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Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule.

ABSTRACT: We introduce a non-myopic, covariate-adjusted response adaptive (CARA) allocation design for multi-armed clinical trials. The allocation scheme is a computationally tractable procedure based on the Gittins index solution to the classic multi-armed bandit problem and extends the procedure recently proposed in Villar et al. (2015). Our proposed CARA randomization procedure is defined by reformulating the bandit problem with covariates into a classic bandit problem in which there are multiple combination arms, considering every arm per each covariate category as a distinct treatment arm. We then apply a heuristically modified Gittins index rule to solve the problem and define allocation probabilities from the resulting solution. We report the efficiency, balance, and ethical performance of our approach compared to existing CARA methods using a recently published clinical trial as motivation. The net savings in terms of expected number of treatment failures is considerably larger and probably enough to make this design attractive for certain studies where known covariates are expected to be important, stratification is not desired, treatment failures have a high ethical cost, and the disease under study is rare. In a two-armed context, this patient benefit advantage comes at the expense of increased variability in the allocation proportions and a reduction in statistical power. However, in a multi-armed context, simple modifications of the proposed CARA rule can be incorporated so that an ethical advantage can be offered without sacrificing power in comparison with balanced designs.

SUBMITTER: Villar SS

PROVIDER: S-EPMC6055987 | biostudies-literature | 2018 Mar

REPOSITORIES: biostudies-literature

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Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule.

Villar Sofía S SS Rosenberger William F WF

Biometrics 20170706 1

We introduce a non-myopic, covariate-adjusted response adaptive (CARA) allocation design for multi-armed clinical trials. The allocation scheme is a computationally tractable procedure based on the Gittins index solution to the classic multi-armed bandit problem and extends the procedure recently proposed in Villar et al. (2015). Our proposed CARA randomization procedure is defined by reformulating the bandit problem with covariates into a classic bandit problem in which there are multiple combi ...[more]

PMID: 28682442

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Project description:This paper studies inference for the average treatment effect in randomized controlled trials with covariate-adaptive randomization. Here, by covariate-adaptive randomization, we mean randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve "balance" within each stratum. Our main requirement is that the randomization scheme assigns treatment status within each stratum so that the fraction of units being assigned to treatment within each stratum has a well behaved distribution centered around a proportion ? as the sample size tends to infinity. Such schemes include, for example, Efron's biased-coin design and stratified block randomization. When testing the null hypothesis that the average treatment effect equals a pre-specified value in such settings, we first show the usual two-sample t-test is conservative in the sense that it has limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level. We show, however, that a simple adjustment to the usual standard error of the two-sample t-test leads to a test that is exact in the sense that its limiting rejection probability under the null hypothesis equals the nominal level. Next, we consider the usual t-test (on the coefficient on treatment assignment) in a linear regression of outcomes on treatment assignment and indicators for each of the strata. We show that this test is exact for the important special case of randomization schemes with ?=12 , but is otherwise conservative. We again provide a simple adjustment to the standard errors that yields an exact test more generally. Finally, we study the behavior of a modified version of a permutation test, which we refer to as the covariate-adaptive permutation test, that only permutes treatment status for units within the same stratum. When applied to the usual two-sample t-statistic, we show that this test is exact for randomization schemes with ?=12 and that additionally achieve what we refer to as "strong balance." For randomization schemes with ??12 , this test may have limiting rejection probability under the null hypothesis strictly greater than the nominal level. When applied to a suitably adjusted version of the two-sample t-statistic, however, we show that this test is exact for all randomization schemes that achieve "strong balance," including those with ??12 . A simulation study confirms the practical relevance of our theoretical results. We conclude with recommendations for empirical practice and an empirical illustration·.

Project description:BackgroundIn cluster-randomized controlled trials (C-RCTs), covariate-constrained randomization (CCR) methods efficiently control imbalance in multiple baseline cluster-level variables, but the choice of imbalance metric to define the subset of "adequately balanced" possible allocation schemes for C-RCTs involving more than two arms and continuous variables is unclear. In an ongoing three-armed C-RCT, we chose the min(three Kruskal-Wallis [KW] test P values) > 0.30 as our metric. We use simulation studies to explore the performance of this and other metrics of baseline variable imbalance in CCR.MethodsWe simulated three continuous variables across three arms under varying allocation ratios and assumptions. We compared the performance of min(analysis of variance [ANOVA] P value) > 0.30, min(KW P value) > 0.30, multivariate analysis of variance (MANOVA) P value > 0.30, min(nine possible t test P values) > 0.30, and min(Wilcoxon rank-sum [WRS] P values) > 0.30.ResultsPairwise comparison metrics (t test and WRS) tended to be the most conservative, providing the smallest subset of allocation schemes (10%-13%) meeting criteria for acceptable balance. Sensitivity of the min(t test P values) > 0.30 for detecting non-trivial imbalance was 100% for both hypothetical and resampled simulation scenarios. The KW criterion maintained higher sensitivity than both the MANOVA and ANOVA criteria (89% to over 99%) but was not as sensitive as pairwise criteria.ConclusionsOur criterion, the KW P value > 0.30, to signify "acceptable" balance was not the most conservative, but it appropriately identified imbalance in the majority of simulations. Since all are related, CCR algorithms involving any of these imbalance metrics for continuous baseline variables will ensure robust simultaneous control over multiple continuous baseline variables, but we recommend care in determining the threshold of "acceptable" levels of (im)balance.Trial registrationThis trial is registered on ClinicalTrials.gov (initial post: December 1, 2016; identifier: NCT02979444 ).

Project description:Randomizing patients among treatments with equal probabilities in clinical trials is the established method to obtain unbiased comparisons. In recent years, motivated by ethical considerations, many authors have proposed outcome adaptive randomization, wherein the randomization probabilities are unbalanced, based on interim data, to favor treatment arms having more favorable outcomes. While there has been substantial controversy regarding the merits and flaws of adaptive versus equal randomization, there has not yet been a systematic simulation study in the multi-arm setting. A simulation study was conducted to evaluate four different Bayesian adaptive randomization methods and compare them to equal randomization in five-arm clinical trials. All adaptive randomization methods included an initial burn-in with equal randomization and some combination of other modifications to avoid extreme randomization probabilities. Trials either with or without a control arm were evaluated, using designs that may terminate arms early for futility and select one or more experimental treatments at the end. The designs were evaluated under a range of scenarios and sample sizes. For trials with a control arm and maximum same size 250 or 500, several commonly used adaptive randomization methods have very low probabilities of correctly selecting a truly superior treatment. Of those studied, the only adaptive randomization method with desirable properties has a burn-in with equal randomization and thereafter randomization probabilities restricted to the interval 0.10-0.90. Compared to equal randomization, this method has a favorable sample size imbalance but lower probability of correctly selecting a superior treatment. In multi-arm trials, compared to equal randomization, several commonly used adaptive randomization methods give much lower probabilities of selecting superior treatments. Aside from randomization method, conducting a multi-arm trial without a control arm may lead to very low probabilities of selecting any superior treatments if differences between the treatment success probabilities are small.

Dataset Information

Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule.

Publications

Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule.

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