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Background  The cohort multiple randomised controlled trial (cmRCT) design provides an opportunity to incorporate the benefits of randomisation within clinical practice; thus reducing costs, integrating electronic healthcare records, and improving external validity. This study aims to address a key concern of the cmRCT design: refusal to treatment is only present in the intervention arm, and this may lead to bias and reduce statistical power.    Methods  We used simulation studies to assess the effect of this refusal, both random and related to event risk, on bias of the effect estimator and statistical power. A series of simulations were undertaken that represent a cmRCT trial with time-to-event endpoint. Intention-to-treat (ITT), per protocol (PP), and instrumental variable (IV) analysis methods, two stage predictor substitution and two stage residual inclusion, were compared for various refusal scenarios.    Results  We found the IV methods provide a less biased estimator for the causal effect when refusal is present in the intervention arm, with the two stage residual inclusion method performing best with regards to minimum bias and sufficient power. We demonstrate that sample sizes should be adapted based on expected and actual refusal rates in order to be sufficiently powered for IV analysis.    Conclusion  We recommend running both an IV and ITT analyses in an individually randomised cmRCT as it is expected that the effect size of interest, or the effect we would observe in clinical practice, would lie somewhere between that estimated with ITT and IV analyses. The optimum (in terms of bias and power) instrumental variable method was the two stage residual inclusion method. We recommend using adaptive power calculations, updating them as refusal rates are collected in the trial recruitment phase in order to be sufficiently powered for IV analysis.

Evaluation of biases present in the cohort multiple randomised controlled trial design: a simulation study