Brunner Norbert, Kühleitner Manfred
Department of Integrative Biology and Biodiversity Research (DIBB), University of Natural Resources and Life Sciences (BOKU), A-1180 Vienna, Austria.
Epidemiol Infect. 2020 Dec 28;149:e6. doi: 10.1017/S0950268820003039.
Using monthly data from the Ebola-outbreak 2013-2016 in West Africa, we compared two calibrations for data fitting, least-squares (SSE) and weighted least-squares (SWSE) with weights reciprocal to the number of new infections. To compare (in hindsight) forecasts for the final disease size (the actual value was observed at month 28 of the outbreak) we fitted Bertalanffy-Pütter growth models to truncated initial data (first 11, 12, …, 28 months). The growth curves identified the epidemic peak at month 10 and the relative errors of the forecasts (asymptotic limits) were below 10%, if 16 or more month were used; for SWSE the relative errors were smaller than for SSE. However, the calibrations differed insofar as for SWSE there were good fitting models that forecasted reasonable upper and lower bounds, while SSE was biased, as the forecasts of good fitting models systematically underestimated the final disease size. Furthermore, for SSE the normal distribution hypothesis of the fit residuals was refuted, while the similar hypothesis for SWSE was not refuted. We therefore recommend considering SWSE for epidemic forecasts.
利用2013 - 2016年西非埃博拉疫情的月度数据，我们比较了两种用于数据拟合的校准方法，即最小二乘法（SSE）和加权最小二乘法（SWSE），权重与新感染病例数的倒数成反比。为了（事后）比较对最终疾病规模的预测（疫情爆发第28个月时观察到实际值），我们将贝塔朗菲 - 普特尔增长模型拟合到截断的初始数据（前11、12、…、28个月）。如果使用16个或更多月份的数据，增长曲线在第10个月确定了疫情高峰，预测的相对误差（渐近极限）低于10%；对于SWSE，相对误差比SSE小。然而，校准方法的不同之处在于，对于SWSE，存在能预测合理上下限的良好拟合模型，而SSE存在偏差，因为良好拟合模型的预测系统性地低估了最终疾病规模。此外，对于SSE，拟合残差的正态分布假设被推翻，而对于SWSE，类似假设未被推翻。因此，我们建议在疫情预测中考虑使用SWSE。
