Randomization for the susceptibility effect of an infectious disease intervention

Daniel J. Eck, Olga Morozova, Forrest W. Crawford

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number37
JournalJournal of Mathematical Biology
Issue number4
StatePublished - Oct 2022


  • Contagion
  • Direct effect
  • Interference
  • Probabilistic coupling
  • Transmission model
  • Vaccine

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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