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add paper attribution for images
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avallecam committed Mar 19, 2024
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Expand Up @@ -85,7 +85,7 @@ $$ b_{t} = \frac{D_{t}}{C_{t}} $$

### What are data sources to estimate CFR?

[Verity et al., 2020](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30243-7/fulltext) summaries the spectrum of COVID-19 cases.
[Verity et al., 2020](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30243-7/fulltext) summaries the spectrum of COVID-19 cases:

![Spectrum of COVID-19 cases. The CFR aims to estimate the proportion of Deaths among confirmed cases in an epidemic.](fig/cfr-spectrum-cases-covid19.jpg)

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[image missing alt-text]: fig/cfr-spectrum-cases-covid19.jpg

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Figures A and B show the cumulative numbers of cases and deaths of SARS, and Figure C shows the observed (biased) CFR estimates as a function of time, i.e. the cumulative number of deaths over cases at time $t$. Due to the delay from the onset of symptoms to death, the biased estimate of CFR at time $t$ underestimates the realised CFR at the end of an outbreak (i.e. 302/1755 = 17.2 %).

![Observed (biased) confirmed case fatality risk of severe acute respiratory syndrome (SARS) in Hong Kong, 2003.](fig/cfr-pone.0006852.g003-fig_abc.png)
![Observed (biased) confirmed case fatality risk of severe acute respiratory syndrome (SARS) in Hong Kong, 2003. ([Nishiura et al., 2009](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0006852))](fig/cfr-pone.0006852.g003-fig_abc.png)

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[image missing alt-text]: fig/cfr-pone.0006852.g003-fig_abc.png

Nevertheless, even by only using the observed data for the period March 19 to April 2, `cfr_static()` can yield an appropriate prediction (Figure D), e.g. the delay-adjusted CFR at March 27 is 18.1 % (95% CI: 10.5, 28.1). An overestimation is seen in the very early stages of the epidemic, but the 95% confidence limits in the later stages include the realised CFR (i.e. 17.2 %).

![Early determination of the delay-adjusted confirmed case fatality risk of severe acute respiratory syndrome (SARS) in Hong Kong, 2003.](fig/cfr-pone.0006852.g003-fig_d.png)
![Early determination of the delay-adjusted confirmed case fatality risk of severe acute respiratory syndrome (SARS) in Hong Kong, 2003. ([Nishiura et al., 2009](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0006852))](fig/cfr-pone.0006852.g003-fig_d.png)

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[image missing alt-text]: fig/cfr-pone.0006852.g003-fig_d.png

We can explore this behaviour using the `cfr_rolling()` function. With `tail()`, we show that the latest CFR estimates are equal to the `cfr_static()` outputs:

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