Differences between Frequentist and Bayesian inference in routine surveillance for influenza vaccine effectiveness: a test-negative case-control study

Michael L. Jackson, Jill Ferdinands, Mary Patricia Nowalk, Richard K. Zimmerman, Burney Kieke, Manjusha Gaglani, Kempapura Murthy, Joshua G. Petrie, Emily T. Martin, Jessie R. Chung, Brendan Flannery, Lisa A. Jackson

Routine influenza vaccine effectiveness (VE) surveillance networks use frequentist methods to estimate VE. With data from more than a decade of VE surveillance from diverse global populations now available, using Bayesian methods to explicitly account for this knowledge may be beneficial. This study explores differences between Bayesian vs. frequentist inference in multiple seasons with varying VE. We used data from the United States Influenza Vaccine Effectiveness (US Flu VE) Network. Ambulatory care patients with acute respiratory illness were enrolled during seasons of varying observed VE based on traditional frequentist methods. We estimated VE against A(H1N1)pdm in 2015/16, dominated by A(H1N1)pdm; against A(H3N2) in 2017/18, dominated by A(H3N2); and compared VE for live attenuated influenza vaccine (LAIV) vs. inactivated influenza vaccine (IIV) among children aged 2-17 years in 2013/14, also dominated by A(H1N1)pdm. VE was estimated using both frequentist and Bayesian methods using the test-negative design. For the Bayesian estimates, prior VE distributions were based on data from all published test-negative studies of the same influenza type/subtype available prior to the season of interest. Across the three seasons, 16,342 subjects were included in the analyses. For 2015/16, frequentist and Bayesian VE estimates were essentially identical (41% each). For 2017/18, frequentist and Bayesian estimates of VE against A(H3N2) viruses were also nearly identical (26% vs. 23%, respectively), even though the presence of apparent antigenic match could potentially have pulled Bayesian estimates upward. Precision of estimates was similar between methods in both seasons. Frequentist and Bayesian estimates diverged for children in 2013/14. Under the frequentist approach, LAIV effectiveness was 62 percentage points lower than IIV, while LAIV was only 27 percentage points lower than IIV under the Bayesian approach. Bayesian estimates of influenza VE can differ from frequentist estimates to a clinically meaningful degree when VE diverges substantially from previous seasons.