  Freeman has considered the following two-stage procedure for finding a
confidence interval for the treatment difference theta, using data from an
AB/BA crossover trial. In the first stage, a preliminary test of the null
hypothesis that the differential carryover is zero, is carried out. If this
hypothesis is accepted then the confidence interval for theta is constructed
assuming that the differential carryover is zero. If, on the other hand, this
hypothesis is rejected then this confidence interval is constructed using only
data from the first period. Freeman has shown that this confidence interval has
minimum coverage probability far below nominal. He therefore concludes that
this confidence interval should not be used. In the present paper, we analyse
the performance of a similar two-stage procedure for an ABAB/BABA crossover
trial. This trial differs in very significant ways from an AB/BA crossover
trial, including the fact that for an ABAB/BABA crossover trial there is an
unbiased estimator of the differential carryover that is unaffected by
between-subject variation. Despite these great differences, we arrive at the
same conclusion as Freeman. Namely, that the confidence interval resulting from
the two-stage procedure should not be used.
