When comparing the risk of a post-infection binary outcome, for example, hospitalisation, for two variants of an infectious pathogen, it is important to adjust for calendar time of infection. Typically, the infection time is unknown and positive test time used as a proxy for it. Positive test time may also be used when assessing how risk of the outcome changes over calendar time. We show that if time from infection to positive test is correlated with the outcome, the risk conditional on positive test time is a function of the trajectory of infection incidence. Hence, a risk ratio adjusted for positive test time can be quite different from the risk ratio adjusted for infection time. We propose a simple sensitivity analysis that indicates how risk ratios adjusted for positive test time and infection time may differ. This involves adjusting for a shifted positive test time, shifted to make the difference between it and infection time uncorrelated with the outcome. We illustrate this method by reanalysing published results on the relative risk of hospitalisation following infection with the Alpha versus pre-existing variants of SARS-CoV-2. Results indicate the relative risk adjusted for infection time may be lower than that adjusted for positive test time.
Bibliographical noteFunding Information:
This work was funded by UKRI Medical Research Council: core Unit funding (Seaman: MC UU 00002/10; De Angelis, Presanis: MC UU 00002/11), JUNIPER consortium (Overton, Pascall: MR/V038613/1), MRC UKRI / DHSC NIHR COVID-19 rapid response call (Presanis, De Angelis, Nyberg: MC PC 19074); by the Wellcome Trust and Royal Society (Overton, 202562/Z/16/Z); by the NIHR Health Protection Unit in Behavioural Science and Evaluation (De Angelis); and was supported by the NIHR Cambridge Biomedical Research Centre (BRC-1215-20014). The views expressed are those of the authors and not necessarily those of UKHSA, the NHS, the NIHR or the Department of Health and Social Care.
© The Author(s) 2022.
- epidemic phase bias
- selection bias