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It is
generally agreed that the most serious potential drawback of cross-over
trials is to do with carry-over. This is the persistence of an
effect in a subsequent period of treatment due to treatment in
a previous period. The consequence of this can be that if we are
unaware that this has happened, we may falsely ascribe the joint
effect of two treatments to the single effect of one. The effect
of carry-over is independent of the period effect with which it
is occasionally confused. A period effect is one that occurs in
a given period, irrespective of the order in which treatments
are given. A carry-over effect has its origin in a preceding treatment
and is thus order-dependent. The phenomenon will be illustrated
with a simple example.
Suppose
that we have an AB/BA cross-over trial comparing an active treatment,
which we shall refer to as a verum, to a placebo. Suppose that
by extreme good fortune we have recruited patients to the two
sequences that are identical on average. Assume that there is
no period effect and no carry-over effect and that the effect
of the verum is to increase a suitable response by 4 from a placebo
level of 6. We thus expect to see the following table of mean
responses at the end of the trial.
| Table
2.1: AB/BA Cross-over trial comparing a verum and a
placebo
|
|---|
| Sequence
| Period
1
| Period
2
| Difference
|
|---|
| PV | 6 | 10 | 4 |
| VP | 10 | 6 | 4 |
|
Mean | | | 4 |
|
By averaging
the differences between treatment for each patient within each
sequence and over sequences we recover the treatment effect of
4. (The estimator that results as a consequence of doing this
will be referred to as "CROS".) Now suppose that we had not been
so lucky as we supposed and that patients in the second sequence
were on average five points better than those in the first. This
is the picture we should then expect to see.
| Table
2.2: AB/BA Cross-over trial comparing a verum and a
placebo
|
|---|
| Sequence
| Period
1
| Period
2
| Difference
|
|---|
| PV | 6 | 10 | 4 |
| VP | 15 | 11 | 4 |
|
Mean | | | 4 |
|
Question
2.1
Does
this difference between patients in the two sequences affect our
estimate of the treatment effect?
 
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