[情報] COVID-19 死亡率

[switch (pura vita!)]

發稿單位：worldometer
發稿時間：Feb.18, 2020
撰 稿 者：worldometer
原文連結：https://www.worldometers.info/coronavirus/coronavirus-death-rate/

摘譯:

死亡率 (CFR, case fatality rate) 通常是以疫情結束後死亡數/總確診數來計算。但在疫情進行中，使用這個公式來計算，有時可能產生誤導。

以 Feb.8 全球累計 37,552 確診, 813 死亡計算。

   deaths/cases = 813/37,552 = 2.2% CFR (有瑕疵的公式)

(註: 以這個公式計算目前中國以外共 1,523 確診, 15死亡, CFR = 0.98%)

另一種方式是以平均確診到死亡日數 T 來估計，假設 T=7，則 Feb.1 的累計確診數為 14,381，可算出：

   Feb.8 deaths/Feb.1 cases = 813/14,381 = 5.7% CFR (正確的公式,假設T=7時)

在估計 T 時也可以用 (總死亡數+總治癒數) 的數目回推到與累計確診數相近的日期，使用這一公式，推出來的日期約 Jan.26/27 之間，相當於 T=12~13天。如果用這種方式推估T，因為使用相同的邏輯所以得出的結果會與第三種算法相同。即，

   CFR = 死亡數/(死亡+治癒數)

使用 Feb.22 的數字時，該公式算出來的死亡率為：

   2,360 / (2,360 + 20,949) = 10% CFR (worldwide)

排除中國的病例後為：

   15 / (15 + 236) = 6.0% CFR (outside of China)

兩者的差異可能來自於中國以外的樣本數較小以及 (輕症與無症狀) 確診比例較高。

另外一個可能影響估計的是未被通報的病例，未通報病例會使 CFR 的估計高於實際的數值。例如若武漢有 10,000 名未通報病例，CFR 就會從 10% 降到 7.1%。英國公衛專家在武漢病例只有2,000時，估計有10,000人已遭感染。

最後可以參考的是，在 2003 年 SARS 疫情進行中，WHO 當時報告的死亡率為 4% (最低為 3%)，但當疫情結束後，死亡率上升到 9.6%。



原文:

How to calculate the mortality rate during an outbreak

The case fatality rate (CFR) represents the proportion of cases who
eventually die from a disease.

Once an epidemic has ended, it is calculated with the formula: deaths / cases.

But while an epidemic is still ongoing, as it is the case with the current
novel coronavirus outbreak, this formula is, at the very least, "naïve" and
can be "misleading if, at the time of analysis, the outcome is unknown for a
non negligible proportion of patients." [8]

(Methods for Estimating the Case Fatality Ratio for a Novel, Emerging
Infectious Disease - Ghani et al, American Journal of Epidemiology).

In other words, current deaths belong to a total case figure of the past, not
to the current case figure in which the outcome (recovery or death) of a
proportion (the most recent cases) hasn't yet been determined.

The correct formula, therefore, would appear to be:

CFR = deaths at day.x / cases at day.x-{T}
(where T = average time period from case confirmation to death)

This would constitute a fair attempt to use values for cases and deaths
belonging to the same group of patients.

One issue can be that of determining whether there is enough data to estimate
T with any precision, but it is certainly not T = 0 (what is implicitly used
when applying the formula current deaths / current cases to determine CFR
during an ongoing outbreak).

Let's take, for example, the data at the end of February 8, 2020: 813 deaths
(cumulative total) and 37,552 cases (cumulative total) worldwide.

If we use the formula (deaths / cases) we get:

813 / 37,552 = 2.2% CFR (flawed formula).

With a conservative estimate of T = 7 days as the average period from case
confirmation to death, we would correct the above formula by using February 1
cumulative cases, which were 14,381, in the denominator:

Feb. 8 deaths / Feb. 1 cases = 813 / 14,381 = 5.7% CFR (correct formula, and
estimating T=7).

T could be estimated by simply looking at the value of (current total deaths
+ current total recovered) and pair it with a case total in the past that has
the same value. For the above formula, the matching dates would be January
26/27, providing an estimate for T of 12 to 13 days. This method of
estimating T uses the same logic of the following method, and therefore will
yield the same result.

