Multivariate analysis of longitudinal rates of change

Abstract

Longitudinal data allow direct comparison of the change in patient outcomes associated with treatment or exposure. Frequently, several longitudinal measures are collected that either reflect a common underlying health status, or characterize processes that are influenced in a similar way by covariates such as exposure or demographic characteristics. Statistical methods that can combine multivariate response variables into common measures of covariate effects have been proposed by Roy and Lin [1]; Proust-Lima, Letenneur and Jacqmin-Gadda [2]; and Gray and Brookmeyer [3] among others. Current methods for characterizing the relationship between covariates and the rate of change in multivariate outcomes are limited to select models. For example, Gray and Brookmeyer [3] introduce an “accelerated time” method which assumes that covariates rescale time in longitudinal models for disease progression. In this manuscript we detail an alternative multivariate model formulation that directly structures longitudinal rates of change, and that permits a common covariate effect across multiple outcomes. We detail maximum likelihood estimation for a multivariate longitudinal mixed model. We show via asymptotic calculations the potential gain in power that may be achieved with a common analysis of multiple outcomes. We apply the proposed methods to the analysis of a trivariate outcome for infant growth and compare rates of change for HIV infected and uninfected infants.

A comparison of approaches for simultaneous inference of fixed effects for multiple outcomes using linear mixed models

“…To simplify the complexity of a joint model, restrictions may be put on the correlation structure or one may turn to shared parameter models. However, if such model assumptions do not hold, the fitted model will loose power to detect treatment effects . One alternative for overcoming the computational challenges is to use a pairwise modelling approach .…”

Using empirical Bayes predictors from generalized linear mixed models to test and visualize associations among longitudinal outcomes

“…only random intercepts in a polynomial model) or by reparametrizing the model. 13 After approximating the multivariate generalized linear mixed model by a multivariate normal linear mixed model Li et al. 14 use an EM algorithm to model random effects with an 8 × 8 covariance matrix.…”

“…only random intercepts in a polynomial model) or by reparametrizing the model. 13 After approximating the multivariate generalized linear mixed model by a multivariate normal linear mixed model Li et al 14 use an EM algorithm to model random effects with an 8 Â 8 covariance matrix. A reasonable alternative might include generating empirical Bayes predictors (EBPs) from a mixed model in the first stage and using them as new variables in a second stage analysis.…”

“…compared, associated) in the second stage (summarized in Grizzle and Allen 17 ). Here, we investigate whether a two-stage analysis of EBPs might facilitate a simpler method for estimating random coefficient associations between outcomes and whether plots of EBPs 13 provide an effective means of visualizing associations from these complex models.…”