Non-Parametric Non-Inferiority Assessment in a Three-Arm Trial with Non-Ignorable Missing Data

A three-arm non-inferiority trial including a placebo is usually utilized to assess the non-inferiority of an experimental treatment to a reference treatment. Existing methods for assessing non-inferiority mainly focus on the fully observed endpoints. However, in some clinical trials, treatment endpoints may be subject to missingness for various reasons, such as the refusal of subjects or their migration. To address this issue, this paper aims to develop a non-parametric approach to assess the non-inferiority of an experimental treatment to a reference treatment in a three-arm trial with non-ignorable missing endpoints. A logistic regression is adopted to specify a non-ignorable missingness data mechanism. A semi-parametric imputation method is proposed to estimate parameters in the considered logistic regression. Inverse probability weighting, augmented inverse probability weighting and non-parametric methods are developed to estimate treatment efficacy for known and unknown parameters in the considered logistic regression. Under some regularity conditions, we show asymptotic normality of the constructed estimators for treatment efficacy. A bootstrap resampling method is presented to estimate asymptotic variances of the estimated treatment efficacy. Three Wald-type statistics are constructed to test the non-inferiority based on the asymptotic properties of the estimated treatment efficacy. Empirical studies show that the proposed Wald-type test procedure is robust to the misspecified missingness data mechanism, and behaves better than the complete-case method in the sense that the type I error rates for the former are closer to the pre-given significance level than those for the latter.