Testing for noninferiority of binomial distributions referring to a modified equivalence region with piecewise linear boundary

Abstract

In testing for noninferiority of two binomial distributions, the hypothesis formulation most commonly considered defines equivalence in terms of a constant bound to the difference of the two parameters. In order to avoid some basic logical difficulty entailed in this formulation we use an equivalence region whose boundary has fixed vertical distance from the diagonal for all values of the reference responder rate above some cutoff point and coincides left from this point with the line joining it with the origin. For the corresponding noninferiority hypothesis we derive and compare two different testing procedures. The first one is based on an objective Bayesian decision rule. The other one is obtained through combining the score tests for noninferiority with respect to the difference and the ratio of the two proportions, respectively, by means of the intersection–union principle. Both procedures are extensively studied by means of exact computational methods.

Keywords:

• binomial two-sample problem
• exact nonconditional test
• intersection–union rule
• objective Bayesian test
• score statisti

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental material

A SAS/IML script implementing the algorithm outlined in Section 5 for the TOSCT procedure can be obtained via email upon request from the author.