Causal Vaccine Effects on Post-infection Outcomes in the Naturally Infected

Abstract

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.

Figures (3)

• Figure 1: Power of a hypothesis test to reject the null hypothesis of no effect of $Z$ on $Y$ under different principal strata mixtures (rows) based on various effect estimators (columns) and under different principal stratum-specific effect sizes (axes of each figure). The horizontal axis is the risk difference (RD) in the Protected strata; the vertical axis is the RD in the Doomed strata. Grayed areas indicate regions where the effect in the Doomed exceeds the effect in the Protected stratum, which are unlikely in vaccine contexts. Contours indicate the size of each effect and outlined regions indicate where tests had at least 80% power to detect the difference. The final column shows these regions for each estimator.
• Figure 2: Sensitivity analysis for PROVIDE data. The green line shows the estimated additive effect as a function of the sensitivity parameter $epsilon$.
• Figure 3: The observed vaccinated (left) and placebo (right) groups can be divided (solid lines) based on observed infection status ($S = 1$, top = infected, $S = 0$, bottom = uninfected). Under monotonicity, these observed strata are mixtures of basic principal strata.

Theorems & Definitions (40)

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