Confidence Intervals for the Ratio of Two Binomial Proportions

Sometimes the ratio of two binomial proportions is the parameter of major interest, for instance as the risk ratio in a two-group cohort study (Fleiss, 1973) or as the likelihood ratio for a diagnostic test procedure (McNeill, Keeler and Adelstein, 1975). Let X and Y be independent binomial variates based on sample sizes m and n and parameters p' and P2, respectively. Let 0 = Pm/P2. We consider the construction of confidence intervals for 0. Santner and Snell (1980) have proposed a nonanalytical procedure which guarantees a lower bound on the confidence coefficient of the 1 a interval for 0. Their algorithm is usable for small m and n but may produce conservative intervals. In ?2, an analytical method for obtaining approximate confidence intervals for 0 is proposed and compared to the one recommended by Katz et al. (1978).