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 2 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, the article shows that the correct effect size for treatment efficacy in GMA--the difference between the estimated means of the 2 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.