On Fixed-Width Confidence Limits for the Risk Ratio with Sequential Sampling

Synoptic Abstract A sequential method is presented for determining confidence intervals of fixed-width and corresponding optimal sample sizes for the risk ratio of probabilities of the two independent binomial variates. In general, since the ratio estimators are biased and asymmetrical, corrections must be made when they are used in practice. We suggest to use a bias-correction term for modification to the maximum likelihood estimator (MLE) to develop the procedure. In addition, we study the following desirable properties of the estimator: Unbiasedness, efficiency in variance, and normality. First-order asymptotic expansions are obtained to investigate large-sample properties of the proposed procedure. Monte Carlo experiment is carried out for various scenarios of samples for examining the finite sample behavior. Through illustrations, we compare these performance of the proposed methods, Wald-based confidence intervals with the likelihood-based confidence intervals in light of invariance, length and sample sizes.