Statistical Methods in Medical Research 4ed

18.9 Special designs 633
If there is a TP interaction, there will usually be little point in testing and
estimating the treatment effect from the whole set of data, as in Example 18.4.
Period 1 alone provides a perfectly valid test of A versus B, since subjects
were assigned randomly to the two treatments. Period 2 is of doubtful value,
since the subjects (although originally randomized) have undergone different
experiences before entering period 2. A reasonable procedure might therefore
seem to be to estimate the treatment effect from the difference between the two
means, y11 y21. Unfortunately, there are a number of difficulties about this
approach.
1 The comparison of the two period 1 means is subject to between-subject
variation, and is therefore less precise than the full crossover approach.
2 The test for the TP interaction, based on s1 s2, is also affected by betweensubject
variation. A substantial, and important, TP interaction may therefore
exist but fail to be detected as significant. The loss in precision, both here and
in the treatment comparison in 1, may be mitigated by use of the baseline
(run-in) readings, zij, which can either be subtracted from the observations
made during the treatment periods or used as covariates.
3 The implication has been that a two-stage procedure would be applied: the
TP interaction is tested, and if it is significant the treatment effect is tested
and estimated from period 1; if TP is not significant the usual crossover
analysis is used. Freeman (1989) pointed out that this would have an important
consequence. If the null hypothesis is true, so that the treatment and TP
effects are zero, and all tests are done at, say, the 5% level, the overall Type I
error probability can be as high as 9 5%. If TP effects are non-zero, the
inflation of Type I error can be much greater. The reason for this inflation
is that the null hypothesis can be rejected at either of the two stages. Moreover,
when TP is significant purely by chance (implying an unbalanced outcome
of the randomization) it is quite likely that the period 1 difference will
also be significant, since the two test statistics are positively correlated.
4 For much the same reason, if there is a non-zero TP effect, the estimate of
treatment effect will be biased in the subset of cases when the period 1
estimate is used, and therefore biased overall. If there is no TP effect, the
bias disappears.
These considerations have cast serious doubt on the two-stage approach to
the simple crossover. The inflation of Type I error probability is not too serious
if the user is made aware: it is a consequence of many other situations in which
different tests are used in sequential order. On the other hand, the interpretation
of the results may clearly be difficult, and much of the advantage of the crossover,
in economizing in the number of subjects required, may have been lost. The
best advice is to avoid this simple design unless the user is confident that the TP
interaction is negligible. Such confidence may be provided by the results of
similar studies conducted in the past, or from pharmacokinetic considerations