Year: 2026
Type: article
Abstract: For clinical trials that address questions of non-inferiority or superiority, the null hypothesis specifies a non-zero difference between response probabilities $$p_0$$ p 0 ( $$p_1$$ p 1 ) under control(treatment) regimens. A confidence interval for $$p_0$$ p 0 under this hypothesis provides a summary of our knowledge of the baseline probability $$p_0$$ p 0 , which can easily be converted into an interval for the treatment probability $$p_1$$ p 1 . When the hypothesised difference between $$p_0$$ p 0 and $$p_1$$ p 1 is zero, there is an exact interval for $$p_0$$ p 0 based on the total number of responses known as the Clopper-Pearson interval. Unfortunately, this construction does not extend to the hypothesis of non-zero difference. There is no quickly computed accurate method currently available. In this paper, we propose and investigate the properties of a conceptually simple and computationally feasible interval and demonstrate that it has reasonable one-sided and excellent two-sided coverage properties. This is not only useful as a summary of post-experimental knowledge, but is a key input into the testing procedure of Berger and Boos (1994).
Source: Sankhya A
Author: Chris J. Lloyd
Institution: The University of Melbourne
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: University of Melbourne
OpenAlex ID: W7204874470