title: Noninferiority trial designs for odds ratios and risk differences.
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.
authors.affiliation: Department of Epidemiology & Biostatistics, University of California San Francisco, 185 Berry Street, Suite 5700, San Francisco, CA 94107-1762, U.S.A.. joan@biostat.ucsf.edu
authors.forename: Joan F
authors.initials: JF
authors.lastname: Hilton
mesh_terms: D000465:Algorithms; D056808:Biostatistics; D006526:Hepatitis C / Q000188:drug therapy / Q000821:virology; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016017:Odds Ratio; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D012307:Risk Factors; D018401:Sample Size; D016896:Treatment Outcome