Order-restricted inference for multivariate longitudinal data with applications to the natural history of hearing loss

Joint modeling of multivariate hearing thresholds measured longitudinally at multiple frequencies

Pure-tone thresholds are used to estimate hearing acuity and, when measured longitudinally, can characterize age-related changes in hearing. Measured at multiple-frequencies, multiple-irregular time points, for right and left ears, these longitudinal studies of age-related hearing loss produce data of inherent complexity due to: 1) multivariate outcomes at different frequencies; 2) longitudinal measurements taken at subject-specific time intervals; and 3) inter-ear correlations due to clustering and nesting. To address limitations in existing methods, we propose a multivariate generalized linear mixed model(mGLMM) and assess its performance. We demonstrate its application using a unique dataset from a cohort study of age-related hearing loss.

Some comments on “The analysis of multivariate longitudinal data: A review”

We provide a commentary on “The analysis of multivariate longitudinal data: a review” by Verbeke et al. The authors provide a comprehensive review of the issues in the analysis of multivariate longitudinal data and use examples to demonstrate the pros and cons of several approaches. In this commentary, we indicate some important omissions in their review paper.

CLME: An R Package for Linear Mixed Effects Models under Inequality Constraints

In many applications researchers are typically interested in testing for inequality constraints in the context of linear fixed effects and mixed effects models. Although there exists a large body of literature for performing statistical inference under inequality constraints, user friendly statistical software for implementing such methods is lacking, especially in the context of linear fixed and mixed effects models. In this article we introduce CLME, a package in the R language that can be used for testing a broad collection of inequality constraints. It uses residual bootstrap based methodology which is reasonably robust to non-normality as well as heteroscedasticity. The package is illustrated using two data sets. The package also contains a graphical interface built using the shiny package.

Linear mixed effects models under inequality constraints with applications

Constraints arise naturally in many scientific experiments/studies such as in, epidemiology, biology, toxicology, etc. and often researchers ignore such information when analyzing their data and use standard methods such as the analysis of variance (ANOVA). Such methods may not only result in a loss of power and efficiency in costs of experimentation but also may result poor interpretation of the data. In this paper we discuss constrained statistical inference in the context of linear mixed effects models that arise naturally in many applications, such as in repeated measurements designs, familial studies and others. We introduce a novel methodology that is broadly applicable for a variety of constraints on the parameters. Since in many applications sample sizes are small and/or the data are not necessarily normally distributed and furthermore error variances need not be homoscedastic (i.e. heterogeneity in the data) we use an empirical best linear unbiased predictor (EBLUP) type residual based bootstrap methodology for deriving critical values of the proposed test. Our simulation studies suggest that the proposed procedure maintains the desired nominal Type I error while competing well with other tests in terms of power. We illustrate the proposed methodology by re-analyzing a clinical trial data on blood mercury level. The methodology introduced in this paper can be easily extended to other settings such as nonlinear and generalized regression models.