Is the ‘simple carry‐over’ model useful?

It is argued that the models usually employed for carry‐over effects in cross‐over trials are not reasonable. The example of a non‐linear dose response for a dose‐finding trial arranged in a Williams square is developed to show that if carry‐over is present to any appreciable degree the usual statistical models provide no guaranteed protection against its effects. It is concluded that the most reasonably defended assumption about carry‐over effects is that no important carry‐over has taken place and that, where this assumption cannot be defended, statistical models provide no satisfactory substitute for it.