University of Rostock, Ulmenstr. 69, 18057, Rostock, Germany.
Max Planck Institute for Demographic Research, Konrad-Zuse-Str. 1, 18057, Rostock, Germany.
Popul Health Metr. 2024 Sep 27;22(1):25. doi: 10.1186/s12963-024-00346-w.
Since the outbreak of the COVID-19 pandemic, the excess mortality P-score has gained prominence as a measure of pandemic burden. The P-score indicates the percentage by which observed deaths deviate from expected deaths. As the P-score is regularly used to compare excess mortality between countries, questions arise regarding the age dependency of the measure. In this paper we present formal and empirical results on the population structure bias of the P-score with a special focus on cross-country comparisons during the COVID-19 pandemic in Europe.
P-scores were calculated for European countries for 2021, 2022, and 2023 using data from the 2024 revision of the United Nations' World Population Prospects and the HMDs Short Term Mortality Fluctuations data series. The expected deaths for 2021, 2022, and 2023 were estimated using a Lee-Carter forecast model assuming pre-pandemic conditions. P-score differences between countries were decomposed using a Kitagawa-type decomposition into excess-mortality and structural components. To investigate the sensitivity of P-score cross-country rankings to differences in population structure we calculated the rank-correlation between age-standardized and classical P-scores.
The P-score is an average of age-specific percent excess deaths weighted by the age-distribution of expected deaths. It can be shown that the effect of differences in the distribution of deaths only plays a marginal role in a European comparison. In most cases, the excess mortality effect is the dominant effect. P-score rankings among European countries during the COVID-19 pandemic are similar under both age-standardized and classical P-scores.
Although the P-score formally depends on the age-distribution of expected deaths, this structural component only plays a minor role in a European comparison, as the distribution of deaths across the continent is similar. Thus, the P-score is suitable as a measure of excess mortality in a European comparison, as it mainly reflects the differences in excess mortality. However, this finding should not be extrapolated to global comparisons, where countries could have very different death distributions. In situations were P-score comparisons are biased age-standardization can be applied as a solution.
自 COVID-19 大流行爆发以来，超额死亡率 P 评分作为衡量大流行负担的指标备受关注。P 评分表示观察到的死亡人数与预期死亡人数的偏差百分比。由于 P 评分经常用于比较各国之间的超额死亡率，因此人们对该指标的年龄依赖性提出了疑问。在本文中，我们提出了 P 评分的人口结构偏差的正式和经验结果，特别关注欧洲 COVID-19 大流行期间的国家间比较。
使用联合国 2024 年修订版《世界人口展望》和 HMDs 短期死亡率波动数据系列的数据，为 2021 年、2022 年和 2023 年计算了欧洲国家的 P 评分。使用假设大流行前条件的 Lee-Carter 预测模型估计了 2021 年、2022 年和 2023 年的预期死亡人数。使用 Kitagawa 型分解将国家间的 P 评分差异分解为超额死亡率和结构成分。为了研究 P 评分的国家间排名对人口结构差异的敏感性，我们计算了年龄标准化和经典 P 评分之间的秩相关系数。
P 评分是按预期死亡的年龄分布加权的年龄特异性超额死亡百分比的平均值。可以证明，死亡分布差异的影响在欧洲比较中仅起次要作用。在大多数情况下，超额死亡率效应是主要效应。在 COVID-19 大流行期间，欧洲国家的 P 评分排名在年龄标准化和经典 P 评分下相似。
尽管 P 评分在形式上取决于预期死亡的年龄分布，但在欧洲比较中，这种结构成分的作用很小，因为欧洲大陆的死亡分布相似。因此，P 评分适合作为欧洲比较中的超额死亡率衡量标准，因为它主要反映了超额死亡率的差异。然而，这一发现不应推断到全球比较中，因为各国的死亡分布可能非常不同。在 P 评分比较存在偏差的情况下，可以应用年龄标准化作为解决方案。
