2022.02.25 一些国家的covid-19死亡人数是否造假？

shiyi18

More equal than others
Are some countries faking their covid-19 death counts?
An elementary statistical test casts doubt on some abnormally neat numbers
FEB 25TH 2022

Sometimes the numbers are simply too tidy to be believed. Irregular statistical variation has proven a powerful forensic tool for detecting possible fraud in academic research, accounting statements and election tallies. Now similar techniques are helping to find a new subgenre of faked numbers: covid-19 death tolls.

That is the conclusion of a new study to be published in Significance, a statistics magazine, by the researcher Dmitry Kobak. Mr Kobak has a penchant for such studies—he previously demonstrated fraud in Russian elections based on anomalous tallies from polling stations. His latest study examines how reported death tolls vary over time. He finds that this variance is suspiciously low in a clutch of countries—almost exclusively those without a functioning democracy or a free press.

Mr Kobak uses a test based on the “Poisson distribution”. This is named after a French statistician who first noticed that when modelling certain kinds of counts, such as the number of people who enter a railway station in an hour, the distribution takes on a specific shape with one mathematically pleasing property: the mean of the distribution is equal to its variance.


This idea can be useful in modelling the number of covid deaths, but requires one extension. Unlike a typical Poisson process, the number of people who die of covid can be correlated from one day to the next—superspreader events, for example, lead to spikes in deaths. As a result, the distribution of deaths should be what statisticians call “overdispersed”—the variance should be greater than the mean. Jonas Schöley, a demographer not involved with Mr Kobak’s research, says he has never in his career encountered death tallies that would fail this test.

That should make it easy to pass. And the vast majority of countries reporting data to the World Health Organisation do. This does not mean that their death tallies were necessarily accurate—undercounting still plagues many countries with insufficient testing (which is why The Economist estimates the pandemic’s death toll using excess deaths). But it does suggest that the numbers reported are not being deliberately tampered with.


Yet data from 17 countries had the opposite pattern. In many weeks, the variance of each distribution was less than the mean. This is a statistical smoking gun. “It seems reasonable to conclude that there’s no way these are independent observations,” says David Steinsaltz, a professor of statistics at the University of Oxford.

Imputing motives is harder. A benign explanation would be bureaucratic bottlenecks in processing death certificates. Yet there are other irregularities: the usual drop-off in weekend reporting is often absent. According to Mr Kobak, the likelier explanation is cackhanded tampering.

The Russian numbers offer an example of abnormal neatness. In August 2021 daily death tallies went no lower than 746 and no higher than 799. Russia’s invariant numbers continued into the first week of September, ranging from 792 to 799. A back-of-the-envelope calculation shows that such a low-variation week would occur by chance once every 2,747 years. ■

Sources: “Underdispersion in the reported covid-19 case and deathnumbers may suggest data manipulations”, by D. Kobak, working paper, 2022; Our World in Data; JHU CSSE



比其他国家更平等
一些国家的covid-19死亡人数是否造假？
一个基本的统计测试对一些异常整齐的数字提出了怀疑
2022年2月25日

有时候，数字太整齐了，让人无法相信。事实证明，不规则的统计变化是检测学术研究、会计报表和选举结果中可能存在的欺诈行为的有力法证工具。现在，类似的技术正在帮助发现一个新的伪造数字的亚流派：19岁的死亡人数。

这是研究人员德米特里-科巴克(Dmitry Kobak)将在统计学杂志《Significance》上发表的一项新研究的结论。科巴克先生对此类研究情有独钟，他曾根据投票站的异常统计数字证明了俄罗斯选举中的欺诈行为。他的最新研究考察了报告的死亡人数如何随时间变化。他发现，在一些国家--几乎全部是那些没有正常的民主或新闻自由的国家--这种差异令人怀疑地低。

Kobak先生使用了一种基于 "泊松分布 "的测试。这是以一位法国统计学家的名字命名的，他首先注意到，在对某些类型的计数进行建模时，如一小时内进入火车站的人数，分布呈现出一种特定的形状，具有一个数学上令人愉快的特性：分布的平均值等于其方差。


这个想法对于建立ovid死亡人数的模型很有用，但需要一个扩展。与典型的泊松过程不同，死于柯维德的人数在一天之内可能是相关的--例如，超级散播者事件会导致死亡人数激增。因此，死亡的分布应该是统计学家所说的 "过度分散"--方差应该大于平均值。没有参与Kobak先生研究的人口学家Jonas Schöley说，在他的职业生涯中，他从未遇到过无法通过这一测试的死亡统计数字。

这应该使它很容易通过。而绝大多数向世界卫生组织报告数据的国家都是如此。这并不意味着他们的死亡统计数字一定是准确的--低估仍然困扰着许多测试不足的国家（这就是为什么《经济学人》用超额死亡来估计大流行病的死亡人数）。但它确实表明，报告的数字没有被故意篡改。


然而，来自17个国家的数据却有相反的模式。在许多星期里，每个分布的方差都小于平均值。这是一把统计学上的烟枪。"牛津大学统计学教授大卫-斯坦萨尔茨（David Steinsaltz）说："似乎可以合理地得出结论，这些不可能是独立的观察结果。

归因于动机则更难。一个良性的解释是在处理死亡证明方面存在官僚主义瓶颈。然而，还有其他一些不正常的现象：周末报告中通常会出现下降的情况。据Kobak先生说，更可能的解释是黑手篡改。

俄罗斯的数字提供了一个不正常的整齐度的例子。在2021年8月，每天的死亡人数不低于746人，不高于799人。俄罗斯的不变数字持续到9月的第一周，从792到799不等。一个逆向计算显示，这样的低变异周每2747年就会偶然出现一次。■

资料来源：《中国科学院学报》。"报告的covid-19病例和死亡人数的低分散性可能表明数据被操纵"，D. Kobak，工作文件，2022年；我们的数据世界；JHU CSSE