如何在疫情中计算死亡率

给你一双慧眼，明白疫情本相。

（所有中文为本人注解，看中文即知脉落，读英文知算法细节和出处。如有异议，以英文原文为准）

死亡率，是衡量疫情严重程度的最重要指标。也是从平民到决策层都最为关注的。

标准的算法是，在疫情结束时（没有在治疗中的患者），死者占总确诊病例的百分比。

但是，疫情在进展，人们更关注在目前的死亡情况，即时死亡比例（ current CFR），以调整适当的治疗方法及社会对应决策（政治、经济、民生等）。

可是，在疫情中（进行时），由于诊断标准和检测方法及人为干扰（如不检测方针，以减少明面总数维稳；或有意扩大病例数以降低死亡率），还有没能及时汇总等因素，在某一特定时刻的确诊人数并不确定。在使用标准算时，产生相当大的假象。

因此有必要引用专业人士的算法，而不是官方为粉饰太平而使用的算法（死亡数/累计确诊数）。

下文取自：https://www.worldometers.info/coronavirus/coronavirus-death-rate/

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]

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:

第一种规范算法：按病程计算即时死亡率（俺在以前的贴子中提到过）

如果知道然病程（从确诊到死亡的平均天数），那么在算“当下”死亡率时，要用死亡者确诊时的总病患案例做为基数，而不是用死亡时的总病例数。

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.

第二种算法比较简单易行, 使用目前累计死亡数和累计治愈数来估算。（就是杜编所使用的算法）
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:

3,303 / (3,303 + 53,708) = 6% CFR (worldwide)

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

290 / (290 + 1,481) = 16.4% CFR (outside of mainland China)

The sample size above is limited, and the data could be inaccurate (for example, the number of recoveries in countries outside of China could be lagging in our collection of data from numerous sources, whereas the number of cases and deaths is more readily available and therefore generally more up to par).

There was a discrepancy in mortality rates (with a much higher mortality rate in China) which however is not being confirmed as the sample of cases outside of China is growing in size. On the contrary, it is now higher outside of China than within. 

That initial discrepancy was generally 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 4.9% (quite different from the CFR of 6% based strictly on confirmed cases).