Statistical considerations for design and analysis of a multiperiod crossover study to compare two treatments for migraine headache

The purpose of this paper is to discuss a long-term, multiperiod crossover study to compare two treatments for migraine headache. Principal attention is given to the analysis of an example in which patients randomly received a treatment sequence with test drug for three migraine headaches and placebo for one. An issue that requires attention for this example is the influence of a carryover effect for test drug that was greater when placebo was the subsequent treatment than when test drug was the subsequent treatment. A way to address this issue without excessive loss of power is to consider tests of "total treatment effects," which are weighted averages across headaches of differences between average response to test drug and average response to placebo. Since these weighted averages are linear combinations of treatment effects and carryover effects, their use requires an argument that carryover effects are at least partly a further form of treatment effects. For the example in this paper, this argument is realistic because the test drug could have provided much better relief to migraine headache than other treatment patients might have previously used. A second purpose of the paper is to present some alternative designs for situations like that represented by the example. The structure of variances for alternative specifications for treatment comparison is provided for models of interest for these designs.