Asymptotic Confidence Intervals (CIs) for a Difference Between Two Independent Proportions

Binary response variables arise in a variety of studies. It is often of interest to summarize a treatment effect in terms of the difference in proportions of successes between groups. Stata produces the Wald-type asymptotic CI for differences in proportions in -cs- and -glm , family(binomial) link(identity)-. The Wald-type CI is easy to compute, but it is sometimes desirable to have a large-sample CI with better coverage properties. Alternative asymptotic CI methods have appeared in the literature with claims of better performance. Miettinen and Nurminen (1985) describe an iterative method for such an improved CI requiring repeatedly solving a cubic equation. A noniterative approximation by Wallenstein (1997) requires only solution to a quadratic equation. Newcombe (1998) favored a method involving Wilson intervals of each of the two proportions (see -ciw-). Agresti and Caffo (2000) describe a simple method inspired by an analogous Wilson-type interval (see -propci-) for single proportions. Each of these CIs' implementations in Stata will be illustrated in the context of a therapeutic equivalence clinical trial.