Comparative randomized inverse sampling

According with previous literature, we define randomized inverse sampling for comparing two treatments with respect to a binary response as the random- ized sampling which stops when a total fixed number of successes is observed. We obtain asymptotic distributions for the counting variables involved and show them to be equivalent to the corresponding asymptotic distributions for multinomial sampling, but to 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 prob- abilities can be constructed in the case of comparative randomized inverse sampling. We discuss this confidence interval in detail, obtain its asymp- totic distribution and discuss its finite sample properties when compared to multinomial sampling.