Statistical considerations in the design and analysis of non-inferiority trials with binary endpoints in the presence of non-adherence: a simulation study

Protocol non-adherence is common and poses unique challenges in the interpretation of trial outcomes, especially in non-inferiority trials. We performed simulations of a non-inferiority trial with a time-fixed treatment and a binary endpoint in order to: i) explore the impact of various patterns of non-adherence and analysis methods on treatment effect estimates; ii) quantify the probability of claiming non-inferiority when the experimental treatment effect is actually inferior; and iii) evaluate alternative methods such as inverse probability weighting and instrumental variable estimation. We found that the probability of concluding non-inferiority when the experimental treatment is actually inferior depends on whether non-adherence is due to confounding or non-confounding factors, and the actual treatments received by the non-adherent participants. With non-adherence, intention-to-treat analysis has a higher tendency to conclude non-inferiority when the experimental treatment is actually inferior under most patterns of non-adherence. This probability of concluding non-inferiority can be increased to as high as 0.1 from 0.025 when the adherence is relatively high at 90%. The direction of bias for the per-protocol analysis depends on the directions of influence the confounders have on adherence and probability of outcome. The inverse probability weighting approach can reduce bias but will only eliminate it if all confounders can be measured without error and are appropriately adjusted for. Instrumental variable estimation overcomes this limitation and gives unbiased estimates even when confounders are not known, but typically requires large sample sizes to achieve acceptable power. Investigators need to consider patterns of non-adherence and potential confounders in trial designs. Adjusted analysis of the per-protocol population with sensitivity analyses on confounders and other approaches, such as instrumental variable estimation, should be considered when non-compliance is anticipated. We provide an online power calculator allowing for various patterns of non-adherence using the above methods.