Estimating community-wide indirect effects of influenza vaccination: triangulation using mathematical models and bias analysis

Understanding whether influenza vaccine promotion strategies produce community-wide indirect effects is important for establishing vaccine coverage targets and optimizing vaccine delivery. Empirical epidemiologic studies and mathematical models have been used to estimate indirect effects of vaccines but rarely for the same estimand in the same data set. Using these approaches together could be a powerful tool for triangulation in infectious disease epidemiology because each approach is subject to distinct sources of bias. We triangulated evidence about indirect effects from a school-located influenza vaccination program using 2 approaches: a difference-in-difference (DID) analysis and an age-structured, deterministic, compartmental model. The estimated indirect effect was substantially lower in the mathematical model than in the DID analysis (2.1% [95% Bayesian credible intervals, 0.4%-4.4%] vs 22.3% [7.6%-37.1%]). To explore reasons for differing estimates, we used sensitivity analyses and probabilistic bias analyses. When we constrained model parameters such that projections matched the DID analysis, results only aligned with the DID analysis with substantially lower preexisting immunity among school-age children and older adults. Conversely, DID estimates corrected for potential bias only aligned with mathematical model estimates under differential outcome misclassification. We discuss how triangulation using empirical and mathematical modeling approaches could strengthen future studies.