Crossover trials, degrees of freedom, the carryover problem and its dual

The problem of carryover in crossover trials has received a great deal of attention in the statistical literature. Carryover is just one form of period by treatment interaction; yet a parallel problem of patient by treatment interaction, which may be regarded as dual to that of carryover, has received little attention. We suggest that the phenomenon of patient by treatment interaction requires a repeated measures approach to the analysis of crossover trials. A simple solution using predefined contrasts is presented and illustrated by example.