Random-effects regression models have become increasingly popular for analysis of longitudinal data. A key advantage of the random-effects approach is that it can be applied when subjects are not measured at the same number of timepoints. In this article we describe use of random-effects pattern-mixture models to further handle and describe the influence of missing data in longitudinal studies. For this approach, subjects are first divided into groups depending on their missing-data pattern and then variables based on these groups are used as model covariates. Tn this way, researchers are able to examine the effect of missing-data patterns on the outcome (or outcomes) of interest. Furthermore, overall estimates can be obtained by averaging over the missing-data patterns. A psychiatric clinical trials data set is used to illustrate the random-effects pattern-mixture approach to longitudinal data analysis with missing data.Longitudinal studies occupy an important role in psychological and psychiatric research. In these stud-

Reporting effect sizes in scientific articles is increasingly widespread and encouraged by journals; however, choosing an effect size for analyses such as mixed-effects regression modeling and hierarchical linear modeling can be difficult. One relatively uncommon, but very informative, standardized measure of effect size is Cohen’s f2, which allows an evaluation of local effect size, i.e., one variable’s effect size within the context of a multivariate regression model. Unfortunately, this measure is often not readily accessible from commonly used software for repeated-measures or hierarchical data analysis. In this guide, we illustrate how to extract Cohen’s f2 for two variables within a mixed-effects regression model using PROC MIXED in SAS® software. Two examples of calculating Cohen’s f2 for different research questions are shown, using data from a longitudinal cohort study of smoking development in adolescents. This tutorial is designed to facilitate the calculation and reporting of effect sizes for single variables within mixed-effects multiple regression models, and is relevant for analyses of repeated-measures or hierarchical/multilevel data that are common in experimental psychology, observational research, and clinical or intervention studies.

A random-effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data. This model is developed for both the probit and logistic response functions. The threshold concept is used, in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects. A maximum marginal likelihood (MML) solution is described using Gauss-Hermite quadrature to numerically integrate over the distribution of random effects. An analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random-effects analysis of clustered ordinal data, while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random-effects approach for longitudinal ordinal data.

SummaryFor longitudinal data, mixed models include random subject effects to indicate how subjects influence their responses over repeated assessments. The error variance and the variance of the random effects are usually considered to be homogeneous. These variance terms characterize the within-subjects (i.e., error variance) and between-subjects (i.e., random-effects variance) variation in the data. In studies using ecological momentary assessment (EMA), up to 30 or 40 observations are often obtained for each subject, and interest frequently centers around changes in the variances, both within and between subjects. In this article, we focus on an adolescent smoking study using EMA where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances, and also extend the standard mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. Additionally, we allow the location and scale random effects to be correlated. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.

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Creative use of new mobile and wearable health information and sensing technologies (mHealth) has the potential to reduce the cost of health care and improve well-being in numerous ways. These applications are being developed in a variety of domains, but rigorous research is needed to examine the potential, as well as the challenges, of utilizing mobile technologies to improve health outcomes. Currently, evidence is sparse for the efficacy of mHealth. Although these technologies may be appealing and seemingly innocuous, research is needed to assess when, where, and for whom mHealth devices, apps, and systems are efficacious. In order to outline an approach to evidence generation in the field of mHealth that would ensure research is conducted on a rigorous empirical and theoretic foundation, on August 16, 2011, researchers gathered for the mHealth Evidence Workshop at NIH. The current paper presents the results of the workshop. Although the discussions at the meeting were cross-cutting, the areas covered can be categorized broadly into three areas: (1) evaluating assessments; (2) evaluating interventions; and, (3) reshaping evidence generation using mHealth. This paper brings these concepts together to describe current evaluation standards, future possibilities and set a grand goal for the emerging field of mHealth research.

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Several approaches have been proposed to model binary outcomes that arise from longitudinal studies. Most of the approaches can be grouped into two classes: the population-averaged and subject-specific approaches. The generalized estimating equations (GEE) method is commonly used to estimate population-averaged effects, while random-effects logistic models can be used to estimate subject-specific effects. However, it is not clear to many epidemiologists how these two methods relate to one another or how these methods relate to more traditional stratified analysis and standard logistic models. The authors address these issues in the context of a longitudinal smoking prevention trial, the Midwestern Prevention Project. In particular, the authors compare results from stratified analysis, standard logistic models, conditional logistic models, the GEE models, and random-effects models by analyzing a binary outcome from two and seven repeated measurements, respectively. In the comparison, the authors focus on the interpretation of both time-varying and time-invariant covariates under different models. Implications of these methods for epidemiologic research are discussed.