ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

CHAPTER 10 ST 520, A. TSIATIS and D. Zhang
10.5 Power and sample size in terms of information
We have discussed the construction of group-sequential tests that have a pre-specified level of
significance α. We also need to consider the effect that group-sequential tests have on power and
its implications on sample size. To set the stage, we first review how power and sample size are
determined with a single analysis using information based criteria.
As shown earlier, the distribution of the test statistic computed at a specific time t; namely T(t),
under the null hypothesis, is
T(t) ∆=0
∼ N(0, 1)
and for a clinically important alternative, say ∆ = ∆A is
T(t) ∆=∆A
∼ N(∆AI 1/2 (t, ∆A), 1),
where I(t, ∆A) denotes statistical information which can be approximated by [se{ ˆ ∆(t)}] −2 , and
∆AI 1/2 (t, ∆A) is the noncentrality parameter. In order that a two-sided level-α test have power
1 − β to detect the clinically important alternative ∆A, we need the noncentrality parameter
or
∆AI 1/2 (t, ∆A) = Zα/2 + Zβ,
I(t, ∆A) =
� Zα/2 + Zβ
∆A
� 2
. (10.7)
From this relationship we see that the power of the test is directly dependent on statistical
information. Since information is approximated by [se{ ˆ ∆(t)}] −2 , this means that the study
should collect enough data to ensure that
[se{ ˆ ∆(t)}] −2 =
� Zα/2 + Zβ
Therefore one strategy that would guarantee the desired power to detect a clinically important
difference is to monitor the standard error of the estimated difference through time t as data
were being collected and to conduct the one and only final analysis at time tF where
� �2 Zα/2 + Zβ
[se{ ˆ ∆(t F )}] −2 =
using the test which rejects the null hypothesis when
∆A
|T(t F )| ≥ Zα/2.
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∆A
� 2
.