As the initial shock of the SARS-CoV-2 pandemic subsides, attention turns to comparison of the effectiveness of countries’ strategies in suppressing the spread of the virus. As is apparent from much of the ongoing political and scientific discussion, this task is more challenging than one might expect and needs careful handling to maintain public trust in the science presented. The difficulty stems from uncertainty in the data compared, from a source that we rarely consider. Most scientists and even most of the public are familiar with the concept of measurement uncertainty. Indeed, it is widely appreciated outside the metrology community that this uncertainty may arise from the variability of repeated measurements and other inputs such as the calibration of measuring equipment. When considering the differing effects of SARS-CoV-2, it is unavoidable that we compare, between countries, the number (usually per head of population) of deaths, new infections, hospital admissions, diagnostic tests, etc. The uncertainty of ‘counting’ measurements such as these is a less familiar concept and, until relatively recently, counting was not even viewed as measurement. Nevertheless, uncertainty in counting is important, especially when we are unable to individually count every event or item because they are too numerous, or because we can only access a sample of the target population, for instance, when measuring the number concentration of respirable particles in ambient air, determining radioactive decay rates, or estimating employment statistics from information gathered from a sample of the whole population. Deaths caused by SARS-CoV-2 may be counted in their entirety, and yet there is still uncertainty present in this apparently simple task, even if this is not expressed in the public presentation of data with error bars and confidence intervals. This is because uncertainty arises from a source rarely considered and certainly not understood by the public: the measurand—the ‘quantity intended to be measured’ [1]. Put simply, we need to describe in enough detail how we are doing the counting, what is included and what is not, otherwise it is unclear, or uncertain, what we mean by our measurement result. Behind the summary statistic, ’number of SARS-CoV-2 associated deaths’ presented to the public is a measurand needing significant qualification and explanation. For instance, does this figure include only deaths in hospital, only those accompanied with a positive diagnostic test (and then what is the cut-off between time of testing and date of death [2]), those where SARS-CoV-2 is mentioned on the death certificate, or all excess deaths over and above the long-term average (and then what long-term average is this judged against)? There are very many options, all potentially credible metrics, but all giving different results. In fact, uncertainty in the measurand is almost always present in measurement science and is often an unrecognised source of irreproducibility in science, but usually this is insignificant in comparison with the traditional measurement uncertainty contributions from repeatability and input calibrations. Where it is not insignificant the metrology community refers to these measurands as ‘method defined’ or ‘operationally defined’ [3]. This consideration is particularly common in chemistry and material science. In these cases, we must give all the details required to adequately reproduce the method in question in order to reap the benefits that good metrology delivers: stability over time to provide confidence in trends and comparability between measurements made in different locations to ensure the overall reproducibility of results and the robustness of the conclusions we draw from them. The same is true for metrics associated with the pandemic. Of course, such method-defined measurands usually have their definitions and measurement processes described in documentary standards or procedures, agreed by committees of experts. For SARS-CoV-2, what is being counted is usually well documented within individual countries [4], even if what should be counted is often contested. Changes to these processes within countries may still cause discontinuities * Richard J. C. Brown richard.brown@npl.co.uk

中文翻译：

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正确计数

随着 SARS-CoV-2 大流行的最初冲击消退，注意力转向比较各国抑制病毒传播战略的有效性。从正在进行的许多政治和科学讨论中可以明显看出，这项任务比人们预期的更具挑战性，需要谨慎处理以保持公众对所提出的科学的信任。困难源于比较数据的不确定性，来自我们很少考虑的来源。大多数科学家甚至大多数公众都熟悉测量不确定度的概念。事实上，在计量学界之外，人们普遍认为这种不确定性可能源于重复测量和其他输入（如测量设备的校准）的可变性。在考虑 SARS-CoV-2 的不同影响时，我们不可避免地会在国家之间比较死亡、新感染、住院、诊断测试等的数量（通常是每人）。诸如此类的“计数”测量的不确定性是一个不太熟悉的概念，并且，直到最近，计数甚至不被视为测量。然而，计数的不确定性很重要，尤其是当我们无法单独计数每个事件或项目时，因为它们太多，或者因为我们只能访问目标人群的样本，例如，在测量可吸入颗粒的数量浓度时在环境空气中，确定放射性衰变率，或根据从整个人口样本中收集的信息估计就业统计数据。由 SARS-CoV-2 引起的死亡人数可能会全部计算在内，然而，在这个看似简单的任务中仍然存在不确定性，即使这没有在带有误差线和置信区间的数据的公开展示中表达出来。这是因为不确定性来自一个很少被公众考虑并且肯定不会被公众理解的来源：被测量——“要测量的数量”[1]。简而言之，我们需要足够详细地描述我们是如何进行计数的，包括什么，不包括什么，否则就不清楚或不确定我们所说的测量结果是什么意思。在汇总统计数据的背后，向公众展示的“与 SARS-CoV-2 相关的死亡人数”是一个需要大量限定和解释的被测量。例如，这个数字是否只包括住院死亡？只有那些伴随着阳性诊断测试的人（然后是测试时间和死亡日期之间的截止日期 [2]），那些在死亡证明上提到 SARS-CoV-2 的人，或者所有超过和高于长期平均水平（然后根据什么长期平均水平来判断）？有很多选项，所有潜在的可信指标，但都给出不同的结果。事实上，被测量的不确定性几乎总是存在于测量科学中，并且通常是科学中不可再现性的一个未被识别的来源，但与可重复性和输入校准的传统测量不确定性贡献相比，这通常是微不足道的。在并非无关紧要的情况下，计量学界将这些被测量称为“方法定义”或“操作定义”[3]。这种考虑在化学和材料科学中尤为常见。在这些情况下，我们必须提供充分重现所讨论方法所需的所有细节，以便获得良好计量所带来的好处：随时间的稳定性以提供对趋势的信心以及在不同位置进行的测量之间的可比性以确保整体重现性结果的可靠性和我们从中得出的结论的稳健性。与大流行相关的指标也是如此。当然，这种方法定义的被测量通常在专家委员会同意的文件标准或程序中描述其定义和测量过程。对于 SARS-CoV-2，计算的内容通常在各个国家/地区都有详细记录 [4]，即使应该计算的内容经常存在争议。