Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022 Oct;31(10):1942-1958.
doi: 10.1177/09622802221107105. Epub 2022 Jun 12.

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

Affiliations

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

Shaun R Seaman et al. Stat Methods Med Res. 2022 Oct.

Abstract

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.

Keywords: COVID-19; epidemic phase bias; selection bias.

PubMed Disclaimer

Conflict of interest statement

Declaration of conflicting interests: The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Figures

Figure 1.
Figure 1.
Illustration of Example 1. Crosses show numbers of infections. Black and white circles represent cases with delays of 1 and 2 days, respectively. In left-hand graph, infection incidence is increasing. A total of 100 individuals are infected on day t2 , of whom half (i.e. 50) test positive with a delay of 2 days on day t . In addition, 150 individuals are infected on day t1 , of whom half (i.e. 75) test positive with a delay of 1 day on day t . So, 75/(50+75)=60 % of the cases who test positive on day t have a delay of 1 day. In right-hand graph, incidence is decreasing. A total of 150 individuals are infected on day t2 , of whom 75 test positive with a delay of 2 days on day t . In addition, 100 individuals are infected on day t1 , of whom 50 test positive with a delay of 1 day on day t . So, 50/(50+75)=40 % of the cases who test positive on day t have a delay of 1 day.
Figure 2.
Figure 2.
Hospitalisation risk conditional on positive test time (solid black line) when risk conditional on infection time is 0.05 (green line). Incidence of infection is shown (dotted line). Time from infection to positive test is assumed to have a gamma distribution with mean 4 and variance 8 for the ultimately hospitalised individuals and a gamma distribution with mean 7 and variance 14 for the ultimately non-hospitalised individuals.
Figure 3.
Figure 3.
Distributions of time from infection to positive test. Solid black line is distribution for ultimately non-hospitalised individuals. Dotted line is same distribution shifted by three days. Red line is distribution for ultimately hospitalised individuals.
Figure 4.
Figure 4.
Summary of implementation of proposed sensitivity analysis.

References

    1. Brookmeyer R, Damiano A. Statistical methods for short-term projections of AIDS incidence. Stat Med 1989; 8: 23–34. - PubMed
    1. Kalbfleisch J, Lawless J. Inference based on retrospective ascertainment: an analysis of the data on transfusion-related AIDS. J Am Stat Assoc 1989; 84: 360–372.
    1. Seaman S, Jackson C, Presanis A. Estimating a Time-to-Event Distribution from Right-Truncated Data in an Epidemic: a Review of Methods. Statistical Methods in Medical Research. 2021; https://doi-org.ezp.lib.cam.ac.uk/10.1177/09622802211023955. - DOI - PMC - PubMed
    1. Keyfitz N, Caswell H. 5. In: Applied Mathematical Demography. 3rd ed. New York: Springer, 2005.
    1. Rydevik G, Innocent G, Marion G. et al.. Using combined diagnostic test results to hindcast trends of infection from cross-sectional data. PLOS Comput Biol 2015; 12: 1–19. - PMC - PubMed

Publication types