  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.
