Causal Vaccine Effects on Post-infection Outcomes in the Naturally Infected
Understanding vaccine effects on post-infection outcomes is critical for evaluating the full value proposition of a vaccine. However, defining appropriate causal effects on such outcomes is challenging because infection is affected by vaccination. Existing principal stratification approaches focus on the \emph{Doomed} stratum, individuals who would be infected regardless of vaccine receipt. For many relevant outcomes, however, this estimand will understate vaccine benefit by excluding individuals whose adverse post-infection outcomes are improved because vaccination prevented infection. We therefore propose causal estimands for post-infection outcomes in the \emph{Naturally Infected}, individuals who would be infected in absence of vaccine. We derive bounds under minimal assumptions and give point identification results under an exclusion restriction and/or a partial principal ignorability assumption. For point-identified settings, we develop efficient one-step estimators with robustness properties under inconsistent nuisance parameter estimation. We further show under what conditions the same identification functional can be interpreted as targeting an effect among individuals exposed to a sufficiently infectious dose of the pathogen, thereby avoiding direct reliance on cross-world parameters and fundamentally untestable causal assumptions. Simulations show that the bounds are valid but often wide, and that the point estimators perform well when their identifying assumptions hold. In a reanalysis of a rotavirus vaccine trial, marginal and Doomed-stratum analyses showed little evidence of an effect on antibiotic use, whereas analyses targeting the Naturally Infected suggested a protective effect under principal ignorability-based assumptions.