Asymptotic properties of covariate-adaptive randomization

Hu, Yanqing; Hu, Feifang

doi:10.1214/12-aos983

Cited by 93 publications

(160 citation statements)

References 42 publications

(68 reference statements)

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“…Stratified permuted block (SPB) randomization and Pocock and Simon's design (1975) are the most popular CAR procedures. Other CAR designs have been developed by Taves (1974), Wei (1978), Nordle and Brantmark (1977), Signorini et al (1993), Heritier et al (2005), and Hu and Hu (2012). Clinical trials that use these designs include Iacono et al (2006), Jakob et al (2012), Anderson et al (2000), Gridelli et al (2003), Krueger et al (2007), Molander et al (2007, and Ohtori et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Sequential Monitoring of Covariate-Adaptive Randomized Clinical Trials

Hu¹,

Hu²

2018

STAT SINICA

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The sequential monitoring of covariate-adaptive randomized clinical trials is standard in modern clinical studies. However, the validity of this sequential procedure is not well studied in the literature. Clinical trialists therefore implement the procedure and perform data analysis based on the theory of the sequential monitoring of fixed designs, and many clinical trials are open to question. In this paper, we study the theoretical properties of the sequential procedure and propose some important adjustments to classical statistical inference. Under different scenarios, we derive the asymptotic joint distribution of the sequential test statistics. Further, we estimate the decreased variability of the estimated treatment effect due to covariate-adaptive randomization, so that the sequential test statistics can be adjusted to be an asymptotic Brownian motion and the type I error rate can be controlled in real trials. Numerical results from simulation and the redesign of a clinical trial support our theoretical findings, showing that our procedure can control the type I error rate well, and also demonstrating the advantages of our method in terms of power and early stopping. Both theoretical and numerical results provide important guidance for future practical clinical trials using covariate-adaptive randomization procedures.

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Section: Introductionmentioning

confidence: 99%

Sequential Monitoring of Covariate-Adaptive Randomized Clinical Trials

Hu¹,

Hu²

2018

STAT SINICA

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“…For example, this might be measured according to the difference in the means of Z i in the treatment and control groups. Our usage follows the usage in Efron (1971) or Hu and Hu (2012), where "balance" refers to the extent to which the of fraction of treated units within a strata differs from the target proportion π.…”

Section: Setup and Notationmentioning

confidence: 99%

“…Another treatment assignment mechanism that has been used in clinical trials is minimization methods. These methods were originally proposed by Pocock and Simon (1975) and more recently extended and further studied by Hu and Hu (2012). In Hu and Hu (2012), treatment assignment is determined recursively for 1 ≤ k ≤ n as follows:…”

Section: Examplesmentioning

confidence: 99%

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Inference under covariate-adaptive randomization

Bugni

Canay

Shaikh

2017

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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 π 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 π = 1 2 , but is otherwise conservative. We again provide a simple adjustment to the standard error 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 π = , 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 π = 1 2. A simulation study confirms the practical relevance of our theoretical results. We conclude with recommendations for empirical practice and an empirical illustration.

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“…We consider a treatment allocation problem with K treatments for which the probabilities of success depend on side information given by covariates; see, for example, [22,24,39]. The response Y t = Y t (X) of a subject with covariates X to treatment t satisfies (1.1)…”

Section: Introductionmentioning

confidence: 99%

Information-regret compromise in covariate-adaptive treatment allocation

Metelkina¹,

Pronzato²

2017

Ann. Statist.

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Covariate-adaptive treatment allocation is considered in the situation when a compromise must be made between information (about the dependency of the probability of success of each treatment upon influential covariates) and cost (in terms of number of subjects receiving the poorest treatment). Information is measured through a design criterion for parameter estimation, the cost is additive and is related to the success probabilities. Within the framework of approximate design theory, the determination of optimal allocations forms a compound design problem. We show that when the covariates are i.i.d. with a probability measure μ, its solution possesses some similarities with the construction of optimal design measures bounded by μ. We characterize optimal designs through an equivalence theorem and construct a covariate-adaptive sequential allocation strategy that converges to the optimum. Our new optimal designs can be used as benchmarks for other, more usual, allocation methods. A response-adaptive implementation is possible for practical applications with unknown model parameters. Several illustrative examples are provided.

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Asymptotic properties of covariate-adaptive randomization

Cited by 93 publications

References 42 publications

Sequential Monitoring of Covariate-Adaptive Randomized Clinical Trials

Sequential Monitoring of Covariate-Adaptive Randomized Clinical Trials

Inference under covariate-adaptive randomization

Information-regret compromise in covariate-adaptive treatment allocation

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