Two-stage Adaptive Design Cluster Randomised Trials

Abstract

Adaptive sample size re-estimation, early stopping, and trial re-design at interim analyses can reduce expected sample sizes in randomised trials. Cluster randomised trials, in which groups of participants are randomly allocated to treatment status, may particularly benefit as they can be costly and their required sample sizes depend on one or more auxiliary parameters governing correlations within and between clusters, which are often estimated with high uncertainty. We adapt a combination test approach to the cluster trial setting allowing for early stopping for futility or efficacy and accounting for correlations between trial stages and other nuisance parameters. We consider design decisions for multi-dimensional sample sizes involving clusters, participants, and time and allowing for modifications to intervention roll-out patterns. We use a Pareto optimality approach to balance objectives relating to different components of the sample size and costs. We also examine the interim estimation of auxiliary parameters and trial re-design for efficiency. We illustrate the methods including examples of stepped-wedge trial re-design and a re-analysis of the large cluster randomised trial E-MOTIVE.

Figures (6)

• Figure 1: Comparison of stage 1 alternative designs for the adaptive parallel trial example, grey crosses indicate designs with insufficient total power. Left column -- expected total number of participants versus stage 1 power; middle column -- maximum number of participants versus stage 1 power; right column -- maximum versus expected costs with Pareto optimal design highlighted; top row -- cost penalised designs; bottom row -- budget constrained designs.
• Figure 2: Decision rules for stage 2 number of new clusters (K2) and stage 2 cluster period size (M2) for the adaptive parallel trial example for a stage 1 test statistic $z_1$, with distribution of stage one test statistic under $H_1$
• Figure 3: Decision rules for stage 2 of the stepped-wedge design for number of time periods (T2), degree of staggering (r) and cluster period size (M2) for different interim estimates of the ICC
• Figure 4: Complete trial designs for the adaptive staggered design with different interim estimates of the ICC for an observed first stage test statistic of $z_1 = -1$.
• Figure 5: Comparison of the expected and maximum total number of patients, and of expected and maximum costs of the range of stage 1 designs considered for E-MOTIVE. k1 is stage 1 clusters per arm.