TY - JOUR

T1 - Optimal allocation to maximize the power of two-sample tests for binary response

AU - Azriel, D.

AU - Mandel, M.

AU - Rinott, Y.

PY - 2012/3

Y1 - 2012/3

N2 - We study allocations that maximize the power of tests of equality of two treatments having binary outcomes. When a normal approximation applies, the asymptotic power is maximized by minimizing the variance, leading to a Neyman allocation that assigns observations in proportion to the standard deviations. This allocation, which in general requires knowledge of the parameters of the problem, is recommended in a large body of literature. Under contiguous alternatives the normal approximation indeed applies, and in this case the Neyman allocation reduces to a balanced design. However, when studying the power under a noncontiguous alternative, a large deviations approximation is needed, and the Neyman allocation is no longer asymptotically optimal. In the latter case, the optimal allocation depends on the parameters, but is rather close to a balanced design. Thus, a balanced design is a viable option for both contiguous and noncontiguous alternatives. Finite sample studies show that a balanced design is indeed generally quite close to being optimal for power maximization. This is good news as implementation of a balanced design does not require knowledge of the parameters.

AB - We study allocations that maximize the power of tests of equality of two treatments having binary outcomes. When a normal approximation applies, the asymptotic power is maximized by minimizing the variance, leading to a Neyman allocation that assigns observations in proportion to the standard deviations. This allocation, which in general requires knowledge of the parameters of the problem, is recommended in a large body of literature. Under contiguous alternatives the normal approximation indeed applies, and in this case the Neyman allocation reduces to a balanced design. However, when studying the power under a noncontiguous alternative, a large deviations approximation is needed, and the Neyman allocation is no longer asymptotically optimal. In the latter case, the optimal allocation depends on the parameters, but is rather close to a balanced design. Thus, a balanced design is a viable option for both contiguous and noncontiguous alternatives. Finite sample studies show that a balanced design is indeed generally quite close to being optimal for power maximization. This is good news as implementation of a balanced design does not require knowledge of the parameters.

KW - Adaptive design

KW - Asymptotic power

KW - Bahadur efficiency

KW - Neyman allocation

KW - Pitman efficiency

UR - http://www.scopus.com/inward/record.url?scp=84857583848&partnerID=8YFLogxK

U2 - 10.1093/biomet/asr077

DO - 10.1093/biomet/asr077

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AN - SCOPUS:84857583848

SN - 0006-3444

VL - 99

SP - 101

EP - 113

JO - Biometrika

JF - Biometrika

IS - 1

ER -