerical results are illustrated with real data from a multiple sclerosis cohort clinical trial.