一个零膨胀地方性-流行性模型及其在德国麻疹时间序列中的应用
A zero-inflated endemic-epidemic model with an application to measles time series in Germany
AI总结：
针对传染病监测数据中的零膨胀问题，提出带随机效应的多元零膨胀地方性-流行性模型扩展HHH框架，新模型参数可通过极大似然高效联合估计，模拟与德国麻疹数据应用均验证了其收敛性与预测提升。
摘要：
在对传染病发生进行建模时，常遇到含有过多零值的计数数据。由于非流行期以及年龄组或地区的差异，零膨胀程度会随时间变化。现有的地方性-流行性建模框架（即HHH）缺乏对含过多零值的监测数据的妥善处理，因其仅限于Poisson分布和负二项分布。本文提出一个带随机效应的多元零膨胀地方性-流行性模型以扩展HHH。通过使用解析导数的（惩罚）极大似然推断，可联合且高效地估计新模型中零膨胀部分和HHH部分的参数。模拟研究证实了置信区间具有良好的收敛性和覆盖概率。将该模型应用于2005至2018年德国16个州的麻疹计数数据，表明新增的零膨胀机制改善了概率预测。
英文摘要：
Count data with excessive zeros are often encountered when modelling infectious disease occurrence. The degree of zero inflation can vary over time due to non-epidemic periods as well as by age group or region. The existing endemic-epidemic modelling framework (aka HHH) lacks a proper treatment for surveillance data with excessive zeros as it is limited to Poisson and negative binomial distributions. In this paper, we propose a multivariate zero-inflated endemic-epidemic model with random effects to extend HHH. Parameters of the new zero-inflation and the HHH part of the model can be estimated jointly and efficiently via (penalized) maximum likelihood inference using analytical derivatives. A simulation study confirms proper convergence and coverage probabilities of confidence intervals. Applying the model to measles counts in the 16 German states, 2005--2018, shows that the added zero-inflation improves probabilistic forecasts.
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