BACKGROUND: Non-inferiority trials comparing different active drugs are often subject to treatment non-adherence. Intention-to-treat (ITT) and per-protocol (PP) analyses have been advocated in such studies but are not guaranteed to be unbiased in the presence of differential non-adherence. METHODS: The REMoxTB trial evaluated two 4-month experimental regimens compared with a 6-month control regimen for newly diagnosed drug-susceptible TB. The primary endpoint was a composite unfavorable outcome of treatment failure or recurrence within 18 months post-randomization. We conducted a simulation study based on REMoxTB to assess the performance of statistical methods for handling non-adherence in non-inferiority trials, including: ITT and PP analyses, adjustment for observed adherence, multiple imputation (MI) of outcomes, inverse-probability-of-treatment weighting (IPTW), and a doubly-robust (DR) estimator. RESULTS: When non-adherence differed between trial arms, ITT, and PP analyses often resulted in non-trivial bias in the estimated treatment effect, which consequently under- or over-inflated the type I error rate. Adjustment for observed adherence led to similar issues, whereas the MI, IPTW and DR approaches were able to correct bias under most non-adherence scenarios; they could not always eliminate bias entirely in the presence of unobserved confounding. The IPTW and DR methods were generally unbiased and maintained desired type I error rates and statistical power. CONCLUSIONS: When non-adherence differs between trial arms, ITT and PP analyses can produce biased estimates of efficacy, potentially leading to the acceptance of inferior treatments or efficacious regimens being missed. IPTW and the DR estimator are relatively straightforward methods to supplement ITT and PP approaches.