Nearly Exact Sample Size Calculation for Powerful Nonrandomized Tests for Differences Between Binomial Proportions

• Activity Number: 458
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Stefan Wellek*+
• Companies: CIMH/University of Heidelberg
• Keywords: binomial two-sample problem ; Boschloo's approach ; exact nonconditional test ; McNemar setting ; nuisance parameter ; score statistic

Abstract

The talk starts from a detailed comparison of the power functions of the most promising nonrandomized procedures of testing for differences between two binomial proportions. In the case of independent samples, it turns out that Boschloo's (1970) technique of raising the nominal level in the standard conditional test as far as admissible performs best in terms of power. Thus, the question of an easy to implement approach to exact sample size calculation for a test of that structure arises. The computational burden entailed in exact sample size calculation is comparatively modest for both the UMPU randomized and the conservative nonrandomized version of the test. Computing these values yields a pair of bounds enclosing the exact sample size required for the Boschloo test. Taking the midpoint of the corresponding interval is shown to provide a very satisfactory solution to the problem. This holds true both for the two-sample setting and the case of paired binary data (McNemar setting). In the latter, the level-corrected score test should tbe preferred to the McNemar-Boschloo test.