Statistical Methods in Medical Research 4ed

ment will exceed, perhaps very considerably, the number on the inferior treatment(s),
even though the evidence for the reality of the effect may be weak. The
latter feature follows because a comparison between two groups of very different
sizes is less precise than if the two groups had been pooled and divided into
groups of equal size. Difficulties may also arise if there is a time trend in the
prognostic characteristics of patients during the trial. Patients entered towards
the end of the trial, and thus assigned predominantly to the favoured treatment,
may have better (or worse) prognoses than those entered early, who were
assigned in equal proportions to different treatments. It may be difficult to adjust
the results to allow for this effect. A more practical difficulty is that doctors may
be unwilling to assign, say, one patient in 10 to an apparently worse treatment,
and may prefer a system by which their ethical equipoise is preserved until the
evidence for an effect is compelling. See Armitage (1985) for a general discussion.
Data-dependent allocation of this sort should perhaps be called `outcomedependent
allocation' to distinguish it from schemes such as minimization,
discussed in the last subsection. In the latter, the allocation may depend on the
values of baseline variables for the patient, but not on the outcome as measured
by a response variable, which is the essential feature of the present discussion.
The term adaptive assignment is also widely used.
Adaptive schemes have rarely been used in practice. A well-known example is
the trial of extracorporeal membrane oxygenation (ECMO) for newborn infants
with respiratory failure (Bartlett et al., 1985). This followed a so-called biased
coin design (Wei & Durham, 1978), which is a modified form of play the winner.
For two treatments, A and B, assignment is determined by drawing an A or B
ball from an urn. Initially, there is one ball of each type. After a success with, say,
A, an A ball is added to the urn and, after a failure with A, a B ball is added; and
vice versa. A higher proportion of successes with A than with B thus leads to a
higher probability of assignment with A. In the event, the first patient was
treated with ECMO and was a success. The second patient received the control
treatment, which failed. There then followed 10 successive successes on ECMO
and the trial stopped. The proportions of successes were thus 11/11 on
ECMO and 0/1 on control. The correct method of analysing this result has
caused a great deal of controversy in the statistical literature (Ware, 1989;
Begg, 1990). Perhaps the most useful comment is that of Cox (1990):
The design has had the double misfortune of producing data from which it would be
hazardous to draw any firm conclusion and yet which presumably makes further
investigation ethically difficult. There is an imperative to set minimum sample sizes.
Randomized consent
18.4 Treatment assignment 603
It is customary to seek the informed consent of each patient before he or she is
entered into a clinical trial. If many patients withhold their consent, or if