Cost-efficient fixed-width confidence intervals for the difference of two Bernoulli proportions

We study the properties of confidence intervals (CIs) for the difference of two Bernoulli distributions’ success parameters, (Formula presented.), in the case where the goal is to obtain a CI of a given half-width while minimising sampling costs when the observation costs may be different between the two distributions. We propose three different methods for constructing fixed-width CIs: (i) a two-stage sampling procedure, (ii) a sequential method that carries out sampling in batches, and (iii) an (Formula presented.) -stage “look-ahead” procedure. Under diverse scenarios, our proposed algorithms obtain significant cost savings versus their baseline counterparts. Furthermore, for the scenarios under study, our sequential-batches and (Formula presented.) -stage “look-ahead” procedures approximately obtain the nominal coverage while meeting the desired width requirement. Our sequential-batching method is more efficient than the “look-ahead” method computationally, with average running times an order-of-magnitude faster over the scenarios tested. We illustrate our procedures on a case study comparing generic and brand-name drugs.