regulatory authorities have a habit of believing
only the most conservative.
At the time of writing, the O’Brien and Fleming
rule is becoming an acceptable standard. As a rule
of thumb, pharmaceutical physicians should
expect statisticians to provide alternatives that
obey a simple subtraction rule. For example, clin-
icians might agree that the study should stop due to
great efficacy whenp¼ 0 :01 at an interim analy-
sis, when sufficient patients (power of 0.8) to detect
such a difference have been recruited. In that case,
if thestudy continues after the interim analysis fails
to achievep< 0 :01, then it will be required to
achieve approximately p< 0 :04 for the whole
patient population in the final statistical analysis
in order to demonstrate the efficacy of the test drug.
Even so, Pocock and Geller (1986) have shown that
trials stopped by reason of efficacy at an interim
stage are likely to have exaggerated the size of the
difference between treatment groups. Marketing
departments should be aware of this error in their
extrapolations to the commercial worth of the
product.
9.14 Bayesian trial designs
A typical Bayesian design might be where, for
example, there are several drugs with preclinical
rationale for the treatment of cancer; as none of
them are clinically proven, one of the test treat-
ments is placebo. Patients are then recruited
sequentially into the study, and the results (e.g.
tumor size reduction) are recorded. After a while,
the proportions of patients responding to each
treatment are compared using a sophisticated pro-
babalistic method which takes into account the
uncertainties associated with small and unequal
treatment group sizes. The randomization code is
then adjusted to favor more patients being allo-
cated to the treatments that have started out looking
better than the others, while very poor, placebo-
equivalent treatments might be dropped altogether.
Eventually, the several test therapies are reduced to
two, and a definitive demonstration of superiority
or nonsuperiority for that pair of treatments can be
reported.
The difficulties with interim analyses do not
arise when a Bayesian approach to the original
design has been taken (Berry, 1985). The Bayesian
methodology essentially revises the proportionate
patient allocation among the test therapies accord-
ing to the latest and best information available (e.g.
Berry, 1995): essentially, after some minimum
numberof patients haveentered the trial,an interim
analysis is done every time another patient com-
pletes the trial. The important distinction between
Bayesian and sequential designs (above) is that
although patient numbers required to complete a
sequential design study are undefined at the begin-
ning, the treatment allocations are nonetheless
according to a fixed randomization schedule.
Thus, the sequential designs are still, essentially,
a frequentist methodology, and not Bayesian.
Bayesian approaches currently find little under-
standing on the part of regulatory authorities, and
thus are, probably unduly, little utilized by clinical
trialists. However, Bayesian methods are finding
increased uses in specialized areas, for example,
trials of cancer chemotherapy and studies in rare
disease. The potential benefits of Bayesian meth-
ods includethe use offewerpatients to demonstrate
efficacy, as well as potential seamlessness of phase
II and phase III development when the number of
drugs or dose sizes of interest has been reduced
during the trial from several to one or two; patients
recruited after this transition may be regarded as
patients in a pivotal trial by an enlightened regula-
tory authority.
The generalist cannot be expected to be able to
generate Bayesian statistical plans for himself or
herself. These require an experienced statistician,
and it may be added a statistician who is not,
himself or herself, philosophically opposed to
Bayesian rather than frequentist thinking. The
decision to employ a Bayesian design for a clinical
trial will be viewed as courageous in most compa-
nies, and therewill be many clinical trials for which
an orthodox, frequentist approach will be selected
for several good reasons. Overall, the generalist
should be advised that, when considering a new
trial, he or she should at least consider whether a
Bayesian approach might help. If this option is
rejectedthenthatisfine,but thebriefconsideration,114 CH9 PHASE II AND PHASE III CLINICAL STUDIES