Multiphase mixed-effects models for repeated measures data.

Behavior that develops in phases may exhibit distinctively different rates of change in one time period than in others. In this article, a mixed-effects model for a response that displays identifiable regimes is reviewed. An interesting component of the model is the change point. In substantive terms, the change point is the time when development switches from one phase to another. In a mixed-effects model, the change point can be a random coefficient. This possibility allows individuals to make the transition from one phase to another at different ages or after different lengths of time in treatment. Two examples are reviewed in detail, both of which can be estimated with software that is widely available. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Normative data on cognitive measures of depression.

The assessment of cognition and cognitive change is important for case conceptualization, monitoring the efficacy of specific interventions, and evaluating treatment outcome in cognitive-behavioral therapy. Unfortunately, a paucity of normative data exists on cognitive measures used for psychotherapy outcome research in depression, and little information is available to guide a practitioner's understanding of the magnitude and clinical significance of a patient's cognitive change. This article presents normative data on 6 self-report instruments that assess negative and positive automatic thoughts, hopelessness, cognitive biases and errors, and dysfunctional attitudes. Normative data were derived from studies published from the date of inception of a given cognitive index to the year 2000. Recommendations for the use of these normative data are provided. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimation and model comparisons for repeated measures data.

Describes and compares alternative approaches to the use of MANOVA for repeated-measures data. It is concluded that 2 approaches that have been advocated in the literature should not be used. Suggestions for obtaining appropriate analyses from the computer program MULTIVARIANCE are included in the 1st of 2 appendices. (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Group sequential monitoring of distribution-free analyses of repeated measures

In many clinical trials the principal analysis consists of a 1 degree of freedom test based on an aggregate summary statistic for a set of repeated measures. Various methods have been proposed for the marginal analysis of such repeated measures that entail estimates of a measure of treatment group difference (the treatment effect) at each of K repeated measures and a consistent estimate of the covariance matrix, where asymptotically these estimates are normally distributed. One can then obtain an overall large sample 1-d.f. test of group differences, such as by taking the average of these K estimates. These methods include the Wei-Lachin family of multivariate rank tests and a corresponding multivariate analysis using the Mann-Whitney difference estimator as a measure of treatment group differences. Other methods, such as O'Brien's non-parametric test, are based on a single summary score for each patient, such as the within-patient mean value. These, and other such methods, allow for some observations to be missing at random. Herein I employ sequential data augmentation to conduct group sequential analyses using a 1 degree of freedom test from a multivariate Mann-Whitney analysis and for the O'Brien rank test. Su and Lachin used this method to perform group sequential analyses of a vector of Hodges-Lehmann estimators. By augmentating the data from the sequential looks in a single analysis, one obtains an estimate of the covariance of the estimates at each look, from which one obtains an estimate of the correlations among the sequential 1-d.f. test statistics. I describe a simple secant algorithm to determine the group sequential boundaries based on recursive integration of the standard multivariate normal distribution with the estimated correlation matrix. Although the boundary obtains readily using the method of Slud and Wei, the more flexible method of Lan and DeMets may be preferred. The true information fraction at each look, needed to apply the spending function method of Lan and DeMets, however, is unknown. Thus, I also describe the use of a surrogate measure of information.     

Statistical analysis of repeated measures data using SAS procedures

Mixed linear models were developed by animal breeders to evaluate genetic potential of bulls. Application of mixed models has recently spread to all areas of research, spurred by availability of advanced computer software. Previously, mixed model analyses were implemented by adapting fixed-effect methods to models with random effects. This imposed limitations on applicability because the covariance structure was not modeled. This is the case with PROC GLM in the SAS System. Recent versions of the SAS System include PROC MIXED. This procedure implements random effects in the statistical model and permits modeling the covariance structure of the data. Thereby, PROC MIXED can compute efficient estimates of fixed effects and valid standard errors of the estimates. Modeling the covariance structure is especially important for analysis of repeated measures data because measurements taken close in time are potentially more highly correlated than those taken far apart in time.     

Size and power of two-sample tests of repeated measures data

One method of using repeated measures data to compare treatment groups in a clinical trial is to summarize each subject's outcomes with a single summary statistic, and then perform a distribution-free comparison based on the resulting statistics. We examine extensions of this approach and conditions under which they retain proper size in the presence of missing data. The asymptotic relative efficiencies of several summary statistic tests are calculated to show which perform best in a variety of situations. The techniques are illustrated using data from an AIDS clinical trial.     

