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This approach
to analysis was originally suggested by Grizzle (Grizzle,
1965) and was popular for many years. As a result of an important
paper by Freeman (Freeman,
1989), it is now known to be extremely biased and is not recommended.
However, unfortunately, the general literature on the design and
analysis of clinical trials does not seem to have caught up with
the specialist literature on cross-over trials, and popular texts
on medical statistics continue to be written that recommend this
inappropriate procedure. It will therefore be described briefly
in order to point out its dangers.
Grizzle's
proposal was that a preliminary test for carry-over (as described
above) should be carried out. Because of its low power he suggested
that a nominal level of significance of ten percent should be
used. If the result was not significant, then the treatment effect
should be tested using CROS at the 5% level. If the result was
significant, the test should be performed using PAR instead again
at the 5% level.
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4.1: The Two Stage Analysis of the AB/BA Design
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Although
this proposal seems intuitively reasonable it is in fact biased
as a strategy for testing the treatment effect and has a type
I error rate that lies between 7% and 9.5% depending on the correlation
between first and second period values. The reason is that the
test for carry-over and PAR are highly correlated so that if the
first is significant the second is highly likely to be. In fact,
either the whole procedure is irrelevant because the test for
carry-over is not significant so that CROS is used, or the type
I error rate conditional on using PAR lies between 25% and 50%.
The message is clear. On no account should this procedure be used
to analyse cross-over trials.
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