Comparing incomplete paired binomial data under non-random mechanisms.

In many paired experiments designed to compare two treatments, various mechanisms can lead to the data being incomplete. Such mechanisms may be of a non-random nature and may depend on the treatment or the outcome. This paper considers several methods for testing the equality of two correlated binomial proportions when the incompleteness is caused by non-random mechanisms. Several simple procedures are justified in certain cases. The tests based on all available data are more efficient compared to those utilizing only portions of the data. McNemar's test based only on the complete paired observations and the likelihood test are the most robust, although no efficient test exists when the mechanisms are not independent.