Sample Size Determination for Studies with Repeated Continuous Outcomes
Authors: Bhaumik Dulal K. , Roy Anindya , Aryal Subhash , Hur Kwan , Duan Naihua , Normand Sharon-Lise T. , Brown C. Hendricks , Gibbons Robert D. 
Published: March 2009

<p>Longitudinal studies, in which the same individuals are repeatedly measured over time, have become routine in psychiatric research. In fact, it is difficult to imagine a randomized clinical trial of a new psychiatric intervention that is not longitudinal in nature. For example, all recent trials of antidepressant medications submitted in support of new drug applications (NDAs) to the U.S. Food and Drug Administration (FDA) involve longitudinal randomized clinical trials (RCTs). However, longitudinal designs are not limited to RCTs and are frequently used in observational studies to investigate associations between treatment and outcomes (eg, the relationship between antidepressants and suicide in U.S. Veterans). We show that the use of repeated measures lead to very important gains in statistical power relative to studies with a single measurement occasion or simple pre- compared with post-treatment comparison. Longitudinal designs are also common in cluster-randomized trials. For example, an intervention is randomly assigned to all children within a family or within a classroom and the members of the family or classroom are repeatedly evaluated over the course of the study. Although statistical methods for the analysis of longitudinal data with clustering of subjects are now routinely applied, the design of such studies often suffers from poorly specified and often inadequate sample sizes because of the application of methods for sample size determination based on a single outcome or for longitudinal studies in which the clustering is ignored. The determination of sample sizes when subjects are both repeatedly measured over time and clustered within research centers (eg, multi-center RCTs) can be erroneous unless both factors are taken into account.

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<h4>ABOUT THE AUTHORS</h4>
<p>Dulal K. Bhaumik, PhD; Anindya Roy, PhD; Subhash Aryal, PhD; Kwan Hur, PhD; and C. Hendricks Brown, PhD, are with the Center for Health Statistics, University of Illinois at Chicago. Robert D. Gibbons, PhD, is Professor of Biostatistics and Psychiatry, and Director of the Center for Health Statistics, University of Illinois at Chicago. Dr. Roy is with the Department of Mathematics and Statistics, University of Maryland, Baltimore County. Dr. Aryal is with the Department of Biostatistics, University of North Texas Health Science Center, Fort Worth. Dr. Hur is with the Cooperative Studies Program Coordinating Center, Hines VA Hospital, Hines, Illinois. Naihua Duan, PhD, is Director, Division of Biostatistics, N.Y. State Psychiatric Institute, New York. Sharon-Lise T. Normand, PhD, is with the Department of Health Care Policy, Harvard Medical School; Department of Biostatistics, Harvard School of Public Health, Boston. Dr. Brown is with the Prevention Science and Methodology Group, Departments of Epidemiology and Biostatistics, College of Public Health, University of South Florida, Tampa.</p>
<p>Address correspondence to: Dulal Bhaumik, PhD, Center for Health Statistics, University of Illinois at Chicago, 1601 W. Taylor, Chicago, IL 60612; fax: 312-996-2113; email: <a href="mailto:dbhaumik@psych.uic.edu">dbhaumik@psych.uic.edu</a>.</p>
<p>Dr. Bhaumik, Dr. Roy, Dr. Aryal, Dr. Hur, Dr. Duan, Dr. Normand, Dr. Brown, and Dr. Gibbons have disclosed no relevant financial relationships.</p>
<p>This work was supported by a grant from the National Institute of Mental Health R01-MH069353.</p>

<h4>EDUCATIONAL OBJECTIVES</h4>
<ol><li>Describe design of clustered and/or longitudinal studies.
</li>
<li>Describe the tradeoffs between person-level and cluster-level randomization.
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<li>Define general guidelines for sample sizes for multi-center randomized controlled trials (RCT).
</li></ol>