Depletion-of-susceptibles bias in influenza vaccine waning studies: how to ensure robust results

Vaccine effectiveness studies are subject to biases due to depletion-of-persons at risk of infection, or at especially high risk of infection, at different rates from different groups (depletion-of-susceptibles bias), a problem that can also lead to biased estimates of waning effectiveness, including spurious inference of waning when none exists. An alternative study design to identify waning is to study only vaccinated persons, and compare for each day the incidence in persons with earlier or later dates of vaccination to assess waning in vaccine protection as a function of vaccination time (namely whether earlier vaccination would result in lower subsequent protection compared to later vaccination). Prior studies suggested under what conditions this alternative would yield correct estimates of waning. Here we define the depletion-of-susceptibles process formally and show mathematically that for influenza vaccine waning studies, a randomised trial or corresponding observational study that compares incidence at a specific calendar time among individuals vaccinated at different times before the influenza season begins will not be vulnerable to depletion-of-susceptibles bias in its inference of waning as a function of vaccination time under the null hypothesis that none exists, and will - if waning does actually occur - underestimate the extent of waning. Such a design is thus robust in the sense that a finding of waning in that inference framework reflects actual waning of vaccine-induced immunity. We recommend such a design for future studies of waning, whether observational or randomised.