Randomized Controlled Trials With Time-to-Event Outcomes: How Much Does Prespecified Covariate Adjustment Increase Power?
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 characteristics usually is performed with Cox proportional hazards model in RCTs with time-to-event outcomes 3, 4, 5, 6, 7, 8, 9, 10. Inclusion of a strongly predictive covariate in addition to the treatment variable in a Cox model provides three important benefits: correction for imbalance 3, 4, 6, 9, acquisition of more individualized treatment effects 3, 7, 9, and increase in statistical power, i.e., the ability to detect a treatment effect when it really exists 2, 5, 6, 7, 8, 9. Moreover, omission or misspecification of prognostic covariates in the analysis produces deviations from the proportional hazards assumptions 5, 10, 11, 12, 13, 14, 15.
The power of covariate-adjustment strategies in RCTs with time-to-event outcomes depends on various characteristics: strength of treatment effect, strength of covariate effect, covariate prevalence, and censoring level 2, 5, 6, 7, 9, 11, 12, 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, 20, 21, 22.
We used various strategies for choice of covariates (prespecified, predictive, and imbalance strategies) in simulated Cox proportional hazards models with one dichotomous covariate, using different treatment effects, covariate effects, covariate prevalences, and censoring levels. We aim to identify the pros and cons of each covariate adjustment strategy, with a focus on the quantification of changes in statistical power. We expressed the gain in statistical power in the decrease in sample size that gives the same power as an unadjusted analysis.
Section snippets
Models and Adjustment Strategies
Cox proportional hazards models were used to analyze the effects of treatment on a time-to-event outcome (e.g., time to death). For simplicity, a single dichotomous baseline characteristic was considered as covariate to adjust the treatment effect. We expected that our results were generalizable to more complex cases (i.e., more covariates included), as shown by others 2, 5, 6, 7, 9, 11, 13, 16. Cox model coefficients and SEs were estimated by using standard maximum-likelihood procedures.
We
Covariate Prevalence 50% and No Censoring
When there was no treatment effect, type I error was similar in all adjustment strategies and with all covariate effects (Table 1). Type I error mainly was slightly less than 5%, especially when the covariate effect was very strong (3.8% for imbalance-adjusted strategy at covariate HR = 10). This conservative estimate implies that fewer false-positive effects were identified. When there was no covariate effect, covariate adjustment strategies on average did not change treatment-effect
Discussion
Covariate adjustment yields greater statistical power than an unadjusted analysis of an RCT with time-to-event outcomes. In our study, the gain in power was translated into potential reductions in sample size, without inflation of type I error. We used several approaches of covariate adjustment in simple simulated Cox models with different treatment effects, covariate effects, covariate prevalences, and censoring levels. We found that prespecified and significant predictor-adjustment
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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.