Farrington-Manning in the Extreme Case

TL;DR

This paper addresses numerical issues in the Farrington-Manning method for equivalence testing of proportions, providing a closed-form solution for extreme cases where sample proportions are both 1.

Contribution

It introduces a closed-form solution to handle extreme cases in the Farrington-Manning method, improving its robustness in software implementations.

Findings

Closed-form solution for extreme cases where proportions are both 1

Addresses numerical issues in SAS and R implementations

Enhances the reliability of equivalence testing in extreme data scenarios

Abstract

The Farrington-Manning method is a common method for evaluating equivalence and non-inferiority of independent proportions. It is implemented in various software, in particular SAS$^\circledR$ PROC FREQ, and the R$^\circledR$ function farrington.manning(), which is part of the DescrTab2 package. The equations for the estimated proportions can create numerical issues in case both sample proportions equal 1, and neither of these packages will yield an acceptable solution in this special case. In this note we demonstrate a closed form solution for the situation in this and other extreme cases.