Multivariatetlinear mixed models for irregularly observed multiple repeated measures with missing outcomes

Abstract

Missing outcomes or irregularly timed multivariate longitudinal data frequently occur in clinical trials or biomedical studies. The multivariate t linear mixed model (MtLMM) has been shown to be a robust approach to modeling multioutcome continuous repeated measures in the presence of outliers or heavy-tailed noises. This paper presents a framework for fitting the MtLMM with an arbitrary missing data pattern embodied within multiple outcome variables recorded at irregular occasions. To address the serial correlation among the within-subject errors, a damped exponential correlation structure is considered in the model. Under the missing at random mechanism, an efficient alternating expectation-conditional maximization (AECM) algorithm is used to carry out estimation of parameters and imputation of missing values. The techniques for the estimation of random effects and the prediction of future responses are also investigated. Applications to an HIV-AIDS study and a pregnancy study involving analysis of multivariate longitudinal data with missing outcomes as well as a simulation study have highlighted the superiority of MtLMMs on the provision of more adequate estimation, imputation and prediction performances.

Censored regression models with autoregressive errors: A likelihood‐based perspective

“…The problem related to the prediction of future values has a great impact in many practical applications. Rao () pointed out that the predictive accuracy of future observations can be taken as an alternative measure of “goodness of fit.” In order to propose a strategy for generating predicted values from our AR(p)‐CR model we use the plug‐in approach proposed by Wang (). Thus let be the observed response vector of dimension and the response vector ‐step‐ahead.…”

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

“…In the simulation, the data were generated from the MNLMM with nonlinear mean curves Equation (31). The presumed model parameters are:…”

“…This specification implies that within-subject errors for all responses measured at the same occasion have variance-covariance Σ. To capture the extra autocorrelation of a given response among irregularly-observed occasions, some parsimonious dependence structures can be made on C i , such as the compound symmetry, the p-order autoregressive model [29,30] and the damped exponential correlation [31]. For simplicity, we write C i = C i (φ), which depends on subject i according to its dimension s i with each entry being a function of a small set of parameters φ describing within-subject autocorrelation.…”

Bayesian Bivariate Linear Mixed-Effects Models with Skew-Normal/Independent Distributions, with Application to AIDS Clinical Studies

“…With this type of multiple outcomes (CD4 and CD8 cell counts), the underlying statistical question is to estimate the functions that model their dependence on covariates and to investigate the relationships between these functions. Similar clinical and epidemiological studies often generate clustered as well as longitudinal follow-up data with bivariate or multivariate outcomes as primary endpoints, which are routinely analyzed using multivariate linear mixed-effects (LME) models (Ghosh et al, 2007;Matsuyama and Ohashi, 1997;Sammel et al, 1999;Shah et al, 1997;Wang andFan, 2010, 2011;Wang, 2013;among others.). In this article, we focus on a bivariate LME (BLME) model on the situation where two response variables (CD4 and CD8 cell counts) are observed simultaneously for each subject to accommodate individual-level clustering within subjects as well as the correlation between bivariate measures, and to facilitate borrowing of strength across all subjects when assessing the effects of covariates through treatment time, baseline age, treatment group, viral load at baseline, and time-varying treatment efficacy, etc., on AIDS progression.…”