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

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CHAPTER 10 ST 520, A. TSIATIS and D. Zhang The shape of these boundaries are also contrasted in the following figure. Bounday Figure 10.1: Pocock and O’Brien-Fleming Boundaries -6 -4 -2 0 2 4 6 1 2 3 4 5 Interim Analysis Time PAGE 180 Pocock O’Brien-Fleming
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. PAGE 181 ∆A � 2 .
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TABLE OF CONTENTS ST 520, A. Tsiati
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ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

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