Why you should not use the two-stage analysis of AB/BA cross-overs

What is it about?

I show that, contrary to what had been claimed in Statistics in Medicine previously, it was not reasonable to use the two-stage analysis of AB/BA cross-over designs.

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Why is it important?

I provided a trick whereby the two-stage procedure could be modified to produce a test with the correct type-I error rate. I showed that when this was done there was no power advantage in using the two-stage analysis of cross-over trials compared to the simple strategy of always using the within-patient test. The previous claimed power advantage had been bought by inflating the Type I error rate.