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. 2021 Nov 11;50(4):848-870.
doi: 10.1080/02664763.2021.1998391. eCollection 2023.

A more powerful test for three-arm non-inferiority via risk difference: Frequentist and Bayesian approaches

Erina Paul  1 , Ram C Tiwari  2 , Shrabanti Chowdhury  1   3 , Samiran Ghosh  1   3
Affiliations

A more powerful test for three-arm non-inferiority via risk difference: Frequentist and Bayesian approaches

Erina Paul et al. J Appl Stat. .

Abstract

Necessity for finding improved intervention in many legacy therapeutic areas are of high priority. This has the potential to decrease the expense of medical care and poor outcomes for many patients. Typically, clinical efficacy is the primary evaluating criteria to measure any beneficial effect of a treatment. Albeit, there could be situations when several other factors (e.g. side-effects, cost-burden, less debilitating, less intensive, etc.) which can permit some slightly less efficacious treatment options favorable to a subgroup of patients. This often leads to non-inferiority (NI) testing. NI trials may or may not include a placebo arm due to ethical reasons. However, when included, the resulting three-arm trial is more prudent since it requires less stringent assumptions compared to a two-arm placebo-free trial. In this article, we consider both Frequentist and Bayesian procedures for testing NI in the three-arm trial with binary outcomes when the functional of interest is risk difference. An improved Frequentist approach is proposed first, which is then followed by a Bayesian counterpart. Bayesian methods have a natural advantage in many active-control trials, including NI trial, as it can seamlessly integrate substantial prior information. In addition, we discuss sample size calculation and draw an interesting connection between the two paradigms.

Keywords: Assay sensitivity; Dirichlet prior; conditional approach; non-inferiority margin; risk difference.

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Conflict of interest statement

No potential conflict of interest was reported by the author(s).

Figures

Figure 1.
Figure 1.
Power curves for different θ under Bayesian conjugate prior on the top left (a) and under Frequentist and Bayesian normal approximation on the top right (b). Comparison of Frequentist, Bayesian non-informative, and informative power curves at the bottom left (c). Comparison of power curves under CBP, PUP, and DP at the bottom right (d).
Figure 2.
Figure 2.
Comparison of informative vs. non-informative power curves under conjugate Beta prior, θ=0.8.
Figure 3.
Figure 3.
Power curves for different allocations, θ=0.8.
See this image and copyright information in PMC

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