<p>Non-compliance in randomised controlled trials poses a significant challenge to accurately estimate treatment effects. Traditional methods of analysis, such as intention-to-treat (ITT) and per-protocol (PP) analyses, are known to have limitations. The ITT analysis tends to underestimate the effect of treatment, while PP is prone to selection bias. The Complier Average Causal Effect (CACE) framework has been proposed to address the issue of non-compliance. In this paper, we propose a novel method that assumes the CACE framework based on logistic regression using multiple imputation technique to estimate the unknown compliance status, with a lemma that provides mathematical proof of identification. Its performance is compared with ITT, PP, instrumental variable method and latent class regression method. The performance of these five methods was evaluated via intensive simulations assuming varying compliance rates, sample sizes and effect sizes. Scenarios that account for selection bias are also considered. The simulation results demonstrate that our proposed method has smaller bias and mean squared error, with wider coverage and larger power, even in the presence of significant selection bias. The methods were also compared using data from the JOBS II randomised clinical trial on depression, where the non-compliance rate was 55%. The performance aligned with simulation results and demonstrated the good potential of LMI in estimating treatment effect in RCTs subject to non-compliance.</p>