Statistical Methods in Medical Research 4ed

636 Clinical trials
independent, and can be analysed by standard methods, such as a two-sample t
test. If the serial observations are subject to trend or to serial correlation, the
effects of these disturbances will be reflected by inflation of the random error. If
necessary, the effect of trend could be reduced by a systematic design such as
permuted blocks, each containing a random permutation of the treatments.
However, such designs make it more difficult to impose masking of treatment
identity, and this may be particularly important in a single-patient trial requiring
a high level of patient cooperation. The use of permutation tests (§10.6) in such
circumstances is discussed by Senn (1993, §7.4.2).
In general, it seems unlikely that n-of-1 trials can be conducted on a sufficiently
wide scale to provide personal guidance on treatment choice for all
patients, and it is therefore likely that this choice will usually be made on the
basis of evidence provided by orthodox trials on groups of patients.
Equivalence trials
The aim in an equivalence trial is not to detect possible differences in efficacy, but
rather to show that treatments are, within certain narrow limits, equally effective.
This need arises in two different contexts. A bioequivalence trial is a Phase I
study, conducted within the pharmaceutical industry, to compare two different
formulations or methods of administration of a drug. The intention is that the
formulations should be regarded as interchangeable. The response variable will
be based on pharmacokinetic studies, where, for each subject, the plasma concentration
of the drug is measured during a short period after administration and
some key feature of the concentration±time curve, such as the area under the
curve, is recorded. Such variables are often skewly distributed, and a log transformation
may simplify the analysis. Requirements are often based on the ratio
of the pharmacokinetic responses for different formulations, and these can
conveniently be expressed in terms of the difference between the means of the
logarithmic transforms, which are required to lie within certain limits. Bioequivalence
trials usually involve very small numbers of subjects and often follow a
simple cross-over design, with suitable precautions to avoid carry-over.
The other scenario is a trial to compare the efficacies of two therapeutic
regimes, where a new treatment, T, is compared against a standard, S. Interest
centres on whether the response for S differs from that for T by less than some
small margin. The comparison may be one-sided, in that a small disadvantage to
T may be tolerated because it produces less severe side-effects than S, or is
otherwise more acceptable, whereas no limit need be placed on a possible
advantage of T over S; the term non-inferiority trial is often used for this
situation.
An important point is that a test of the null hypothesis of zero difference is
completely irrelevant, partly because a small non-zero true difference may be