Interval estimation for the difference between independent proportions: comparison of eleven methods

TLDR

Computationally simpler methods for confidence intervals of differences between binomial proportions often exhibit aberrations and poor coverage. The study aims to evaluate existing unconditional methods and develop two new approaches that avoid aberrations. The authors assessed eleven methods, including the Mee–Miettinen–Nurminen, tail area profile likelihood, and Wilson score combination, through simulation and analytical comparison. The Mee–Miettinen–Nurminen and tail area profile likelihood methods achieved the best coverage, though the latter is computationally intensive for large samples, while the Wilson score combination performed well and is easily implemented. © 1998 John Wiley & Sons, Ltd.

Abstract

Several existing unconditional methods for setting confidence intervals for the difference between binomial proportions are evaluated. Computationally simpler methods are prone to a variety of aberrations and poor coverage properties. The closely interrelated methods of Mee and Miettinen and Nurminen perform well but require a computer program. Two new approaches which also avoid aberrations are developed and evaluated. A tail area profile likelihood based method produces the best coverage properties, but is difficult to calculate for large denominators. A method combining Wilson score intervals for the two proportions to be compared also performs well, and is readily implemented irrespective of sample size. © 1998 John Wiley & Sons, Ltd.