Comparative randomized inverse sampling

According to previous literature, we define randomized inverse sampling for comparing two treatments with respect to a binary response as the sampling that stops when a total fixed number of successes, irrespective of the treatments, are observed. We have obtained elsewhere the asymptotic distributions for the counting variables involved and have shown them to be equivalent to the corresponding asymptotic distributions for multinomial sampling. In this paper, we start deriving the same basic results using different techniques, and we then show how they give rise to genuinely novel procedures when translated into finite sample approximations. As the main example, a novel confidence interval for the logarithm of the odds ratio of two success probabilities can be constructed in the case of comparative randomized inverse sampling. Some advantages over the standard multinomial sampling in terms of coverage probabilities are visible when no adjustment for cells with zero counts is applied; otherwise, the two sampling schemes appear to be fairly equivalent. This is a reassurance that under certain circumstances, inverse sampling can be safely chosen over more traditional sampling schemes.