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Rethinking case fatality ratios for covid-19 from a data-driven viewpoint

2020; Elsevier BV; Volume: 81; Issue: 2 Linguagem: Inglês

10.1016/j.jinf.2020.06.010

1532-2742

Phoebus Rosakis, Maria Marketou,

Machine Learning in Healthcare

While examining the association between the Case Fatality Ratio (CFR) and the cumulative number of COVID-19 infections in this journal, Kenyon1Kenyon C. Flattening-the-curve associated with reduced COVID-19 case fatality rates-an ecological analysis of 65 countries.J Infect. Apr 16, 2020; Abstract Full Text Full Text PDF PubMed Scopus (69) Google Scholar recently came across various difficulties in estimating the CFR. One of these was addressed by Baud and colleagues2Baud D. Qi X. Nielsen-Saines K. Musso D. Pomar L. Favre G Real estimates of mortali- ty following COVID-19 infection.Lancet Infect Dis. Mar 12, 2020; Abstract Full Text Full Text PDF Scopus (810) Google Scholar, who pointed out that the CFR (number of reported deaths divided by reported cases) ignores the time delay between incubation and death. Various problems3Spychalski P. Błażyńska-Spychalska A. Kobiela J Estimating case fatality rates of COVID-19.Lancet Infect Dis. Mar 31, 2020; Abstract Full Text Full Text PDF PubMed Scopus (93) Google Scholar with their approach have been identified, but a concrete solution is unclear. While we agree that time lag plays an important role, it is overestimated by Baud and coworkers2Baud D. Qi X. Nielsen-Saines K. Musso D. Pomar L. Favre G Real estimates of mortali- ty following COVID-19 infection.Lancet Infect Dis. Mar 12, 2020; Abstract Full Text Full Text PDF Scopus (810) Google Scholar, whereas reported CFR values4Roser M. Ritchie H. Ortiz-Ospina E. Hasell J Coronavirus pandemic (COVID-19).Our World Data. Mar 4, 2020; (Published online at OurWorldInData.org. Retrieved from:)https://ourworldindata.org/coronavirusGoogle Scholar ignore time lag completely. We find that either of these approaches introduces a spurious time dependence that severely distorts the magnitude and true meaning of the CFR. Instead, a suitably corrected CFR is far more useful as an indicator of COVID-19 fatality, because it turns out to be constant in time for many countries, as we show. The CFR is unfavorably compared with the Infection Fatality Ratio (IFR)2Baud D. Qi X. Nielsen-Saines K. Musso D. Pomar L. Favre G Real estimates of mortali- ty following COVID-19 infection.Lancet Infect Dis. Mar 12, 2020; Abstract Full Text Full Text PDF Scopus (810) Google Scholar, 3Spychalski P. Błażyńska-Spychalska A. Kobiela J Estimating case fatality rates of COVID-19.Lancet Infect Dis. Mar 31, 2020; Abstract Full Text Full Text PDF PubMed Scopus (93) Google Scholar, 4Roser M. Ritchie H. Ortiz-Ospina E. Hasell J Coronavirus pandemic (COVID-19).Our World Data. Mar 4, 2020; (Published online at OurWorldInData.org. Retrieved from:)https://ourworldindata.org/coronavirusGoogle Scholar, 5Russell T.W. Hellewell J. Jarvis C.I. Van Zandvoort K. Abbott S. Ratnayake R. Flasche S. Eggo R.M. Edmunds W.J. Kucharski A.J. CMMID COVID-19 working groupEstimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted data from the outbreak on the Diamond Princess cruise ship, February 2020.Eurosurveillance. Mar 26, 2020; 262000256Google Scholar, 6Lipsitch M. Donnelly C.A. Fraser C. Blake I.M. Cori A. Dorigatti I. Ferguson N.M. Garske T. Mills H.L. Riley S. Van Kerkhove M.D Potential biases in estimating absolute and relative case-fatality risks during outbreaks.PLoS Negl Trop Dis. Jul. 2015; 9Crossref PubMed Scopus (116) Google Scholar of deaths over total actual infections, often because asymptomatic cases do not contribute to it, unless identified by testing. The IFR is important, but practically impossible to measure, due to lack of data for the denominator, which requires widespread, continuous random testing7Bendavid E. Mulaney B. Sood N. Shah S. Ling E. Bromley-Dulfano R. Lai C. Weissberg Z. Saavedra R. Tedrow J. Tversky D COVID-19 antibody seroprevalence in Santa Clara County. MedRxiv, CaliforniaJan 1, 2020Crossref Google Scholar. The CFR (only including reported cases) may have its uses in estimating fatalities1Kenyon C. Flattening-the-curve associated with reduced COVID-19 case fatality rates-an ecological analysis of 65 countries.J Infect. Apr 16, 2020; Abstract Full Text Full Text PDF PubMed Scopus (69) Google Scholar. Assuming random testing is very limited4Roser M. Ritchie H. Ortiz-Ospina E. Hasell J Coronavirus pandemic (COVID-19).Our World Data. Mar 4, 2020; (Published online at OurWorldInData.org. Retrieved from:)https://ourworldindata.org/coronavirusGoogle Scholar, the majority of reported cases have developed symptoms severe enough to seek medical assistance; these individuals are far more likely to die from the disease than asymptomatic cases8Onder G. Rezza G. Brusaferro S Case-fatality rate and characteristics of patients dying in relation to COVID-19 in Italy.JAMA. Mar 23, 2020; Crossref PubMed Scopus (2971) Google Scholar, which would go undetected in the absence of testing. In this sense, the CFR is a meaningful measure of fatality risk among symptomatic individuals. This begs the question whether CFR versus time might be roughly constant for each country, at least during a period of fixed social distancing measures. This constant value would be different for each country, because of differing age distributions, mortality being a strongly increasing function of age8Onder G. Rezza G. Brusaferro S Case-fatality rate and characteristics of patients