I don't have time to hunt for references, but none of the existing answers
mentioned alternate methods (internally generated, such as organizers giving out pins / etc... and counting how many were given); and then there's a related question discussed on a resent 538 podcast over the accuracy of internal estimates by organizations.
In my post about the pregnancy and prenatal care options I chose, I
mention that I don't take the pregnancy glucose test that requires drinking glucola (that syrupy orange or grape drink) and that I use an
alternate method of testing.