On Powerful Exact Nonrandomized Tests for the Poisson Two-Sample Setting

• Activity Number: 296 - SPEED: Biometrics - Methods and Application, Part 1
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Stefan Wellek*
• Companies: CIMH Mannheim/University of Heidelberg, Germany/University of Mainz, Germany
• Keywords: conditioning; increased nominal level; noninferiority; Poisson distribution; unifomly most powerful unbiased test; sample-size calculation

Abstract

In the case of two independent samples from Poisson distributions, the natural target parameter for hypotheses testing is the ratio of the two population means. The conditional tests which have been derived for this class of problems already in the 1940s are optimal only when randomized decisions between the hypotheses are admitted. The major objective of this contribution is to show how the approach used by Boschloo (1970) for constructing a powerful nonrandomized version of Fisher's exact test for hypotheses about the odds ratio between two binomial parameters can successfully be adapted for the Poisson case. The resulting procedure, which we propose to term Poisson-Boschloo test, depends on some cutoff for the observed total number of events, the variable upon which conditioning has to be done. We show, that for any fixed specific alternative, this cutoff can be chosen in such a way that the resulting nonrandomized test falls short in power of the randomized UMPU test only by a negligible amount. Thus, sample size calculation for the Poisson-Boschloo test can be carried out nearly exactly by means of the same algorithm as has to be used for the randomized UMPU test.