Large-Sample Confidence Intervals for the Treatment Difference in a Two-Period Crossover Trial, Utilizing Uncertain Prior Information
by Paul Kabaila
Abstract: We consider a two-treatment two-period crossover trial, with responses that are continuous random variables. The purpose of this trial is to carry out inference about the difference theta in the effects of two treatments, A and B. Subjects are randomly allocated to either group 1 or group 2. Subjects in group 1 receive treatment A in the first period and then receive treatment B in the second period. Subjects in group 2 receive treatment B in the first period and then receive treatment A in the second period. This design is efficient under the assumption that there is no differential carryover effect. It is not an appropriate design unless there is strong prior information that this assumption holds. We consider the commonly-occurring scenario that it is not certain that this assumption holds.
To deal with this uncertainty, it has been suggested that a preliminary test of the null hypothesis that this assumption holds be carried out before proceeding with further inference. Using a large-sample analysis, Freeman (1989) showed that this use of a preliminary test â€œis too potentially misleading to be of practical useâ€.
We describe a new large-sample frequentist 1-alpha confidence interval for theta that utilizes this prior information. This confidence interval has expected length that (a) is relatively small when the prior information is correct and (b) has maximum value that is not too large. In addition, this interval coincides with the standard 1-alpha confidence interval when the data happen to strongly contradict the prior information.
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