Comparing two independent samples using the risk difference under inverse sampling

Tang and Tian (2009) derived formulas for the development of confidence bounds for the risk difference under inverse sampling. Unfortunately, the last formula in the appendix for the inverse of the expected Fisher Information matrix I-1 contains an error which leads-if used-to incorrect confidence bounds: I-1 does not remain invariant if (x0,y0) is exchanged with (x1,y1) and, simultaneously, [Delta] is exchanged with -[Delta]. In the following I will present an idea that corrects this error and that thereby leads to a considerable simplification of the formulas needed for the calculation of the confidence bounds. Furthermore I point out an existing alternative for the calculation of the zeros of a cubic equation that may be of interest.