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

CHAPTER 10 ST 520, A. TSIATIS and D. Zhang
although the difference between the two tests is inconsequential with equal randomization and
large samples. What we discussed above is essentially the approach taken for sample size calcu-
lations used in Chapter 6 of the notes. The important point here is that power is driven by the
amount of statistical information we have regarding the parameter of interest from the available
data. The more data the more information we have. To achieve power 1 − β to detect the
clinically important difference ∆A using a two-sided test at the α level of significance means that
we need to have collected enough data so that the statistical information equals
� Zα/2 + Zβ
∆A
Let us examine how issues of power and information relate to group-sequential tests. If we are
planning to conduct K interim analyses after equal increments of information, then the power
� 2
.
of the group-sequential test to detect the alternative ∆ = ∆A is given by
1 − P∆=∆A {|T(t1)| < b1, . . .,|T(tK)| < bK}.
In order to compute probabilities of events such as that above we need to know the joint distri-
bution of the vector {T(t1), . . .,T(tK)} under the alternative hypothesis ∆ = ∆A.
It will be useful to consider the maximum information at the final analysis which we will denote
as MI. A K-look group-sequential test with equal increments of information and with maximum
information MI would have interim analyses conducted at times tj where j ×MI/K information
has occurred; that is,
I(tj, ∆A) = j × MI/K, j = 1, . . .,K. (10.8)
Using the results (10.2)-(10.4) and (10.8) we see that the joint distribution of {T(t1), . . .,T(tK)},
under the alternative hypothesis ∆ = ∆A, is a multivariate normal with mean vector
�
j × MI
∆A , j = 1, . . .,K
K
and covariance matrix VT given by (10.6). If we define
√
δ = ∆A MI,
then the mean vector is equal to
� � �
1 2 K − 1
(δ , δ , . . .,δ , δ). (10.9)
K K K
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