Approximating instantaneous vaccine efficacy from cumulative vaccine efficacy

Few methods exist to estimate vaccine efficacy and its decay following immunisation. Existing methods are largely based on survival analyses such as Poisson or Cox-regression, applied to individual-level data from randomised placebo-controlled trials (RCTs), however, such are often not easily available for analysing pooling evidence across trials. Hence, cumulative vaccine efficacy (VE), the commonly reported endpoint, is implicitly assumed a reasonable proxy for the instantaneous vaccine efficacy (iVE). This assumption is violated if the relative risk (RR) of vaccinated vs unvaccinated is not constant over time, i.e. if vaccine efficacy changes after immunisation. We propose a method to overcome this issue. We use estimates of VE stratified by time since completed immunisation, and estimate time-dependent iVE. We validate the method against simulated data for two forms of vaccine protection: all-or-nothing protection and leaky protection. We illustrate how VE estimates are biased by time-dependent effects in the baseline force of infection and in iVE. Our proposed method improves upon available iVE estimation techniques, particularly if the vaccine induced leaky-like protection and the disease outcome is rare.