Randomized Controlled Trials With Time-to-Event Outcomes: How Much Does Prespecified Covariate Adjustment Increase Power? ADRIA ´ N V. HERNA ´ NDEZ, MD, MSC,PHD, MARINUS J.C. EIJKEMANS, MSC,PHD, AND EWOUT W. STEYERBERG, PHD PURPOSE: We evaluated the effects of various strategies of covariate adjustment on type I error, power, and potential reduction in sample size in randomized controlled trials (RCTs) with time-to-event outcomes. METHODS: We used Cox models in simulated data sets with different treatment effects (hazard ratios [HRs] Z 1, 1.4, and 1.7), covariate effects (HRs Z 1, 2, and 5), covariate prevalences (10% and 50%), and censoring levels (no, low, and high). Treatment and a single covariate were dichotomous. We exam- ined the sample size that gives the same power as an unadjusted analysis for three strategies: prespecified, significant predictive, and significant imbalance. RESULTS: Type I error generally was at the nominal level. The power to detect a true treatment effect was greater with adjusted than unadjusted analyses, especially with prespecified and significant-predictive strat- egies. Potential reductions in sample size with a covariate HR between 2 and 5 were between 15% and 44% (covariate prevalence 50%) and between 4% and 12% (covariate prevalence 10%). The significant- imbalance strategy yielded small reductions. The reduction was greater with stronger covariate effects, but was independent of treatment effect, sample size, and censoring level. CONCLUSIONS: Adjustment for one predictive baseline characteristic yields greater power to detect a true treatment effect than unadjusted analysis, without inflation of type I error and with potentially mod- erate reductions in sample size. Analysis of RCTs with time-to-event outcomes should adjust for predictive covariates. Ann Epidemiol 2006;16:41–48. Ó 2006 Elsevier Inc. All rights reserved. KEY WORDS: Statistical Data Interpretation, Computer Simulation, Covariate, Power, Proportional Hazards Models, Randomized Controlled Trials, Sample Size. INTRODUCTION Randomized controlled trials (RCTs) are important research tools to evaluate the usefulness of treatments and interventions (1). Heterogeneity is common among patients participating in RCTs with time-to-event outcomes (2). Prognosis commonly varies according to patient baseline characteristics, which are recorded routinely in RCTs. After proper randomization, imbalance in patient characteristics may arise by chance (3). Covariate adjustment for prognostic baseline characteris- tics usually is performed with Cox proportional hazards model in RCTs with time-to-event outcomes (3–10). Inclusion of a strongly predictive covariate in addition to the treatment variable in a Cox model provides three impor- tant benefits: correction for imbalance (3, 4, 6, 9), acquisi- tion of more individualized treatment effects (3, 7, 9), and increase in statistical power, i.e., the ability to detect a treat- ment effect when it really exists (2, 5–9). Moreover, omis- sion or misspecification of prognostic covariates in the analysis produces deviations from the proportional hazards assumptions (5, 10–15). The power of covariate-adjustment strategies in RCTs with time-to-event outcomes depends on various character- istics: strength of treatment effect, strength of covariate ef- fect, covariate prevalence, and censoring level (2, 5–7, 9, 11–13, 16). Effects of covariate-adjustment strategies on statistical power and type I error, using plausible clinical scenarios, have been insufficiently studied (17, 18). Some examples of covariate adjustment in RCTs with survival outcomes are available in the medical literature, especially in oncology and cardiology (19–22). We used various strategies for choice of covariates (pre- specified, predictive, and imbalance strategies) in simulated Cox proportional hazards models with one dichotomous co- variate, using different treatment effects, covariate effects, From the Center for Clinical Decision Sciences, Department of Public Health, Erasmus University Medical Center, Rotterdam, The Netherlands. Address correspondence to: Adria ´n V. Herna ´ndez, M.D., M.Sc., Center for Clinical Decision Sciences, Room Ee2010, Department of Public Health, Erasmus MC, PO Box 1738, 3000 DR Rotterdam, The Nether- lands. Tel.: C31-10-408-7721; fax: C31-10-408-9449. E-mail: a.her nandez@erasmusmc.nl A.V.H. was supported by the Netherlands Organization for Scientific Research (ZON/MW 908-02-117) and E.W.S. was supported by the Royal Netherlands Academy of Arts and Sciences. Received March 19, 2005; accepted September 19, 2005. Ó 2006 Elsevier Inc. All rights reserved. 1047-2797/06/$–see front matter 360 Park Avenue South, New York, NY 10010 doi:10.1016/j.annepidem.2005.09.007