Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic-epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed. Notably, we show that this leads to a downward bias in model-based estimates of the effective reproductive number. A marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease. The good performance of the proposed methodology is demonstrated in simulation studies. An extension to time-varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in Berlin, Germany.

中文翻译：

---

一种边际时刻匹配方法，用于将地方流行病模型与少报的疾病监测计数拟合

计数数据经常被漏报，尤其是在传染病监测中。我们提出了一种近似最大似然法来拟合从地方流行类到漏报数据的计数时间序列模型。该方法基于边际矩匹配，其中被低估的过程通过来自同一类的完全观察到的过程来近似。此外，分析了通过乘法因素忽略或考虑少报时的偏差形式。值得注意的是，我们表明这会导致基于模型的有效繁殖数估计值出现向下偏差。边际矩匹配方法也可用于解释比疾病的平均序列间隔更长的报告间隔。所提出的方法的良好性能在模拟研究中得到证明。在德国柏林每周轮状病毒胃肠炎计数的案例研究中讨论并应用了对时变参数和报告概率的扩展。