An alternative method, which has the advantage of not having to estimate a
variable, and that is mentioned in the American Journal of Epidemiology study
cited previously as a simple method that nevertheless could work reasonably
well if the hazards of death and recovery at any time t measured from
admission to the hospital, conditional on an event occurring at time t, are
proportional, would be to use the formula:

CFR = deaths / (deaths + recovered)

which, with the latest data available, would be equal to:

2,360 / (2,360 + 20,949) = 10% CFR (worldwide)

If we now exclude cases in mainland China, using current data on deaths and
recovered cases, we get:

15 / (15 + 236) = 6.0% CFR (outside of mainland China)

The sample size above is extremely limited, but this discrepancy in mortality
rates, if confirmed as the sample grows in size, could be explained with a
higher case detection rate outside of China especially with respect to Wuhan,
where priority had to be initially placed on severe and critical cases, given
the ongoing emergency.

Unreported cases would have the effect of decreasing the denominator and
inflating the CFR above its real value. For example, assuming 10,000 total
unreported cases in Wuhan and adding them back to the formula, we would get a
CFR of 7.1% (quite different from the CFR of 10% based strictly on confirmed
cases).

Neil Ferguson, a public health expert at Imperial College in the UK, said his
“best guess” was that there were 100,000 affected by the virus even though
there were only 2,000 confirmed cases at the time. [11]

Without going that far, the possibility of a non negligible number of
unreported cases in the initial stages of the crisis should be taken into
account when trying to calculate the case fatally rate.

As the days go by and the city organized its efforts and built the
infrastructure, the ability to detect and confirm cases improved. As of
February 3, for example, the novel coronavirus nucleic acid testing
capability of Wuhan had increased to 4,196 samples per day from an initial
200 samples.[10]

A significant discrepancy in case mortality rate can also be observed when
comparing mortality rates as calculated and reported by China NHC: a CFR of
3.1% in the Hubei province (where Wuhan, with the vast majority of deaths is
situated), and a CFR of 0.16% in other provinces (19 times less).

Finally, we shall remember that while the 2003 SARS epidemic was still
ongoing, the World Health Organization (WHO) reported a fatality rate of 4%
(or as low as 3%), whereas the final case fatality rate ended up being 9.6%.

--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 36.226.178.1 (臺灣)
※ 文章網址: https://www.ptt.cc/bbs/nCoV2019/M.1582340382.A.E44.html
推 s505015: 有趣
推 jagdzaku: 一堆假設根本無意義
→ fongtoy: 統計武漢封城前跟解封後的人口差
推 a7788783: 這個先擱置好了，最大基數的中國數字並
→ a7788783: 不受信任，目前開始爆發的各國，還在醫
→ a7788783: 治階段，然後又還有其他完全沒在檢測可
→ a7788783: 能患者的國家，目前要從數字取出結論還
→ a7788783: 太早
→ dansy: 其實一大堆輕症的都不在統計數據內....
→ dansy: 要探究真實的死亡率非常困難
→ dansy: 頂多就是分析重症死亡率 才比較有意義
→ oceanpuma: 這個時間一堆還沒出院，死亡率參考而已
→ BlueSausage: garbage in, garbage out
→ BlueSausage: 無參考價值
推 kbty245: SARS的死亡率還是高多了，SARS當時沒有出
→ kbty245: 現像武漢這樣醫療體系崩壞的情況，但死亡
→ kbty245: 率還遠超過這次，跟這次死亡數大多集中在
→ kbty245: 武漢拉高平均數不一樣
推 piliwu: 以中國以外的地區看來之前2%嚴重低估
→ kuma660224: 武漢的死亡是沒計算間接影響
→ kuma660224: 如果算進去應該會海放SARS
→ kuma660224: 因為洗腎病患也因肺炎導致醫療崩潰而
→ kuma660224: 死，等於間接致死
→ kuma660224: 這才是武漢肺炎可怕的地方
→ kuma660224: 它不全靠致死率殺人
→ kuma660224: 塞爆醫院後 連普通肺炎流感都能殺人
→ kuma660224: 它癱瘓醫療後 所有病毒細菌聯手進攻
→ kuma660224: 它致死率1%還是5%也就不重要了
→ kuma660224: 細菌病毒的“國家隊”總和致死率暴增
推 dan310546: 還有病程長，二月初爆發中的，可能三月
→ dan310546: 中以後數據才有意義
→ kuma660224: SARS是單人球星  我自幹模式
→ kuma660224: 武漢肺炎有靈氣開群體Buff打組織戰
推 ECZEMA: 感謝分享
→ jeff0811: 這個死亡率的也要灰色吧，還是說官方出
→ jeff0811: 的就不用？？？？？
推 zs111: 輕症無症狀那麼多
推 ynanlin: Pubmed 上有關於之前致死率的研究分析，
→ ynanlin: 大家都可以去看一下
噓 saveme: 中國的算法有問題
→ chiangdapang: https://lih.kg/1891334
→ chiangdapang: 武漢一條街可以數到20具屍
→ chiangdapang: 這些都不算在確診病例