MRC Centre for Global Infectious Disease Analysis, Imperial College London, London, United Kingdom.
PLoS Comput Biol. 2021 Sep 7;17(9):e1009347. doi: 10.1371/journal.pcbi.1009347. eCollection 2021 Sep.
We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.
我们构建了一个递归贝叶斯平滑器，称为 EpiFilter，用于实时和回溯估计传染病的有效繁殖数 R。我们的方法借鉴了卡尔曼滤波理论，计算速度快、易于计算、通用性强、确定性强，与许多当前方法不同，不需要更改点或窗口大小假设。我们将 R 建模为一个灵活的隐马尔可夫状态过程，并通过精确求解前向-后向算法，得出包含所有可用发病信息的 R 估计值。这统一并扩展了两种流行的方法，EpiEstim 考虑过去的发病情况，而 Wallinga-Teunis 方法则着眼于未来的时间。我们发现，这种最大化信息和最小化假设的组合显著降低了 R 估计的偏差和方差。此外，这些特性使 EpiFilter 在发病低的时期更具有统计学稳健性，在这些时期，一些现有的方法可能会变得不稳定。因此，EpiFilter 提供了改进的时变传播模式推断，有利于实时和各种空间尺度评估即将到来的感染浪潮或干预措施的影响。
