Heterogeneity in disease risk induces falling vaccine protection with rising disease incidence

ABSTRACT

This paper is concerned with the analysis of phase 3 vaccine trials. In a randomized controlled trial, a representative sample of a population is given a vaccine and a matched sample is given a placebo. These individuals are followed for a stipulated length of time, while infection (or disease) occurrences are registered. Vaccine efficacy is then calculated to measure the reduction in disease rate (or risk) attributed to the vaccine. Seemingly very reasonable, this procedure often results in the most disparate estimates when conducted in different parts of the world. Here, we argue that this is due to cohort selection acting on the trial participants as follows. The more susceptible individuals are infected first, leaving behind a pool whose mean susceptibility decreases over time. As a result, infection rates decrease, and this effect is stronger in the control group, provided that the vaccine reduces susceptibility. Therefore, any direct measure of vaccine efficacy is expected to decrease as the trial progresses, and this happens faster in settings where the intensity of pathogen exposure is higher. We propose an analytical scheme that takes this phenomenon into account while estimating efficacy more consistently across settings. We provide analytical results concerning the dependence of vaccine efficacy on the intensity of pathogen exposure as well as on the mean and variance of the distribution of disease risk.

KEYWORDS:

• Mathematical epidemiology
• vaccine efficacy
• individual heterogeneity
• cohort selection
• clinical trials

Acknowledgments

We thank two anonymous reviewers for constructive comments. M. Gabriela M. Gomes is grateful to the Mathematical Biosciences Institute, Ohio State University, particularly Marty Golubitsky, for hosting during development of the theory on ‘equally-variant’ disease risks introduced here.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The study was supported by Fundação para a Ciência e aTecnologia [UID/MAT/04561/2013]; Fundação para a Ciência e a Tecnologia [UID/MAT/04561/2013]; Fundação para a Ciência e a Tecnologia (FCT – IF/01346/2014); and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES – Science without Borders).