title: Bayesian approach for assessing non-inferiority in a three-arm trial with pre-specified margin.
abstract: Non-inferiority trials are becoming increasingly popular for comparative effectiveness research. However, inclusion of the placebo arm, whenever possible, gives rise to a three-arm trial which has lesser burdensome assumptions than a standard two-arm non-inferiority trial. Most of the past developments in a three-arm trial consider defining a pre-specified fraction of unknown effect size of reference drug, that is, without directly specifying a fixed non-inferiority margin. However, in some recent developments, a more direct approach is being considered with pre-specified fixed margin albeit in the frequentist setup. Bayesian paradigm provides a natural path to integrate historical and current trials' information via sequential learning. In this paper, we propose a Bayesian approach for simultaneous testing of non-inferiority and assay sensitivity in a three-arm trial with normal responses. For the experimental arm, in absence of historical information, non-informative priors are assumed under two situations, namely when (i) variance is known and (ii) variance is unknown. A Bayesian decision criteria is derived and compared with the frequentist method using simulation studies. Finally, several published clinical trial examples are reanalyzed to demonstrate the benefit of the proposed procedure.
authors.affiliation: Department of Family Medicine and Public Health Sciences, Wayne State University, Detroit, MI, U.S.A.|Center of Molecular Medicine and Genetics, Wayne State University, Detroit, MI, U.S.A.
authors.forename: Samiran
authors.initials: S
authors.lastname: Ghosh
authors.affiliation: Center of Molecular Medicine and Genetics, Wayne State University, Detroit, MI, U.S.A.|Department of Biostatistics and Epidemiology, Georgia Regents University, Augusta, GA, U.S.A.
authors.forename: Santu
authors.initials: S
authors.lastname: Ghosh
authors.affiliation: Office of Biostatistics, CDER, FDA, Silver Spring, MD, U.S.A.
authors.forename: Ram C
authors.initials: RC
authors.lastname: Tiwari
mesh_terms: D001499:Bayes Theorem; D057186:Comparative Effectiveness Research / Q000379:methods / Q000706:statistics & numerical data; D006801:Humans; D008390:Markov Chains; D012107:Research Design
keywords: Bayesian Method; Jeffreys' prior; Markov chain Monte Carlo; assay sensitivity; non-inferiority margin