Donald Hedeker

Application of random-effects pattern-mixture models for missing data in longitudinal studies

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. In 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 studies the same individuals are repeatedly measured on a number of important variables over a series of timepoints. As an example, a longitudinal design is often used to determine whether a particular therapeutic agent can produce changes in clinical status over the course of an illness. Another application for the longitudinal study is to assess potential indicators of a change, in the subjects clinical status; for example, the assessment of whether drug plasma level measurements indicate clinical outcome. Even in well-controlled situations, missing data invariably occur in longitudinal studies. Subjects can be

A random-effects ordinal regression model for multilevel analysis.

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.

The Altman Self-Rating Mania Scale

We report on the development, reliability, and validity of the Altman Self-Rating Mania Scale (ASRM). The ASRM was completed during medication washout and after treatment by 22 schizophrenic, 13 schizoaffective, 36 depressed, and 34 manic patients. The Clinician-Administered Rating Scale for Mania (CARS-M) and Mania Rating Scale (MRS) were completed at the same time to measure concurrent validity. Test-retest reliability was assessed separately on 20 depressed and 10 manic patients who completed the ASRM twice during washout. Principal components analysis of ASRM items revealed three factors: mania, psychotic symptoms, and irritability. Baseline mania subscale scores were significantly higher for manic patients compared to all other diagnostic groups. Manic patients had significantly decreased posttreatment scores for all three subscales. ASRM mania subscale scores were significantly correlated with MRS total scores (r = .718) and CARS-M mania subscale scores (r = .766). Test-retest reliability for the ASRM was significant for all three subscales. Significant differences in severity levels were found for some symptoms between patient ratings on the ASRM and clinician ratings on the CARS-M. Mania subscale scores of greater than 5 on the ASRM resulted in values of 85.5% for sensitivity and 87.3% for specificity. Advantages of the ASRM over other self-rating mania scales are discussed.

MIXOR: a computer program for mixed-effects ordinal regression analysis

MIXOR provides maximum marginal likelihood estimates for mixed-effects ordinal probit, logistic, and complementary log-log regression models. These models can be used for analysis of dichotomous and ordinal outcomes from either a clustered or longitudinal design. For clustered data, the mixed-effects model assumes that data within clusters are dependent. The degree of dependency is jointly estimated with the usual model parameters, thus adjusting for dependence resulting from clustering of the data. Similarly, for longitudinal data, the mixed-effects approach can allow for individual-varying intercepts and slopes across time, and can estimate the degree to which these time-related effects vary in the population of individuals. MIXOR uses marginal maximum likelihood estimation, utilizing a Fisher-scoring solution. For the scoring solution, the Cholesky factor of the random-effects variance-covariance matrix is estimated, along with the effects of model covariates. Examples illustrating usage and features of MIXOR are provided.

Mobile health technology evaluation: the mHealth evidence workshop.

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, discuss future possibilities, and set a grand goal for the emerging field of mHealth research.

Full-information item bi-Factor analysis

A plausibles-factor solution for many types of psychological and educational tests is one that exhibits a general factor ands − 1 group or method related factors. The bi-factor solution results from the constraint that each item has a nonzero loading on the primary dimension and at most one of thes − 1 group factors. This paper derives a bi-factor item-response model for binary response data. In marginal maximum likelihood estimation of item parameters, the bi-factor restriction leads to a major simplification of likelihood equations and (a) permits analysis of models with large numbers of group factors; (b) permits conditional dependence within identified subsets of items; and (c) provides more parsimonious factor solutions than an unrestricted full-information item factor analysis in some cases.

Initial severity and differential treatment outcome in the National Institute of Mental Health Treatment of Depression Collaborative Research Program

Random regression models (RRMs) were used to investigate the role of initial severity in the outcome of 4 treatments (cognitive-behavior therapy [CBT], interpersonal psychotherapy [IPT], imipramine plus clinical management [IMI-CM], and placebo plus clinical management [PLA-CM]) for outpatients with major depressive disorder seen in the National Institute of Mental Health Treatment of Depression Collaborative Research Program. Initial severity of depression and impairment of functioning significantly predicted differential treatment effects. A larger number of differences than previously reported were found among the active treatments for the more severely ill patients; this was due, in large part, to the greater power of the present statistical analyses.

MIXREG: a computer program for mixed-effects regression analysis with autocorrelated errors

MIXREG is a program that provides estimates for a mixed-effects regression model (MRM) for normally-distributed response data including autocorrelated errors. This model can be used for analysis of unbalanced longitudinal data, where individuals may be measured at a different number of timepoints, or even at different timepoints. Autocorrelated errors of a general form or following an AR(1), MA(1), or ARMA(1,1) form are allowable. This model can also be used for analysis of clustered data, where the mixed-effects model assumes data within clusters are dependent. The degree of dependency is estimated jointly with estimates of the usual model parameters, thus adjusting for clustering. MIXREG uses maximum marginal likelihood estimation, utilizing both the EM algorithm and a Fisher-scoring solution. For the scoring solution, the covariance matrix of the random effects is expressed in its Gaussian decomposition, and the diagonal matrix reparameterized using the exponential transformation. Estimation of the individual random effects is accomplished using an empirical Bayes approach. Examples illustrating usage and features of MIXREG are provided.

Sample Size Estimation for Longitudinal Designs with Attrition: Comparing Time-Related Contrasts Between Two Groups

Formulas for estimating sample sizes are presented to provide specified levels of power for tests of significance from a longitudinal design allowing for subject attrition. These formulas are derived for a comparison of two groups in terms of single degree-of-freedom contrasts of population means across the study timepoints. Contrasts of this type can often capture the main and interaction effects in a two-group repeated measures design. For example, a two-group comparison of either an average across time or a specific trend across time (e.g., linear or quadratic) can be considered. Since longitudinal data with attrition are often analyzed using an unbalanced repeated measures model (with a structured variance-covariance matrix for the repeated measures) or a random-effects model for incomplete longitudinal data, the variance-covariance matrix of the repeated measures is allowed to assume a variety of forms. Tables are presented listing sample size determinations assuming compound symmetry, a first-order autoregressive structure, and a non-stationary random-effects structure. Examples are provided to illustrate use of the formulas, and a computer program implementing the procedure is available from the first author.

A Practical Guide to Calculating Cohen’s f2, a Measure of Local Effect Size, from PROC MIXED

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.