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. © 2011 International Chinese Statistical Association.