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Abstract
Asymptotic methods for interval estimating and testing of functions of binomial and Poisson parameters are considered. These methods reflect the distinction between symmetric and asymmetric comparisons, where asymmetric comparisons deal with cases where one group represents the compelling standard for the other, and symmetric comparisons are performed for settings where this is not the case. First, a symmetric setting is considered where an application of a simultaneous confidence band for a function of binomial proportions is given. Here, a pair-wise comparison method is illustrated in the context of complex survey responses for smoking behavior. Next, individual confidence interval methods for the difference of binomial proportions are presented in the setting of asymmetric comparisons. These proposed methods include applications of continuity corrections in the setting of non-inferiority trials.
Next, research focusing on Poisson-distributed outcomes is presented. In this setting, first, confidence intervals are explored with respect to the difference and ratio of two Poisson rates in symmetric settings. Proposed methods, including several with applications of continuity corrections, are compared to previously studied confidence interval methods. Additionally, in settings where confidence intervals are used to make hypothesis testing decisions regarding the equality of two Poisson rates, the Type I error rate and power of the discussed methods are evaluated to determine the ideal methodology to use.
Next, an evaluation of simultaneous confidence band methodology for Poisson outcomes is given. Specifically, the stepwise confidence interval method proposed by Hsu and Berger in conjunction with the previously presented individual methods is considered. A study of the performance of these methods in terms of family-wise error rate and power is presented.
Finally, hypothesis testing and interval-estimation methods for asymmetric comparisons in terms of the difference and ratio of two Poisson rates are proposed, with a focus on Wald-type methodology. Hypothesis testing methods and corresponding confidence interval methods are presented and their performance is evaluated using simulation studies.
