Estimating treatment effects in randomised controlled trials with non-compliance: a simulation study

OBJECTIVE Randomised controlled trials (RCTs) are often considered as the gold standard for assessing new health interventions. Patients are randomly assigned to receive an intervention or control. The effect of the intervention can be estimated by comparing outcomes between groups, whose prognostic factors are expected to balance by randomisation. However, patients' non-compliance with their assigned treatment will undermine randomisation and potentially bias the estimate of treatment effect. Through simulation, we aim to compare common approaches in analysing non-compliant data under different non-compliant scenarios. SETTINGS Based on a real study, we simulated hypothetical trials by varying three non-compliant factors: the type, randomness and degree of non-compliance. We compared the intention-to-treat (ITT), as-treated (AT), per-protocol (PP), instrumental variable (IV) and complier average casual effect (CACE) analyses to estimate large (50% improvement over the control), moderate (25% improvement) and null (same as the control) treatment effects. Different approaches were compared by the bias of estimate, mean square error (MSE) and 95% coverage of the true value. RESULTS For a large or moderate treatment effect, the ITT estimate was considerably biased in all scenarios. The AT, PP, IV and CACE estimates were unbiased when non-compliant behaviours were random. The IV estimate was unbiased when non-compliant behaviours were symmetrically dependent on patients' conditions. The PP estimate was mostly unbiased when patients in the control group did not have access to the intervention. When the intervention was not different from the control, the ITT was less biased than the other approaches. Similar results were found when comparing the MSE and 95% coverage. CONCLUSIONS The standard ITT analysis under non-compliance is biased when the intervention has a moderate or large effect. Alternative analyses can provide unbiased or less biased estimates. Based on the results, we make some suggestions on choosing optimal approaches for analysing specific non-compliant scenarios.