In non-inferiority trials with non-adherence to interventions, where some participants do not receive their randomly assigned intervention as intended, intention-to-treat and per-protocol analyses are often performed. In the presence of non-adherence, both of these approaches can result in biased estimates of efficacy and therefore agreement between them does not guarantee that non-inferiority conclusions are valid. This PhD aims to identify statistical methods that can account for non-adherence to interventions in non-inferiority trials and assess their performance under different patterns of non-adherence. First, a systematic review was conducted that identified eleven techniques for handling non-adherence to interventions in non-inferiority trials, including instrumental variable approaches and inverse-probability-of-treatment weighting (IPTW). However, very few trials reported using relevant statistical methods and so firm inferences about their impacts on non-inferiority conclusions could not be drawn. Next, a simulation study based on the REMoxTB trial was conducted to assess the performance of different methods for handling treatment non-adherence in non-inferiority trials comparing active drugs. When non-adherence differed between trial arms, ITT and PP analyses often produced biased estimates of efficacy, potentially in the same direction and by similar amounts. In contrast, the more sophisticated methods (multiple imputation [MI] of outcomes, IPTW, and a doubly-robust [DR] estimator) were able to correct bias under most non-adherence scenarios without meaningful losses in statistical power. Finally, the MI, IPTW and DR methods were used to analyse the primary efficacy outcome of the Study 31/A5349 trial assuming that all participants had been fully adherent. After accounting for nonadherence, the estimated effects of the rifapentine and rifapentine-moxifloxacin regimens were roughly 1.9 and 1.7 times larger in favour of the control regimen, compared with the primary analysis conducted in the assessable population. Non-inferiority conclusions were consistent with the primary analysis. Collectively, these findings support the case for routine adoption of the MI, IPTW and DR methods to account for treatment non-adherence in non-inferiority trials of active drugs. Whilst further validation of these methods is ongoing, ITT and PP analyses of the primary efficacy outcome should be supplemented with sensitivity analyses that correct for the impact of treatment non-adherence, ensuring that non-inferiority conclusions are robust to different assumptions. The next steps should involve engaging with relevant regulatory bodies to promote the wider use of these methods in suitable studies.