Journal
STATISTICS IN MEDICINE
Volume 29, Issue 9, Pages 982-993Publisher
WILEY
DOI: 10.1002/sim.3846
Keywords
active-controlled trial; allocation ratio; ancillary parameter
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Funding
- Commonwealth Fund [20070769]
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This study presents constrained maximum likelihood derivations of the design parameters of noninferiority trials for binary outcomes with the margin defined on the odds ratio (psi) or risk-difference (delta) scale. The derivations show that, for trials in which the group-specific response rates are equal under the point-alternative hypothesis, the common response rate, pi(N), is a fixed design parameter whose value lies between the control and experimental rates hypothesized at the point-null, {pi(C),pi(E)}. We show that setting pi(N) equal to the value of pi(C) that holds under H-0 underestimates the overall sample size requirement. Given {pi(C),psi} or {pi(C),delta} and the type I and II error rates, or algorithm finds clinically meaningful design values of pi(N), and the corresponding minimum asymptotic sample size, N = n(E) + n(C), and optimal allocation ratio, gamma = n(E)/n(C). We find that optimal allocations are increasingly imbalanced as psi increases, with gamma(psi) < 1 and gamma(delta) approximate to 1/gamma(psi), and that ranges of allocation ratios map to the minimum sample size. The latter characteristic allows trialists to consider trade-offs between optimal allocation at a smaller N and a preferred allocation at a larger N. For designs with relatively large margins (e.g. psi > 2.5), trial results that are presented on both scales will differ in power, with more power lost if the study is designed on the risk-difference scale and reported on the odds ratio scale than vice versa. Copyright (C) 2010 John Wiley & Sons, Ltd.
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