Adjusting for baseline measurements in the two-period crossover study: a cautionary note

It is intuitively appealing in planning a two-period crossover study to have each patient measured on the response variable at the beginning as well as at the end of both periods, and to take the change from the value at the start of the period to the value at the end as the measure of the patient's response to the treatment given during that period. This apparently innocuous procedure may, contrary to one's intuition, produce bias in the analysis of the data for a difference between the residual effects and a difference between the direct treatment effects.