[论文解读] Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update

Seth Flaxman, Swapnil Mishra+21 more|arXiv (Cornell University)|Apr 23, 2020

COVID-19 epidemiological studies参考文献 5被引用 83

一句话总结

这篇论文扩展了一个半机械式贝叶斯层次模型，以推断非药物干预如何影响 SARS-CoV-2 传播，并估计跨14个欧洲国家的感染随时间的变化，结果在线报告。

ABSTRACT

Following the emergence of a novel coronavirus (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions including case isolation, the closure of schools and universities, banning of mass gatherings and/or public events, and most recently, wide-scale social distancing including local and national lockdowns. In this technical update, we extend a semi-mechanistic Bayesian hierarchical model that infers the impact of these interventions and estimates the number of infections over time. Our methods assume that changes in the reproductive number - a measure of transmission - are an immediate response to these interventions being implemented rather than broader gradual changes in behaviour. Our model estimates these changes by calculating backwards from temporal data on observed to estimate the number of infections and rate of transmission that occurred several weeks prior, allowing for a probabilistic time lag between infection and death. In this update we extend our original model [Flaxman, Mishra, Gandy et al 2020, Report #13, Imperial College London] to include (a) population saturation effects, (b) prior uncertainty on the infection fatality ratio, (c) a more balanced prior on intervention effects and (d) partial pooling of the lockdown intervention covariate. We also (e) included another 3 countries (Greece, the Netherlands and Portugal). The model code is available at https://github.com/ImperialCollegeLondon/covid19model/ We are now reporting the results of our updated model online at https://mrc-ide.github.io/covid19estimates/ We estimated parameters jointly for all M=14 countries in a single hierarchical model. Inference is performed in the probabilistic programming language Stan using an adaptive Hamiltonian Monte Carlo (HMC) sampler.

研究动机与目标

• Motivate the need to quantify how NPIs influenced transmission (Rt) during Europe’s COVID-19 epidemics.
• Extend the original model to include population saturation, uncertain infection fatality ratio, and partial pooling for lockdown effects.
• Estimate time-varying reproduction numbers and infections jointly for multiple countries using observed deaths as the data source.

提出的方法

• Use a semi-mechanistic Bayesian hierarchical framework fitted with Stan and adaptive Hamiltonian Monte Carlo.
• Model daily deaths as negative binomial with mean tied to infections via infection-to-death delay and country-specific IFR with uncertainty.
• Link infections over time via a discrete renewal process using a generation time distribution and a susceptible depletion factor S_t,m.
• Represent Rt as a multiplicative function of six interventions with shared effects across countries and a country-specific lockdown effect.
• Incorporate priors for Rt, intervention effects, and IFR based on previous literature, with seeding of initial infections and a generation distribution assumed to match serial interval.
• Provide data and code publicly (GitHub) and report results online.

实验结果

研究问题

• RQ1 六项主要非药物干预对跨欧洲国家时变传播数 Rt 的影响如何？
• RQ2 在考虑干预效应以及 IFR 和时延分布不确定性的情况下，估计每个国家随时间的感染数量？
• RQ3 相比其他 NPIs，人口饱和和国家特定的封锁效应在传播动力学中有多大影响？
• RQ4 推断结果对先验选择和模型假设（如感染到死亡的时延、IFR、代际时间）有多大的鲁棒性？

主要发现

• 该模型通过跨国共享信息的分层结构，估计干预对 Rt 的变化。
• 由于封锁具有可辨识的影响，因此对封锁引入了国家特定的随机效应，而其他干预具有共享效应。
• 该方法将 IFR 和感染到死亡的时延的不确定性纳入，并考虑人口的易感性耗竭。
• 结果在单一框架内为14个国家联合产生，并与代码一起在线提供。
• 使用敏感性分析（如 PSIS-LOO）评估对某些建模选择的鲁棒性。
• 技术更新增加了人口饱和、IFR 的先验不确定性、对干预效应的改进先验和封锁的部分 pooling。