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Randomization for the susceptibility effect of an infectious disease intervention

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Abstract

Randomized trials of infectious disease interventions, such as vaccines, often focus on groups of connected or potentially interacting individuals. When the pathogen of interest is transmissible between study subjects, interference may occur: individual infection outcomes may depend on treatments received by others. Epidemiologists have defined the primary parameter of interest—called the “susceptibility effect”—as a contrast in infection risk under treatment versus no treatment, while holding exposure to infectiousness constant. A related quantity—the “direct effect”—is defined as an unconditional contrast between the infection risk under treatment versus no treatment. The purpose of this paper is to show that under a widely recommended randomization design, the direct effect may fail to recover the sign of the true susceptibility effect of the intervention in a randomized trial when outcomes are contagious. The analytical approach uses structural features of infectious disease transmission to define the susceptibility effect. A new probabilistic coupling argument reveals stochastic dominance relations between potential infection outcomes under different treatment allocations. The results suggest that estimating the direct effect under randomization may provide misleading conclusions about the effect of an intervention—such as a vaccine—when outcomes are contagious. Investigators who estimate the direct effect may wrongly conclude an intervention that protects treated individuals from infection is harmful, or that a harmful treatment is beneficial.

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Acknowledgements

We are especially grateful to Michael Hudgens and M. Elizabeth Halloran for helpful comments. In addition, we thank P. M. Aronow, Xiaoxuan Cai, Ted Cohen, Soheil Eshghi, Gregg S. Gonsalves, Eben Kenah, Zehang Li, Wen Wei Loh, Sida Peng, Fredrik Sävje, Yushuf Sharker, and Daniel Weinberger for helpful comments. This work was supported by NIH grants NICHD DP2 HD091799-01 and NIDA R36 DA042643.

Funding

This work was supported by NIH grants NICHD DP2 HD091799-0 and NIDA R36 DA042643.

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Authors and Affiliations

  1. Department of Statistics, University of Illinois Urbana-Champaign, Champaign, USA

    Daniel J. Eck

  2. Department of Public Health Sciences, Biological Sciences Division, The University of Chicago, Chicago, USA

    Olga Morozova

  3. Department of Biostatistics, Yale School of Public Health, New Haven, USA

    Forrest W. Crawford

  4. Department of Statistics and Data Science, Yale University, New Haven, USA

    Forrest W. Crawford

  5. Department of Ecology and Evolutionary Biology, Yale University, New Haven, USA

    Forrest W. Crawford

  6. Yale School of Management, New Haven, USA

    Forrest W. Crawford

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  1. Daniel J. Eck
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Correspondence to Daniel J. Eck.

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Eck, D.J., Morozova, O. & Crawford, F.W. Randomization for the susceptibility effect of an infectious disease intervention. J. Math. Biol. 85, 37 (2022). https://doi.org/10.1007/s00285-022-01801-8

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  • DOI: https://doi.org/10.1007/s00285-022-01801-8

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