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

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CHAPTER 7 ST 520, A. TSIATIS and D. Zhang Because Tn = (p1 − p2 + ∆A) � p1(1−p1) n1 ≈ p2(1−p2) + straightforward calculations can be used to show that and Hence Tn E(Tn) (π1=π2=π) ≈ (π1=π2=π) ∼ N and the non-centrality parameter equals If n1 = n2 = n/2, then To get the desired power, we solve or φ(·) = n2 p1 − p2 + ∆A � π1(1−π1) n1 ∆A � π(1 − π) � 1 1 + n1 n2 var(Tn) (π1=π2=π) ≈ 1. ⎛ φ(·) = ⎜ ∆A ⎜ ⎝ � π(1 − π) � 1 1 + n1 n2 ∆A � π(1 − π) � 1 1 + n1 n2 ∆A � π(1 − π) � �. 4 n ∆A � π(1 − π) � � = Zα + Zβ 4 n �. , π2(1−π2) + �, n2 ⎞ ⎟ �, 1⎟ ⎠ , n = (Zα + Zβ) 2 × 4π(1 − π) ∆2 . (7.15) A Generally, it requires larger sample sizes to establish equivalency because the tolerable limit ∆A that the regulatory agency will agree to is small. For example, a pharmaceutical company has developed a new drug that they believe has similar effects to drugs already approved and decides to conduct an equivalency trial to get approval from the FDA to market the new drug. Suppose the clinical trial that was used to demonstrate that the positive control was significantly better than placebo had a 95% confidence interval for ∆ (treatment difference) that ranged from .10- .25. Conservatively, one can only be relatively confident that this new treatment has a response rate that exceeds the response rate of placebo by .10. Therefore the FDA will only allow a new PAGE 116
CHAPTER 7 ST 520, A. TSIATIS and D. Zhang treatment to be declared equivalent to the positive control if the company can show that their new drug has a response rate that is no worse than the response rate of the positive control minus .05. Thus they require a randomized two arm equivalency trial to compare the new drug to the positive control with a type I error of α = .05. The response rate of the positive control is about .30. (This estimate will be used for planning purposes). The company believes their drug is similar but probably not much better than the positive control. Thus, they want to have good power, say 90%, that they will be successful (i.e. be able to declare equivalency by rejecting H0) if, indeed, their drug was equally efficacious. Thus they use formula (7.15) to derive the sample size or 1432 patients per treatment arm. n = (1.64 + 1.28)2 × 4 × .3 × .7 (.05) 2 PAGE 117 = 2864,
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ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

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