Confidence limits for the averted infections ratio estimated via the counterfactual placebo incidence rate.

David T Dunn,David V Glidden,Oliver T Stirrup

doi:10.1515/scid-2021-0002

Abstract

ObjectivesThe averted infections ratio (AIR) is a novel measure for quantifying the preservation-of-effect in active-control non-inferiority clinical trials with a time-to-event outcome. In the main formulation, the AIR requires an estimate of the counterfactual placebo incidence rate. We describe two approaches for calculating confidence limits for the AIR given a point estimate of this parameter, a closed-form solution based on a Taylor series expansion (delta method) and an iterative method based on the profile-likelihood.MethodsFor each approach, exact coverage probabilities for the lower and upper confidence limits were computed over a grid of values of (1) the true value of the AIR (2) the expected number of counterfactual events (3) the effectiveness of the active-control treatment.ResultsFocussing on the lower confidence limit, which determines whether non-inferiority can be declared, the coverage achieved by the delta method is either less than or greater than the nominal coverage, depending on the true value of the AIR. In contrast, the coverage achieved by the profile-likelihood method is consistently accurate.ConclusionsThe profile-likelihood method is preferred because of better coverage properties, but the simpler delta method is valid when the experimental treatment is no less effective than the control treatment. A complementary Bayesian approach, which can be applied when the counterfactual incidence rate can be represented as a prior distribution, is also outlined.

Highlights

In a series of papers we have considered the analysis of active-control non-inferiority trials with a time-to-event outcome in the context of HIV prevention trials (Dunn and Glidden 2019; Dunn et al 2018; Glidden, Stirrup, and Dunn 2020)
We describe two approaches for calculating confidence limits for the averted infections ratio (AIR) given a point estimate of this parameter, a closed-form solution based on a Taylor series expansion and an iterative method based on the profile-likelihood
Focussing on the lower confidence limit, which determines whether non-inferiority can be declared, the coverage achieved by the delta method is either less than or greater than the nominal coverage, depending on the true value of the AIR

Summary

Introduction

In a series of papers we have considered the analysis of active-control non-inferiority trials with a time-to-event outcome in the context of HIV prevention trials (Dunn and Glidden 2019; Dunn et al 2018; Glidden, Stirrup, and Dunn 2020). T. Dunn et al.: Confidence limits for the AIR observed in trial subjects if they had received no treatment (counterfactual placebo arm) or (b) the effectiveness of the control arm relative to the counterfactual placebo arm. Dunn et al.: Confidence limits for the AIR observed in trial subjects if they had received no treatment (counterfactual placebo arm) or (b) the effectiveness of the control arm relative to the counterfactual placebo arm With this information, in combination with the observed incidence rates in the control and experimental arms, we can estimate a measure called the averted infections ratio (AIR). In the context of non-inferiority trials, it is a natural criterion for assessing the degree to which the experimental treatment preserves the effect of the control treatment relative to no treatment (“preservation-of-effect”) (Ghosh et al 2011; Pigeot et al 2003; Snapinn and Jiang 2008). We consider the derivation of confidence limits for the AIR when it is estimated via the counterfactual placebo incidence

Objectives

Methods

Results

Conclusion