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Optimal designs in three-level cluster randomized trials with a binary outcome.

ABSTRACT: Cluster randomized trials (CRTs) were originally proposed for use when randomization at the subject level is practically infeasible or may lead to a severe estimation bias of the treatment effect. However, recruiting an additional cluster costs more than enrolling an additional subject in an individually randomized trial. Under budget constraints, researchers have proposed the optimal sample sizes in two-level CRTs. CRTs may have a three-level structure, in which two levels of clustering should be considered. In this paper, we propose optimal designs in three-level CRTs with a binary outcome, assuming a nested exchangeable correlation structure in generalized estimating equation models. We provide the variance of estimators of three commonly used measures: risk difference, risk ratio, and odds ratio. For a given sampling budget, we discuss how many clusters and how many subjects per cluster are necessary to minimize the variance of each measure estimator. For known association parameters, the locally optimal design is proposed. When association parameters are unknown but within predetermined ranges, the MaxiMin design is proposed to maximize the minimum of relative efficiency over the possible ranges, that is, to minimize the risk of the worst scenario.

SUBMITTER: Liu J

PROVIDER: S-EPMC6905388 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature

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Optimal designs in three-level cluster randomized trials with a binary outcome.

Liu Jingxia J Liu Lei L Colditz Graham A GA

Statistics in medicine 20190604 20

Cluster randomized trials (CRTs) were originally proposed for use when randomization at the subject level is practically infeasible or may lead to a severe estimation bias of the treatment effect. However, recruiting an additional cluster costs more than enrolling an additional subject in an individually randomized trial. Under budget constraints, researchers have proposed the optimal sample sizes in two-level CRTs. CRTs may have a three-level structure, in which two levels of clustering should ...[more]

PMID: 31162709

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Project description:IntroductionEfforts to develop biomarker-targeted anti-cancer therapies have progressed rapidly in recent years. With efforts to expedite regulatory reviews of promising therapies, several targeted cancer therapies have been granted accelerated approval on the basis of evidence acquired in single-arm phase II clinical trials. And yet, in the absence of randomization, patient prognosis for progression-free survival and overall survival may not have been studied under standard of care chemotherapies for emerging biomarker subpopulations prior to the submission of an accelerated approval application. Historical control rates used to design and evaluate emerging targeted therapies often arise as population averages, lacking specificity to the targeted genetic or immunophenotypic profile. Thus, historical trial results are inherently limited for inferring the potential "comparative efficacy" of novel targeted therapies. Consequently, randomization may be unavoidable in this setting. Innovations in design methodology are needed, however, to enable efficient implementation of randomized trials for agents that target biomarker subpopulations.MethodsThis article proposes three randomized designs for early phase biomarker-guided oncology clinical trials. Each design utilizes the optimal efficiency predictive probability method to monitor multiple biomarker subpopulations for futility. Only designs with type I error between 0.05 and 0.1 and power of at least 0.8 were considered when selecting an optimal efficiency design from among the candidate designs formed by different combinations of posterior and predictive threshold. A simulation study motivated by the results reported in a recent clinical trial studying atezolizumab treatment in patients with locally advanced or metastatic urothelial carcinoma is used to evaluate the operating characteristics of the various designs.ResultsOut of a maximum of 300 total patients, we find that the enrichment design has an average total sample size under the null of 101.0 and a total average sample size under the alternative of 218.0, as compared to 144.8 and 213.8 under the null and alternative, respectively, for the stratified control arm design. The pooled control arm design enrolled a total of 113.2 patients under the null and 159.6 under the alternative, out of a maximum of 200. These average sample sizes that are 23-48% smaller under the alternative and 47-64% smaller under the null, as compared to the realized sample size of 310 patients in the phase II study of atezolizumab.DiscussionOur findings suggest that potentially smaller phase II trials to those used in practice can be designed using randomization and futility stopping to efficiently obtain more information about both the treatment and control groups prior to phase III study.

Project description:Background Cluster randomised trials (CRTs) are often designed with a small number of clusters, but it is not clear which analysis methods are optimal when the outcome is binary. This simulation study aimed to determine (i) whether cluster-level analysis (CL), generalised linear mixed models (GLMM), and generalised estimating equations with sandwich variance (GEE) approaches maintain acceptable type-one error including the impact of non-normality of cluster effects and low prevalence, and if so (ii) which methods have the greatest power. We simulated CRTs with 8–30 clusters, altering the cluster-size, outcome prevalence, intracluster correlation coefficient, and cluster effect distribution. We analysed each dataset with weighted and unweighted CL; GLMM with adaptive quadrature and restricted pseudolikelihood; GEE with Kauermann-and-Carroll and Fay-and-Graubard sandwich variance using independent and exchangeable working correlation matrices. P-values were from a t-distribution with degrees of freedom (DoF) as clusters minus cluster-level parameters; GLMM pseudolikelihood also used Satterthwaite and Kenward-Roger DoF. Results Unweighted CL, GLMM pseudolikelihood, and Fay-and-Graubard GEE with independent or exchangeable working correlation matrix controlled type-one error in > 97% scenarios with clusters minus parameters DoF. Cluster-effect distribution and prevalence of outcome did not usually affect analysis method performance. GEE had the least power. With 20–30 clusters, GLMM had greater power than CL with varying cluster-size but similar power otherwise; with fewer clusters, GLMM had lower power with common cluster-size, similar power with medium variation, and greater power with large variation in cluster-size. Conclusion We recommend that CRTs with ≤ 30 clusters and a binary outcome use an unweighted CL or restricted pseudolikelihood GLMM both with DoF clusters minus cluster-level parameters. Supplementary Information The online version contains supplementary material available at 10.1186/s12874-022-01699-2.

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Optimal designs in three-level cluster randomized trials with a binary outcome.

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Optimal designs in three-level cluster randomized trials with a binary outcome.

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