A robust approach tot linear mixed models applied to multiple sclerosis data

Abstract

We discuss a robust extension of linear mixed models based on the multivariate t distribution. Since longitudinal data are successively collected over time and typically tend to be auto-correlated, we employ a parsimonious first-order autoregressive dependence structure for the within-subject errors. A score test statistic for testing the existence of autocorrelation among the within-subject errors is derived. Moreover, we develop an explicit scoring procedure for the maximum likelihood estimation with standard errors as a by-product. The technique for predicting future responses of a subject given past measurements is also investigated. Results are illustrated with real data from a multiple sclerosis clinical trial.

A robust approach to joint modeling of mean and scale covariance for longitudinal data

“…Results suggest that TLMM with random intercepts and slopes plus AR(1) dependence (ˆ = 9.06, BIC = 2.84), denoted by TLMM-RIS-AR(1), is the most preferred choice among some selected normal/t mixed models. The prediction approach for TLMM with autoregressive dependence was described in Lin and Lee (2006).…”

Estimation in nonlinear mixed-effects models using heavy-tailed distributions

“…The class of distributions we consider is scale mixtures of multivariate normal distributions that are often useful for robust inference. Therefore, this work represents a natural generalization of previous works of Pinheiro et al (2001), Lin and Lee (2006) and Lin (2008), for the nonlinear mixed-effects context. Thus, our propose is an alternative to the works of Yeap and Davidian (2001) and Yeap et al (2003).…”

“…For instance, Welsh and Richardson (1997) make a review of procedures for robust estimation using multivariate symmetrical distributions. Pinheiro et al (2001), Lin and Lee (2006) and Staudenmayer et al (2009) studied robust approaches to estimation in which both random effects and errors have multivariate Student-t distributions, while Choy and Smith (1997), Rosa et al (2003Rosa et al ( , 2004 discussed Markov chain Monte Carlo (MCMC) implementations considering a Bayesian formulation. However, few alternatives have been studied for outlier accommodation in the context of nonlinear mixed-effects models.…”

Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

“…However, the multivariate normality assumption in the MNLMM might not provide robust inference if the data, even after being transformed, and exhibit fat tails and/or skewness [48][49][50]. To alleviate such limitations, it is natural to replace the multivariate normally-distributed random effects and within-subject errors of the MNLMM by a broader family, such as the multivariate skew-normal distribution [51], the multivariate skew-t distribution [52], the multivariate skew-elliptical distribution [53], or the multivariate skew-normal independent distribution [54,55].…”