On Confidence Interval Construction for Establishing Equivalence of Two Binary-Outcome Treatments in Matched-Pair Studies in the Presence of Incomplete Data

Abstract

Matched-pair design is often adopted in equivalence or non-inferiority trials to increase the efficiency of binary-outcome treatment comparison. Briefly, subjects are required to participate in two binary-outcome treatments (e.g., old and new treatments via crossover design) under study. To establish the equivalence between the two treatments at the α significance level, a (1−α)100% confidence interval for the correlated proportion difference is constructed and determined if it is entirely lying in the interval (−δ ₀,δ ₀) for some clinically acceptable threshold δ ₀ (e.g., 0.05). Nonetheless, some subjects may not be able to go through both treatments in practice and incomplete data thus arise. In this article, a hybrid method for confidence interval construction for correlated rate difference is proposed to establish equivalence between two treatments in matched-pair studies in the presence of incomplete data. The basic idea is to recover variance estimates from readily available confidence limits for single parameters. We compare the hybrid Agresti–Coull, Wilson score and Jeffreys confidence intervals with the asymptotic Wald and score confidence intervals with respect to their empirical coverage probabilities, expected confidence widths, ratios of left non-coverage probability, and total non-coverage probability. Our simulation studies suggest that the Agresti–Coull hybrid confidence intervals is better than the score-test-based and likelihood-ratio-based confidence interval in small to moderate sample sizes in the sense that the hybrid confidence interval controls its true coverage probabilities around the pre-assigned coverage level well and yield shorter expected confidence widths. A real medical equivalence trial with incomplete data is used to illustrate the proposed methodologies.