Practical inference for a complier average causal effect in cluster randomised trials with a binary outcome

Background: Individual non-compliance with an intervention in cluster randomised trials can occur and estimating an intervention effect according to intention-to-treat ignores non-compliance and underestimates efficacy. The effect of the intervention among compliers (the complier average causal effect) provides an unbiased estimate of efficacy but inference can be complex in cluster randomised trials. 

Methods: We evaluated the performance of a pragmatic bootstrapping approach accounting for clustering to obtain a 95% confidence interval (CI) for a CACE for cluster randomised trials with monotonicity and one-sided non-compliance. We investigated a variety of scenarios for correlated cluster-level prevalence of a binary outcome and non-compliance (5%, 10%, 20%, 30%, 40%). Cluster randomised trials were simulated with the minimum number of clusters to provide at least 80% and at least 90% power, to detect an ITT odds ratio (OR) of 0.5 with 100 individuals per cluster. 

Results: Under all non-compliance scenarios (5%–40%), there was negligible bias for the CACE. In the worst-case of bias, a true OR of 0.18 was estimated as 0.15 for the rarest outcome (5%) and highest non-compliance (40%). There was no under-coverage of bootstrap CIs. CIs were the correct width for an outcome prevalence of 20%–40% but too wide for a less common outcome. Loss of power for a CACE bootstrap analysis versus ITT regression analysis increased as the prevalence of the outcome decreased across all non-compliance scenarios, particularly for an outcome prevalence of less than 20%. 

Conclusions: Our bootstrapping approach provides an accessible and computationally simple method to evaluate efficacy in support of ITT analyses in cluster randomised trials.