Confidence intervals for a difference between proportions based on paired data

Abstract

We construct several explicit asymptotic two-sided confidence intervals (CIs) for the difference between two correlated proportions using the method of variance of estimates recovery (MOVER). The basic idea is to recover variance estimates required for the proportion difference from the confidence limits for single proportions. The CI estimators for a single proportion, which are incorporated with the MOVER, include the Agresti-Coull, the Wilson, and the Jeffreys CIs. Our simulation results show that the MOVER-type CIs based on the continuity corrected Phi coefficient and the Tango score CI perform satisfactory in small sample designs and spare data structures. We illustrate the proposed CIs with several real examples.

Confidence intervals for the difference of marginal probabilities in clustered matched‐pair binary data

“…For each of the 112 combinations, the true value of δ is set as δ = 0.1; the simulation generates 10,000 data sets and then estimates the corresponding coverage probability for CIs. The results are presented in Figures and which are the basis for the following conclusions: The CI from maintains the nominal coverage probability best, which agrees with the advocation from researchers that the score‐based CI for difference of marginal probability in matched‐pair binary data is the best approximate CI and has been shown to consistently, although only slightly, outperform other existing asymptotic CIs. For the clustered matched‐pair binary data, the can effectively control the empirical coverage probability under the nominal level, especially for small numbers of cluster ( K < 50); when the number of clusters becomes medium ( K ≥ 50), it tends to be conservative.…”

Calculating unreported confidence intervals for paired data

“…These entities, in part or full, are rarely reported, even when they were used to compute a p-value via appropriate tests like the McNemar's test, paired t -test, paired z -test, or a paired exact test. If only group level proportions (or means and standard deviations) are given, additional measures, such as between-group correlation, are required to determine the relevant standard error [7,8]. Such entities are hardly reported.…”

“…These methods can be used to estimate one when the other is given. Tang et al [8] described and evaluated methods to find the variance of the difference between paired proportions using a specialized variance recovery method that utilizes the variances of the individual proportions.…”

Measures of Location for Confidence Intervals for Proportions

“…These results show the clear gradation from grossly predominantly mesial non coverage (Wald) to predominantly distal (Wilson). A preliminary version of Tang et al (2010) used an alternative difference measure MNCP-DNCP. It seems preferable to use a ratio measure, which more effectively separates the function of assessing location from the assessment of overall coverage.…”