Constrained inference in mixed-effects models for longitudinal data with application to hearing loss

Abstract

In medical studies, endpoints are often measured for each patient longitudinally. The mixed-effects model has been a useful tool for the analysis of such data. There are situations in which the parameters of the model are subject to some restrictions or constraints. For example, in hearing loss studies, we expect hearing to deteriorate with time. This means that hearing thresholds which reflect hearing acuity will, on average, increase over time. Therefore, the regression coefficients associated with the mean effect of time on hearing ability will be constrained. Such constraints should be accounted for in the analysis. We propose maximum likelihood estimation procedures, based on the expectation-conditional maximization either algorithm, to estimate the parameters of the model while accounting for the constraints on them. The proposed methods improve, in terms of mean square error, on the unconstrained estimators. In some settings, the improvement may be substantial. Hypotheses testing procedures that incorporate the constraints are developed. Specifically, likelihood ratio, Wald, and score tests are proposed and investigated. Their empirical significance levels and power are studied using simulations. It is shown that incorporating the constraints improves the mean squared error of the estimates and the power of the tests. These improvements may be substantial. The methodology is used to analyze a hearing loss study.

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

“…However, despite the existence of a large body of literature on constrained inference spanning over five decades and three books on testing for order restrictions (Barlow, Bartholomew, Brenner, and Brunk 1972;Robertson, Wright, and Dykstra 1988;Silvapulle and Sen 2005), it was only recently that researchers developed methods for performing constrained inference in linear mixed effects models (Rosen and Davidov 2012;Davidov and Rosen 2011;Farnan, Ivanova, and Peddada 2014). While Rosen and Davidov (2012) and Davidov and Rosen (2011) developed likelihood ratio based methods, Farnan et al (2014) developed a residual bootstrap based method that is designed to be robust to non-normality as well as to heteroscedasticity. Furthermore, Farnan et al (2014)'s methodology allows for modeling categorical as well as continuous covariates.…”

Constrained fuzzy evidential multivariate model identified by EM algorithm: a soft sensor to monitoring imprecise and uncertain process parameters

“…Shi et al (2005) considered the incomplete-data problem with convex cone restrictions which are special cases of inequality restrictions. Davidov and Rosen (2011) developed maximum likelihood estimate procedures and proposed asymptotic tests in mixed-effect models with linear inequality restrictions for longitudinal data. In Zheng et al (2012), the authors considered a multivariate linear model with complete/incomplete data, where the regression coefficients are subject to a set of linear inequality restrictions.…”

Linear Mixed Effects Models under Inequality Constraints with Applications

“…It was not until [18]–[20] that statistical inference under inequality constraints in linear mixed effects models was formally addressed. In particular [18] developed an asymptotic likelihood ratio test (LRT) for linear mixed effects model under homoscedastic errors.…”

“…In particular [18] developed an asymptotic likelihood ratio test (LRT) for linear mixed effects model under homoscedastic errors. Since the asymptotic null distribution of LRT depends upon nuisance parameters, they also provided suitable bounds for the distribution using central chi-square distributions with appropriate degrees of freedom.…”