Statistical Methods in Medical Research 4ed

18.3 Planning a Phase III trial 599
level a in a test of the null hypothesis that d ˆ 0, and for the power 1 b against
the alternative value d ˆ d1. With some assumptions about the distribution of
the estimate of d, in particular its variance, the sample size is determined by
formulae such as (4.41).
As noted in §4.6, sample-size determination is an inexact science, if only
because the choice of d1, a and b are to an extent arbitrary, and the variability
of the test statistic may be difficult to estimate in advance. Nevertheless, the
exercise gives the investigators some idea of the sensitivity likely to be achieved
by a trial of any specific size. We note here some additional points that may be
relevant in a clinical trial.
1 In a chronic disease study the primary response variable may be the incidence
over time of some adverse event, such as the relapse of a patient with malignant
disease, the reoccurrence of a cardiovascular event or the patient's death. The
precision of a treatment comparison is determined largely by the expected
number of events in a treatment group, and this can be increased either by
enrolling more patients or by lengthening the follow-up time. The latter choice
has the advantage of extending the study over a longer portion of the natural
course of the disease, but the disadvantage of delaying the end of the trial.
2 Many early trials can now be seen to have been too small, resulting often in
the dismissal of new treatments because of non-significant results when the
test had too low a power to detect worthwhile effects (Pocock et al., 1978).
Yusuf et al. (1984) have argued strongly in favour of large, simple trials, on
the grounds that large trials are needed in conditions such as cardiovascular
disease, where the event rate is low but relatively small reductions would be
beneficial and cost-effective. Substantial increases in sample size are made
more feasible if protocols are `simple' and the administrative burdens on the
doctors are minimized. However, as Powell-Tuck et al. (1986) demonstrate,
small trials, efficiently analysed, may sometimes provide evidence sufficiently
conclusive to affect medical practice.
3 As noted in §6.4, some of the uncertainties in the determination of sample size
may be resolved by a Bayesian approach (Spiegelhalter & Freedman, 1986;
Spiegelhalter et al., 1994). In particular, a prior distribution may be introduced
for the difference parameter d, as indicated in §6.4. Investigators are
likely to differ in their prior assessments, and a compromise may be necessary.
Calculations may be performed with alternative prior distributions,
representing different degrees of enthusiasm or scepticism about a possible
treatment effect. In a Bayesian approach, inference about the parameter
value should be expressed in terms of the posterior distribution. Suppose
that a value dS > 0 would be regarded as indicating superiority of one of the
treatments. The requirement that the posterior probability that d > dS should
be high will determine a critical value XS for the relevant test statistic X. The
predictive probability that X will exceed XS may be determined by the