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.
翻译:在建立传染病发生模型时,往往会遇到计数数据零度过高的传染性疾病发生情况。由于非流行病时期以及年龄组或区域的不同,零通货膨胀率可能随时间而变化。现有的流行性流行病建模框架(aka HHHH)缺乏对监测数据零度过高的适当处理方法,因为它仅限于Poisson和负二元性分布。在本文中,我们提出了一个多变量零膨胀地方流行病模型,其随机效应可以扩展HHHHH。新的零通货膨胀参数和模型的HHH部分可以通过使用分析衍生物进行(惩罚性)最大概率推断,共同和有效地估算。模拟研究证实了信任期的适当趋同性和覆盖概率。在16个德国州(2005-2018年)将模型应用于麻疹计数,表明增加的零通货膨胀可以改善概率预测。