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

CHAPTER 10 ST 520, A. TSIATIS and D. Zhang
A group-sequential level-α test from the Wang-Tsiatis family rejects the null hypothesis at the
first time tj, j = 1, . . ., K where
|T(tj)| ≥ c(α, K, Φ)j (Φ−.5) .
For the alternative HA : ∆ = ∆A and maximum information MI, the power of this test is
K�
1 − Pδ[ {|T(tj)| < c(α, K, Φ)j (Φ−.5) }],
j=1
√
where δ = ∆A MI, and {T(t1), . . ., T(tK)} is multivariate normal with mean vector (10.9) and
covariance matrix VT given by (10.6). For fixed values of α, K, and Φ, the power is an increasing
function of δ which can be computed numerically using recursive integration. Consequently, we
can solve for the value δ that gives power 1 − β above. We denote this solution by δ(α, K, Φ, β).
Remark: The value δ plays a role similar to that of a noncentrality parameter.
√
Since δ = ∆A MI, this implies that a group-sequential level-α test with shape parameter Φ,
computed at equal increments of information up to a maximum of K times needs the maximum
information to equal
or
√
∆A MI = δ(α, K, Φ, β)
MI =
� δ(α, K, Φ, β)
to have power 1 − β to detect the clinically important alternative ∆ = ∆A.
10.5.1 Inflation Factor
A useful way of thinking about the maximum information that is necessary to achieve prespecified
power with a group-sequential test is to relate this to the information necessary to achieve
prespecified power with a fixed sample design. In formula (10.7), we argued that the information
necessary to detect the alternative ∆ = ∆A with power 1 − β using a fixed sample test at level
α is
I FS =
∆A
� Zα/2 + Zβ
∆A
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� 2
� 2
.