Statistical Methods in Medical Research 4ed

628 Clinical trials
on different occasions to the same individual. Treatments would then be
assessed against within-subject random error, which would be expected to be less
than between-subject error. An additional advantage would be economy in the
number of subjects, since each subject would provide more than one observation.
A design in which treatments are given in sequence to each subject is called a
cross-over (or, in many non-medical applications, change-over) design.
In many, perhaps most, clinical trials, such a design would be infeasible,
because the treatments are intended to produce irreversible changes in the
patient's health, or because they must be administered for long periods of time.
A cross-over design is most suitable for treatments intended for rapid relief of
symptoms in chronic diseases, where the long-term condition of the patient
remains fairly stable. The design is used extensively for Phase I and Phase II
studies, and for equivalence trials (see below).
Extensive accounts of cross-over trials are given in the books by Jones and
Kenward (1989), Ratkowsky et al. (1993) and Senn (1993), in several articles in a
special issue of Statistical Methods in Medical Research (1994, Volume 3, No. 4),
and in the article by Senn (1998).
The simple cross-over design
In the simplest case, with two treatments, A and B, one randomly chosen group
of patients (group I) receives treatments in the order AB, while the other group
(group II) receives them in the order BA. There may be different numbers of
patients in the two groups. The design is variously called the simple cross-over,
the two-treatment, two-period design or the AB/BA design.
The design has the following layout:
Run-in Period 1 Wash-out Period 2
Reading zij yij1 yij2
Group I (n1) Ð A Ð B
Group II (n2) Ð B Ð A
Here, the `readings' are observations of some appropriate measure of the
patient's condition (e.g. respiratory test measurement, frequency of attacks of
some sort, etc.). The two periods of administration are separated by a `wash-out'
period to enable the patient's condition to return to a level uninfluenced as far as
possible by the treatment previously received. (In a drug trial, for instance, it
should be long enough to allow for virtual elimination of a drug used in period
1.) The `run-in' period is optional, but it may provide an opportunity for the