Effect sizes for growth-modeling analysis for controlled clinical trials in the same metric as for classical analysis.

Abstract

The use of growth-modeling analysis (GMA)--including Hierarchical Linear Models, Latent Growth Models, and General Estimating Equations--to evaluate interventions in psychology, psychiatry, and prevention science has grown rapidly over the last decade. However, an effect size associated with the difference between the trajectories of the intervention and control groups that captures the treatment effect is rarely reported. This article first reviews two classes of formulas for effect sizes associated with classical repeated-measures designs that use the standard deviation of either change scores or raw scores for the denominator. It then broadens the scope to subsume GMA, and demonstrates that the independent groups, within-subjects, pretest-posttest control-group, and GMA designs all estimate the same effect size when the standard deviation of raw scores is uniformly used. Finally, it is shown that the correct effect size for treatment efficacy in GMA--the difference between the estimated means of the two groups at end of study (determined from the coefficient for the slope difference and length of study) divided by the baseline standard deviation--is not reported in clinical trials.Keywords effect size; growth modeling; hierarchical linear models; clinical trials Social scientists contribute to human well-being through the development of interventions to prevent and to treat a wide range of psychological, educational, and behavioral problems. Intervention research is a broad interdisciplinary field, with contributors from clinical psychology, psychiatry, applied developmental psychology, prevention science, and education. An important objective of these investigators is to conduct clinical trials to examine the efficacy of psychosocial and psychopharmacological treatments. Thus, controlled clinical trials are needed to answer two questions: Is a particular intervention effective? How powerful are its effects? The former is addressed in data analysis through tests of statistical significance, and the latter through calculation of effect sizes (McGrath & Meyer, 2006). Growth-Modeling Designs for Controlled Clinical TrialsTraditionally, data from controlled clinical trials have been examined with classical statistical techniques, such as analysis of variance (ANOVA), which use Ordinary Least Squares (OLS) and the General Linear Model (GLM). Over the last decade, however, growth-modeling analysis (GMA)--based on Generalized Least Squares (GLS) and the expectationmaximization (EM) algorithm (Dempster, Laird, & Rubin, 1977)--has emerged as a competing (c) 2009 APA, all rights reserved.Correspondence concerning this article should be addressed to Alan Feingold, Oregon Social Learning Center, 10 Shelton McMurphey Blvd., Eugene, OR, 97401−4928. E-mail: E-mail: alanf@oslc.org.. statistical framework for use in the evaluation of intervention efficacy. GMA compares temporal trajectories (growth curves) between the treatment and comparison groups, with the difference in the slopes for linear trend a common test of...

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