Article

Noninferiority trial designs for odds ratios and risk differences

Department of Epidemiology & Biostatistics, University of California San Francisco, 185 Berry Street, Suite 5700, San Francisco, CA 94107-1762, U.S.A..
Statistics in Medicine (Impact Factor: 2.04). 01/2010; 29(9):982-93. DOI: 10.1002/sim.3846
Source: PubMed

ABSTRACT 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 (ψ) or risk-difference (δ) 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, π(N), is a fixed design parameter whose value lies between the control and experimental rates hypothesized at the point-null, {π(C), π(E)}. We show that setting π(N) equal to the value of π(C) that holds under H(0) underestimates the overall sample size requirement. Given {π(C), ψ} or {π(C), δ} and the type I and II error rates, or algorithm finds clinically meaningful design values of π(N), and the corresponding minimum asymptotic sample size, N=n(E)+n(C), and optimal allocation ratio, γ=n(E)/n(C). We find that optimal allocations are increasingly imbalanced as ψ increases, with γ(ψ)<1 and γ(δ)≈1/γ(ψ), 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. ψ>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.

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