Physiological Controls Research Center, Obuda University, Budapest, Hungary.
Department of Statistics, Corvinus University of Budapest, Budapest, Hungary.
BMC Med Res Methodol. 2023 Oct 18;23(1):239. doi: 10.1186/s12874-023-02061-w.
The World Health Organization (WHO)'s excess mortality estimates presented in May 2022 stirred controversy, due in part to the high estimate provided for Germany, which was later attributed to the spline model used. This paper aims to reproduce the problem using synthetic datasets, thus allowing the investigation of its sensitivity to parameters, both of the mortality curve and of the used method, thereby shedding light on the conditions that gave rise to this error and identifying possible remedies.
A negative binomial model was used accounting for long-term change, seasonality, flu seasons, and heat waves. Simulated mortality curves from this model were then analysed using simple methods (mean, linear trend), the WHO method, and the method of Acosta and Irizarry.
The performance of the WHO's method with its original parametrization was indeed very poor, however it can be profoundly improved by a better choice of parameters. The Acosta-Irizarry method outperformed the WHO method despite being also based on splines, but it was also dependent on its parameters. Linear extrapolation could produce very good results, but was highly dependent on the choice of the starting year, while the average was the worst in almost all cases.
Splines are not inherently unsuitable for predicting baseline mortality, but caution should be taken. In particular, the results suggest that the key issue is that the splines should not be too flexible to avoid overfitting. Even after having investigated a limited number of scenarios, the results suggest that there is not a single method that outperforms the others in all situations. As the WHO method on the German data illustrates, whatever method is chosen, it remains important to visualize the data, the fit, and the predictions before trusting any result. It will be interesting to see whether further research including other scenarios will come to similar conclusions.
世界卫生组织（WHO）在 2022 年 5 月发布的超额死亡率估计值引起了争议，部分原因是为德国提供的高估计值，后来归因于使用的样条模型。本文旨在使用合成数据集重现该问题，从而可以研究其对死亡率曲线和所用方法的参数的敏感性，从而揭示导致该错误的条件，并确定可能的补救措施。
使用负二项模型来解释长期变化、季节性、流感季节和热浪。然后使用简单的方法（平均值、线性趋势）、WHO 方法和 Acosta 和 Irizarry 方法分析来自该模型的模拟死亡率曲线。
WHO 方法的原始参数化的性能确实很差，但是通过更好地选择参数，可以得到很大的改善。尽管 Acosta-Irizarry 方法也基于样条，但它优于 WHO 方法，尽管它也依赖于其参数。线性外推可以产生非常好的结果，但高度依赖于起始年份的选择，而平均值在几乎所有情况下都是最差的。
样条本身并不适合预测基线死亡率，但应谨慎使用。特别是，结果表明关键问题是样条不应过于灵活以避免过度拟合。即使在研究了有限数量的情况下，结果表明，在所有情况下，没有一种方法都优于其他方法。正如德国数据中的 WHO 方法所示，无论选择哪种方法，在信任任何结果之前，可视化数据、拟合度和预测结果仍然很重要。有趣的是，看看是否会有其他包含其他场景的进一步研究得出类似的结论。
