Power series estimator for binary data

There are several commonly used measures of association between treatment and control event rates in the population, including odds ratios, relative risk and number needed to treat. Conventionally those parameters are estimated by the sample proportion estimators. In this paper, we show that the sample proportional estimators tend to overestimate. Fortunately, those measurements are estimable by the power series estimators and they converge to UMVUE with a speed of convergency depending on big-O. For instance, it converges slowly for the number needed to treat if the difference between two sample proportions is close to zero.