Coding subjects in repeated measures designs.

Presents a method for coding Ss in repeated measures designs when the data are subjected to a multiple regression analysis. Instead of having to use a multitude of vectors to code Ss, a single vector is used. The method is illustrated for randomized blocks and split plot designs. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Validity conditions in repeated measures designs.

This article has 2 objectives. The 1st is to present necessary and sufficient conditions for the validity of traditional within-S F tests in repeated measures designs. It is shown that the Mauchly sphericity criterion (W) and possibly the Box test for the equality of covariance matrices are appropriate to judge the validity of these conditions. Valid applications of both tests are conducted on sets of orthogonal normalized variables that are associated with each cluster of within-S mean square ratios. The 2nd objective of the article is to present empirical results on the appropriateness of using the W criterion when the variates are not normally distributed. For light-tailed distributions the W criterion was shown to be moderately conservative, whereas for heavy-tailed distributions, empirical Type I error rates exceeded nominal alpha. Since most social science applications typically involve light-tailed rather than heavy-tailed distributions, the W criterion should provide useful results in most cases. (29 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Comparative data on child and adolescent cognitive measures associated with depression.

As a way to better understand the effects of treatment for depression, comparative data on measures of cognition have been compiled previously for adults. Such data should be able to aid the evaluation of cognition and cognitive change, and may provide valuable information for clinicians and researchers alike. In this article, analogous comparative data on cognitive measures associated with depression in children and adolescents are presented. The reviewed instruments assess cognitive errors, attributional style, dysfunctional attitudes, hopelessness, negative self-statements, and Beck's negative cognitive triad. As with adults, these data may have implications for enhancing understanding of empirically supported treatments for children and adolescents, may be useful in vulnerability research, and may be useful to clinicians seeking to develop treatment strategies and to gauge treatment effectiveness. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing multiple outcomes in repeated measures designs.

This study investigates procedures for controlling the familywise error rate (FWR) when testing hypotheses about multiple, correlated outcome variables in repeated measures (RM) designs. A content analysis of RM research articles published in 4 psychology journals revealed that 3 quarters of studies tested hypotheses about 2 or more outcome variables. Several procedures originally proposed for testing multiple outcomes in 2-group designs are extended to 2-group RM designs. The investigated procedures include 2 modified Bonferroni procedures that adjust the level of significance, α, for the effective number of outcomes and a permutation step-down (PSD) procedure. The FWR, any-variable power, and all-variable power are investigated in a Monte Carlo study. One modified Bonferroni procedure frequently resulted in inflated FWRs, whereas the PSD procedure controlled the FWR. The PSD procedure could be substantially more powerful than the conventional Bonferroni procedure, which does not account for dependencies among the outcome variables. However, the difference in power between the PSD procedure, which does account for these dependencies, and Hochberg's step-up procedure, which does not, were negligible. A numeric example illustrates implementation of these multiple-testing procedures. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Analysis of dichotomous variables in repeated measures experiments.

Provides an alternative to the method of L. A. Marascuilo and R. Serlin (1977) for the analysis of repeated measures experiments with dichotomous outcomes. Weighted linear regression methods are used to provide tests analogous to ANOVA. Tests of main effects and interactions are presented. (14 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Interactions for dichotomous variables in repeated measures designs.

Describes a method for analyzing interactions in a repeated measures design for a dichotomous dependent variable. The method is based upon the Cochran Q model but is restricted to the case in which a planned analysis is adopted. The model is illustrated for ordered and unordered independent variables. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Correlation analysis of twin data with repeated measures based on generalized estimating equations

Repeated measures allow additional tests of common assumptions in twin correlation analysis. Analysis of log serum triglyceride level in NHLBI male twins using generalized estimating equations disclosed that the mean and variance shifted across exams, presumably because of changes in laboratory practice.     

Mixed-model pairwise multiple comparisons of repeated measures means.

One approach to the analysis of repeated measures data allows researchers to model the covariance structure of the data rather than presume a certain structure, as is the case with conventional univariate and multivariate test statistics. This mixed-model approach was evaluated for testing all possible pairwise differences among repeated measures marginal means in a Between-Subjects?×?Within-Subjects design. Specifically, the authors investigated Type I error and power rates for a number of simultaneous and stepwise multiple comparison procedures using SAS (1999) PROC MIXED in unbalanced designs when normality and covariance homogeneity assumptions did not hold. J. P. Shaffer's (1986) sequentially rejective step-down and Y. Hochberg's (1988) sequentially acceptive step-up Bonferroni procedures, based on an unstructured covariance structure, had superior Type I error control and power to detect true pairwise differences across the investigated conditions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Regression analysis of proportional cell data.

