Conditional Inference Functions for Mixed-Effects Models With Unspecified Random-Effects Distribution

Response transformations for random effect and variance component models

Random effect models have been popularly used as a mainstream statistical technique over several decades; and the same can be said for response transformation models such as the Box–Cox transformation. The latter aims at ensuring that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for inference based on a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. We develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the ‘Nonparametric Maximum Likelihood’ towards a ‘Nonparametric profile maximum likelihood’ technique, allowing to deal with overdispersion as well as two-level data scenarios.

Inference for variance components in linear mixed-effect models with flexible random effect and error distributions

In many biomedical investigations, parameters of interest, such as the intraclass correlation coefficient, are functions of higher-order moments reflecting finer distributional characteristics. One popular method to make inference for such parameters is through postulating a parametric random effects model. We relax the standard normality assumptions for both the random effects and errors through the use of the Fleishman distribution, a flexible four-parameter distribution which accounts for the third and fourth cumulants. We propose a Fleishman bootstrap method to construct confidence intervals for correlated data and develop a normality test for the random effect and error distributions. Recognizing that the intraclass correlation coefficient may be heavily influenced by a few extreme observations, we propose a modified, quantile-normalized intraclass correlation coefficient. We evaluate our methods in simulation studies and apply these methods to the Childhood Adenotonsillectomy Trial sleep electroencephalogram data in quantifying wave-frequency correlation among different channels.

Measuring the individual benefit of a medical or behavioral treatment using generalized linear mixed-effects models

We propose statistical definitions of the individual benefit of a medical or behavioral treatment and of the severity of a chronic illness. These definitions are used to develop a graphical method that can be used by statisticians and clinicians in the data analysis of clinical trials from the perspective of personalized medicine. The method focuses on assessing and comparing individual effects of treatments rather than average effects and can be used with continuous and discrete responses, including dichotomous and count responses. The method is based on new developments in generalized linear mixed-effects models, which are introduced in this article. To illustrate, analyses of data from the Sequenced Treatment Alternatives to Relieve Depression clinical trial of sequences of treatments for depression and data from a clinical trial of respiratory treatments are presented. The estimation of individual benefits is also explained. Copyright © 2016 John Wiley & Sons, Ltd.

A moving blocks empirical likelihood method for longitudinal data

In the analysis of longitudinal or panel data, neglecting the serial correlations among the repeated measurements within subjects may lead to inefficient inference. In particular, when the number of repeated measurements is large, it may be desirable to model the serial correlations more generally. An appealing approach is to accommodate the serial correlations nonparametrically. In this article, we propose a moving blocks empirical likelihood method for general estimating equations. Asymptotic results are derived under sequential limits. Simulation studies are conducted to investigate the finite sample performances of the proposed methods and compare them with the elementwise and subject-wise empirical likelihood methods of Wang et al. (2010, Biometrika 97, 79-93) and the block empirical likelihood method of You et al. (2006, Can. J. Statist. 34, 79-96). An application to an AIDS longitudinal study is presented.

Estimating and Identifying Unspecified Correlation Structure for Longitudinal Data

Identifying correlation structure is important to achieving estimation efficiency in analyzing longitudinal data, and is also crucial for drawing valid statistical inference for large size clustered data. In this paper, we propose a nonparametric method to estimate the correlation structure, which is applicable for discrete longitudinal data. We utilize eigenvector-based basis matrices to approximate the inverse of the empirical correlation matrix and determine the number of basis matrices via model selection. A penalized objective function based on the difference between the empirical and model approximation of the correlation matrices is adopted to select an informative structure for the correlation matrix. The eigenvector representation of the correlation estimation is capable of reducing the risk of model misspecification, and also provides useful information on the specific within-cluster correlation pattern of the data. We show that the proposed method possesses the oracle property and selects the true correlation structure consistently. The proposed method is illustrated through simulations and two data examples on air pollution and sonar signal studies.