dying in relation to COVID-19 in Italy.JAMA. Mar 23, 2020; Crossref PubMed Scopus (2971) Google Scholar, and possibly other factors. At first glance, this hypothesis is not supported by the COVID-19 data4Roser M. Ritchie H. Ortiz-Ospina E. Hasell J Coronavirus pandemic (COVID-19).Our World Data. Mar 4, 2020; (Published online at OurWorldInData.org. Retrieved from:)https://ourworldindata.org/coronavirusGoogle Scholar. Most countries have an increasing, and some a decreasing CFR that eventually levels off to a constant. To test the constant CFR hypothesis, we started with a hard-hit country, Italy, plotted deaths and reported cases versus time (Fig. 1a), and observed that multiplying deaths by roughly a factor of 7, made the two graphs almost the same (Fig. 1b), except for a shift Δt = 4 days; after compensating for which they became nearly indistinguishable (Fig. 1c), implying a CFR 1/7 = 0.14 that remains virtually constant within 3% of cCFR. Baud and coworkers2Baud D. Qi X. Nielsen-Saines K. Musso D. Pomar L. Favre G Real estimates of mortali- ty following COVID-19 infection.Lancet Infect Dis. Mar 12, 2020; Abstract Full Text Full Text PDF Scopus (810) Google Scholar used a lag of 14 days, representing symptom onset to death. Instead we feel that the time lag Δt should reflect time from reporting to death. Delays from onset to reporting do occur5Russell T.W. Hellewell J. Jarvis C.I. Van Zandvoort K. Abbott S. Ratnayake R. Flasche S. Eggo R.M. Edmunds W.J. Kucharski A.J. CMMID COVID-19 working groupEstimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted data from the outbreak on the Diamond Princess cruise ship, February 2020.Eurosurveillance. Mar 26, 2020; 262000256Google Scholar,9Leung K. Wu J.T. Liu D. Leung G.M First-wave COVID-19 transmissibility and severity in China outside Hubei after control measures, and second-wave scenario planning: a mod- elling impact assessment.Lancet. Apr 8, 2020; Abstract Full Text Full Text PDF Scopus (558) Google Scholar. In Singapore these delays had a mean of a week10Tariq A. Lee Y. Roosa K. Blumberg S. Yan P. Ma S. Chowell G Real-time monitoring the transmission potential of COVID-19 in Singapore, February 2020.medRxiv. Jan 1, 2020; Google Scholar and could exceed two weeks. Moreover, delays in reporting bring delays in critical medical care, hence may accelerate death. By increasing the time from onset to reporting, such factors decrease the time lag Δt from reporting to death, so we might expect Δt to be much less than 14 days, but uncertainty is introduced. Here, instead of arbitrarily picking CFR and Δt, or using estimates from a different location5Russell T.W. Hellewell J. Jarvis C.I. Van Zandvoort K. Abbott S. Ratnayake R. Flasche S. Eggo R.M. Edmunds W.J. Kucharski A.J. CMMID COVID-19 working groupEstimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted data from the outbreak on the Diamond Princess cruise ship, February 2020.Eurosurveillance. Mar 26, 2020; 262000256Google Scholar, we let the data decide. Data-driven predictions11Barmparis G.D. Tsironis G.P. Estimating the infection horizon of COVID-19 in eight countries with a data-driven approach.Chaos, Solitons Fractals. Apr 27, 2020; 109842Crossref PubMed Scopus (76) Google Scholar of epidemic metrics are promising. We use a simple data-driven approach to find the right constant values, cCFR and cΔt. Simply put, we choose these values to be the ones that minimize the root mean square deviation between cases and deaths versus time, with deaths multiplied by cCFR and shifted back by cΔt; see the Appendix for details. This gives cΔt=4 days for Italy. Shifting deaths back in time by this cΔt, then dividing by cases, yields a virtually constant CFR versus time (red curve, Fig. 1d), equal to cCFR=0.14 (black dashed line, Fig. 1d) within a few percent. The statement "14% of reported cases die after four days" remains closer to the truth for much longer than any analogous statement regarding the reported, variable CFR that nearly doubles its value in two months (orange curve Fig. 1d). This procedure works for many countries (Fig. 2), producing a different cCFR and cΔt for each, but also for the entire world: cCFR=0.08, cΔt=3 days (black dashed line, Fig. 2), but a nearly constant corrected CFR for all cases considered. The reported4Roser M. Ritchie H. Ortiz-Ospina E. Hasell J Coronavirus pandemic (COVID-19).Our World Data. Mar 4, 2020; (Published online at OurWorldInData.org. Retrieved from:)https://ourworldindata.org/coronavirusGoogle Scholar CFR (orange curve, Fig. 1d), which ignores time lag, increases with time and underestimates Italy's cCFR by a time-dependent amount. Baud et al. approach, shifting deaths back by Δt=14 days2Baud D. Qi X. Nielsen-Saines K. Musso D. Pomar L. Favre G Real estimates of mortali- ty following COVID-19 infection.Lancet Infect Dis. Mar 12, 2020; Abstract Full Text Full Text PDF Scopus (810) Google Scholar (green curve, Fig. 1d) overestimates Italy's cCFR and decreases with time. In summary, by allowing for an initially unknown time lag between case reporting and death, we find that many countries, and the entire world, exhibit a corrected CFR that is essentially constant during a long period of imposed social distancing. This value can be estimated long before the full evolution of the pandemic, hence it is useful for early prediction of fatalities, in situations where extensive random testing is not available. PR and MEM designed the research. PR performed the analysis with input from MEM. Both authors discussed the results and wrote the manuscript. None.