Previous researchers contend that a general regression method (Method 1) for estimating factor effects by adjusting for all other factors and interactions in the model does not give results consistent with standard methods when one has a proportional cell size data set. The present author argues that the inconsistency is due simply to a disregard of the standard analysis of variance restrictions usually employed within a factor, and hence to an improper coding of the predictor vectors. Taking standard procedures into account, Method 1 does yield results consistent with those obtained by other methods. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the recording of sample times and parameter estimation from repeated measures pharmacokinetic data

A pharmacokinetic screen has been advocated for the characterization of the population pharmacokinetics of drugs during Phase 3 clinical trials. A common perception encountered in the collection of such data is that the accuracy of sampling times relative to dose is inadequate. A prospective simulation study was carried out to evaluate the effect of error in the recording of sampling times on the accuracy and precision of population parameter estimates from repeated measures pharmacokinetic data. A two-compartment model with intravenous bolus input(s) (single and multiple doses) was assumed. Random and systematic error in sampling times ranging from 5-50% using profile (block) randomized design were introduced. Sampling times were simulated in EXCEL while concentration data simulation and analysis were done in NONMEM. The effect of error in sampling times was studied at levels of variability ranging from 15-45% for a drug assumed to be dosed at its elimination half-life. One hundred replicate data sets of 100 subjects each were simulated for each case. Although estimates of clearance (CL) and variability in clearance were robust for most of the sampling time errors, there was an increase in bias and imprecision in overall parameter estimation as intersubject variability was increased. If there is interest in parameters other than CL, then the design of prospective population studies should include procedures for minimizing the error in the recording of sample times relative to dosing history.     

Confirmatory hierarchical factor analyses of psychological distress measures.

Previous factor-analytic research examining the dimensionality of psychological distress and depression has generally minimized the importance of the interrelationships existing among primary components of depression and distress. The present authors developed restricted hierarchical factor-analysis models that simultaneously test for the presence and necessity of both primary and second-order factors for the Beck Depression Inventory (BDI) and the Psychiatric Epidemiology Research Interview (PERI). Similarities in the latent structure of these 2 instruments are examined, and implications for a taxonomy of psychological distress and depression are discussed. Results show that the primary factor structure of both the PERI and BDI were similar in terms of yielding factors that corresponded to hypothetical constructs thought to exist in a theoretical taxonomy of depression. Both the BDI and PERI yielded primary constructs that could be thought of as reflecting physiological, cognitive, and motivational manifestations of depressive symptomatology. From examining the second-order loadings, it appears that each of these primary factors contributes equally in defining the second-order factor of psychological distress. (46 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Tolman's cognitive analyses: Predecessors of current approaches in psychology.

Comments on an article by E. C. Tolman et al (see PA, Vols 20:2297 and 12366) using rats in mazes to examine the cognitive mechanisms used to represent space and direct movement through it. The popularity of maze procedures to assess memory continues to illustrate the usefulness of these techniques. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Demonstration of presbycusis across repeated measures in a nonhuman primate species.

Over a period of 3 yrs, the authors repeatedly examined the progress of age-related hearing loss in 7 rhesus monkeys; 3 were 31 yrs old, 2 were 24 yrs old, and 2 were 9 yrs old. Pure-tone audiograms for 7 frequencies (.125, .500, 2.000, 4.000, 16.000, 22.667, and 32.000 kHz) were obtained by the psychophysical tracking method. Analysis indicated the presence of presbycusis in the older Ss. Ss demonstrating presbycusis showed a progressive decrement in the ability to detect higher frequencies and an overall hearing loss at all frequencies. (13 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A note on repeated measures in the study of short-term memory.

Keppel's (1965) objection to averaging over repeated measures is discussed. Several possibilities for minimizing proactive interference are suggested, including increasing time between tests. Consideration is given to acceptance of a constant amount of proactive interference over conditions in which other variables are studied. The advantages of using repeated measures in regard to efficiency as well as interpretation are noted. (PsycINFO Database Record (c) 2010 APA, all rights reserved)