3: Three doses of a new formulation of formoterol were compared
to three doses of a standard formulation and also to placebo in
a single-dose pharmacodynamic trial in asthma (Senn
et al., 1997). The main outcome variable was area under the
curve for forced expiratory volume in one second (FEV1)
measured over twelve hours. Although there were seven treatments
in total, each patient was treated in five periods only. The design
used 21 sequences. These
sequences were chosen so that every treatment appeared equally
often in each of the five periods (three sequences each), so that
every patient received five treatments and so that every possible
pair of treatments (of which there were 21) appeared in an equal
number of sequences (10 each). There was a washout between treatment
periods. The intention was to recruit six patients to each sequence
but in the end recruitment exceeded expectation and161 patients
were randomised to the 21 sequences.
an example of a so-called 'balanced incomplete blocks' design.
The episodes of treatment for a given patient form a block and
these are incomplete because each patient receives only five of
the seven treatments. The design is balanced because each pair
of treatments is represented equally often.
three increasingly complex designs are very different but have
some common features, as follows. 1) Each patient received sequential
treatment with at least two treatments. 2) The purpose of each
trial was to study the effects of the individual treatments and
not of the sequences of treatments. 3) The conditions being studied
were what might be broadly termed as chronic. 4) There was an
attempt to balance the trial treatments by period of treatment.
5) A wash-out period was employed. 6) Patients were randomized
to the sequences used.
two features are defining features of cross-over trials. The third
is an essential condition of applying them and the last three
are precautions of design that it is almost always appropriate
to observe. The reason that only chronic conditions are suitable
for applying cross-over trials is that the units of the experiment
are episodes and not patients. If death or cure is the possible
result of a treatment, episode a subsequent episode becomes unavailable
for study. Designs for which treatments are balanced by period
(the technical term is 'uniform' on the periods) are wise choices
where practical, since it is possible that there may be trend
effects either in conditions of the experiment or in patients
over the trial. If treatments are uniform on the periods, such
trend effects can be eliminated efficiently. A wash-out period
helps to deal with the problem of carry-over (to be discussed
below) and randomizing patients to treatment assists in blinding
trials, in avoiding unconscious bias, in promoting utmost good
faith and in providing a basis for significance tests.
feature of all these trials that is not immediately obvious, but
would become so if compared with a possible alternative parallel
group trial, is how very few patients were required. All of these
trials reached convincing conclusions, and they were not underpowered.
The corresponding parallel group trials would have needed many
times more patients. The extreme efficiency of such trials arises
principally from the fact that, patients being able to act as
their own controls, the between patient component of variation
is eliminated and, also, patients provide evidence about more
than one episode of treatment. (The latter advantage only applies,
however, if, as is usually the case, there is a cost associated
with recruiting patients above and beyond the cost associated
with each treatment episode.)
of cross-over trials is, in fact, their principal attraction.
Another is the potential, given a suitable choice of design, to
study individual response to treatment. This will be discussed
in connection with n-of-1 trials in due course. For the moment
we consider the problem of carry-over.