Estimating the Complier Average Causal Effect in Randomised Controlled Trials with Non-Compliance: A Comparative Simulation Study of the Instrumental Variables and Per-Protocol Analyses

Objective: Randomised controlled trials (RCTs) are widely considered as gold standard for assessing the effectiveness of new health interventions. When treatment non-compliance is present in RCTs, the treatment effect in the subgroup of participants who complied with their original treatment allocation, the Complier Average Causal Effect (CACE), is a more representative measure of treatment efficacy than the average treatment effect. Through simulation we aim to compare the two most common methods employed in practice to estimate CACE. Methods: We considered the Per-Protocol and Instrumental Variables (IV) analyses. Based on a real study, we simulated hypothetical trials by varying factors related to non-compliance and compared the two methods by the bias of the estimate, mean squared error and $95\%$ coverage of the true value. Results: For binary compliance, the IV estimator was always unbiased for CACE, while the Per-Protocol estimator was unbiased for random non-compliance or when participants with good or bad conditions always received the treatment. For partial compliance, the IV estimator was less biased when participants with better conditions always received the treatment and those with worse conditions always received the control or vice versa, while the Per-Protocol estimator was less biased when participants with good or bad conditions never received the treatment.