Temporal Properties of Vaccine Effectiveness Measures in Presence of Multiple Pathogen Variants and Multiple Vaccines

TL;DR

This paper investigates how vaccine effectiveness measures behave over time in complex scenarios with multiple pathogen variants and vaccines, providing new definitions, theoretical insights, and practical tools for study design.

Contribution

It introduces variant-specific and relative VE measures for multi-variant, multi-vaccine contexts, analyzes their temporal properties, and offers sample size calculators and an R package for study planning.

Findings

All VE measures are time-varying for all-or-none vaccines in multi-variant scenarios.

Most VE measures are time-varying for leaky vaccines, except those based on incidence rate ratios.

Practical implications for VE study designs and sample size calculations are discussed.

Abstract

Vaccine effectiveness (VE) is typically defined as incidence rate ratio, cumulative-risk ratio, or odds ratio. The VE based on incidence rate ratio is known to be time-invariant over the study period for leaky action vaccines and, the VE based on cumulative-risk ratio is time-invariant for all-or-none action vaccines. Consequently, these VE measures are recommended as appropriate measures of VE for leaky and all-or-none vaccines, respectively. However, in diseases with multiple pathogen variants and multiple vaccines, investigators may also be interested in variant-specific VE of a vaccine, the relative VE of a vaccine against two variants, or the relative VE of different vaccines against a given variant. In this multi-variant and multi-vaccine scenario, the temporal properties of the aforementioned VE measures have not been studied entirely yet. Furthermore, no general-purpose sample size calculator is available for either studies that intend to estimate variant-specific VE or relative VE. As a solution, we define variant-specific and relative VE measures while accounting for multiple competing pathogen variants. We then propose a generic mode of action for all-or-none vaccines in a multi-variant setting. Subsequently, we evaluate the conditions and the extent to which various VE measures can be time-varying. We show that every VE measure is time-varying for all-or-none action vaccines in a multi-variant and multi-vaccine scenario. For leaky vaccines, we show that all measures other than those based on incidence rate ratios are time-varying. We discuss the practical implications of these results on VE studies in the context of the commonly used cohort, cumulative case-control, and test-negative study designs. Lastly, for the multi-variant and multi-vaccine scenario, we implement sample size calculations for both variant-specific and relative VE in an R package and an online calculator.