School-located influenza vaccination and community-wide indirect effects: reconciling mathematical models to epidemiologic models

Background Mathematical models and empirical epidemiologic studies (e.g., randomized and observational studies) are complementary tools but may produce conflicting results for a given research question. We used sensitivity analyses and bias analyses to explore such discrepancies in a study of the indirect effects of influenza vaccination. Methods We fit an age-structured, deterministic, compartmental model to estimate indirect effects of a school-based influenza vaccination program in California that was evaluated in a previous matched cohort study. To understand discrepancies in their results, we used 1) a model with constrained parameters such that projections matched the cohort study; and 2) probabilistic bias analyses to identify potential biases (e.g., outcome misclassification due to incomplete influenza testing) that, if corrected, would align the empirical results with the mathematical model. Results The indirect effect estimate (% reduction in influenza hospitalization among older adults in intervention vs. control) was 22.3% (95% CI 7.6% – 37.1%) in the cohort study but only 1.6% (95% Bayesian credible intervals 0.4 – 4.4%) in the mathematical model. When constrained, mathematical models aligned with the cohort study when there was substantially lower pre-existing immunity among school-age children and older adults. Conversely, empirical estimates corrected for potential bias aligned with mathematical model estimates only if influenza testing rates were 15-23% lower in the intervention vs. comparison site. Conclusions Sensitivity and bias analysis can shed light on why results of mathematical models and empirical epidemiologic studies differ for the same research question, and in turn, can improve study and model design. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study was supported by the Flu Lab () through a grant (Award number: 20142281, PI: AR) awarded to the University of California, Berkeley and by the National Institute of Allergy and Infectious Diseases of the National Institutes of Health under Award Number K01AI141616 (PI: Jade Benjamin-Chung). Jade Benjamin-Chung is a Chan Zuckerberg Biohub Investigator. Nimalan Arinaminpathy was supported by FluLab. He also acknowledges funding from the MRC Centre for Global Infectious Disease Analysis (reference MR/R015600/1), jointly funded by the UK Medical Research Council (MRC) and the UK Foreign, Commonwealth & Development Office (FCDO), under the MRC/FCDO Concordat agreement and is also part of the EDCTP2 programme supported by the European Union; and acknowledges funding by Community Jameel. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data produced are available online at: