Case fatality risk estimated from routinely collected disease surveillance data: application to COVID–19

Abstract

Case fatality risk (CFR) is the probability of death among cases of a disease. A crude CFR estimate is the ratio of the number deaths to the number of cases of the disease. This estimate is biased, however, particularly during outbreaks of emerging infectious diseases such as COVID-19, because the death time of recent cases is subject to right censoring. Instead, we propose deconvolution methods applied to routinely collected surveillance data of unlinked case and death counts over time. We begin by considering the death series to be the convolution of the case series and the fatality distribution, which is the subdistribution of the time between diagnosis and death. We then use deconvolution methods to estimate this fatality distribution. This provides a CFR estimate together with information about the distribution of time to death. Importantly, this information is extracted without the need to make strong assumptions used in previous analyses. The methods are applied to COVID-19 surveillance data from a range of countries illustrating substantial CFR differences. Simulations show that crude approaches lead to underestimation, particularly early in an outbreak, and that the proposed approach can rectify this bias. An R package called covidSurv is available for implementing the analyses.

Keywords:

• Case fatality
• COVID-19
• deconvolution
• quasi-likelihood
• surveillance data

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability

All data analyzed were obtained from public domain sources described in the paper.

Additional information

Notes on contributors

Ian C. Marschner

Ian C. Marschner, PhD is Professor of Biostatistics at the University of Sydney, Australia, within the National Health and Medical Research Council Clinical Trials Center. He has over 30 years of experience in biostatistics research applied to epidemiology and clinical trials, particularly in the areas of infectious diseases, cardiovascular disease and oncology. He has written over 100 peer reviewed papers and made extensive contributions to biostatistical methodology and theory. He has contributed open source packages for statistical computation in the R computing environment that have been downloaded over 100,000 times. His previous appointments include Associate Professor of Biostatistics at Harvard University, Head of the Department of Statistics at Macquarie University and Director of the Asia Biometrics Center for the pharmaceutical company Pfizer.