STATISTICS IN MEDICINE Statist. Med. 2007; 26:110–123 Published online 12 December 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/sim.2458 Bias reduction in eectiveness analyses of longitudinal ordinal doses with a mixed-eects propensity adjustment ¶ Andrew C. Leon 1; ∗; † , Donald Hedeker 2;‡ and Jedediah J. Teres 1;§ 1 Department of Psychiatry; Weill Medical College of Cornell University; New York; NY 10021; U.S.A. 2 Division of Epidemiology & Biostatistics; University of Illinois at Chicago; Chicago; IL; U.S.A. SUMMARY A mixed-eects propensity adjustment is described that can reduce bias in longitudinal studies involving non-equivalent comparison groups. There are two stages in this data analytic strategy. First, a model of propensity for treatment intensity examines variables that distinguish among subjects who receive various ordered doses of treatment across time using mixed-eects ordinal logistic regression. Second, the eectiveness model examines multiple times until recurrence to compare the ordered doses using a mixed-eects grouped-time survival model. Eectiveness analyses are initially stratied by propensity quintile. Then the quintile-specic results are pooled, assuming that there is not a propensity × treatment interaction. A Monte Carlo simulation study compares bias reduction in fully specied propensity model relative to misspecied models. In addition, type I error rate and statistical power are examined. The approach is illustrated by applying it to a longitudinal, observational study of maintenance treatment of major depression. Copyright ? 2005 John Wiley & Sons, Ltd. KEY WORDS: treatment eectiveness; propensity adjustment; longitudinal study; observational study; misspecication 1. INTRODUCTION An observational study of treatment eectiveness is typically challenged by non-equivalent comparison groups. That is, when subjects are not randomized to a treatment, there are se- lection biases that contribute to outcome. In clinical settings, for instance, patients who receive ∗ Correspondence to: Andrew C. Leon, Department of Psychiatry, Weill Medical College of Cornell University, Box 140, 525 East 68th Street, New York, NY 10021, U.S.A. † E-mail: acleon@med.cornell.edu ‡ E-mail: hedeker@uic.edu § E-mail: jjt2002@med.cornell.edu ¶ Presented, in part, at the Meeting of the Eastern North American Region (ENAR) of the International Biometric Society, 28–31 March 2004, Pittsburgh, PA, U.S.A. Contract=grant sponsor: NIH; contract=grant numbers: MH60447, MH68638 Received 23 December 2004 Copyright ? 2005 John Wiley & Sons, Ltd. Accepted 17 October 2005