Adjusting for time of infection or positive test when estimating the risk of a post-infection outcome in an epidemic

When comparing the risk of a post-infection binary outcome, e.g. hospitalisation, for two variants of an infectious pathogen, it is important to adjust for calendar time of infection to avoid the confounding that would occur if the relative incidence of the two variants and the variant-specific risks of the outcome both change over time. Infection time is typically unknown and time of positive test used instead. Likewise, time of positive test may be used instead of infection time when assessing how the risk of the binary outcome changes over calendar time. Here we show that if mean time from infection to positive test is correlated with the outcome, the risk conditional on positive test time depends on whether incidence of infection is increasing or decreasing over calendar time. This complicates interpretation of risk ratios adjusted for positive test time. We also propose a simple sensitivity analysis that indicates how these risk ratios may differ from the risk ratios adjusted for infection time.