EXACT CONFIDENCE INTERVALS FOR SUMS OF INDEPENDENT BINOMIAL PROPORTIONS

Three approaches for constructing exact (test-based) confidence intervals (CIs) for sums of two independent binomial parameters are presented and compared with each other: (1) a method based on rectangular confidence regions - this method is implemented using either Pearson-Clopper CIs or Sterne's method; (2) CIs based on nonrectangular confidence regions produced by a generalization of Sterne's method; and (3) an "unconditional method" which is equivalent to inverting a test based on the supremum of the p-values over all nuisance parameters. The unconditional method turns out to be the most satisfactory one with respect to the length of the CIs, the coverage and conceptual aspects. All methods can be generalized to weighted sums of more than two binomial parameters. However, in case of Methods 2 and 3, this may lead to a considerable computational burden.