Exploring the space-time pattern of log-transformed infectious count of COVID-19: a clustering-segmented autoregressive sigmoid model
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新冠感染计数的时空模式：聚类分段自回归 S 形曲线模型
- 研究问题
- 如何同时刻画对数感染计数的空间分组、增长曲线、时间依赖和未知变点，并用统一模型比较不同地区疫情演化及防控政策相关差异？
- 方法与思路
- 作者结合未知聚类、变点、伸展 S 形曲线与自回归项，提出非参数图聚类和惩罚过度聚类的纯度分数，以 BIC 选择变点并估计均值区间。
- 材料陈述的贡献
- 摘要称，图聚类获得理论支持，且在所设模拟中比参数聚类更快、更准确；模型应用于中国及部分国家数据，用于解释疫情曲线与政策差异。
- 阅读关注点
- 应核对图构建与聚类条件、纯度指标、变点选择和区间覆盖率，以及病例口径和报告变化如何处理，政策解释是否有额外识别依据。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未列理论条件或模拟设计，疫情曲线拟合和国家比较不足以确认防控政策的因果效果。
原文摘要
At the end of April 20, 2020, there were only a few new COVID-19 cases remaining in China, whereas the rest of the world had shown increases in the number of new cases. It is of extreme importance to develop an efficient statistical model of COVID-19 spread, which could help in the global fight against the virus. We propose a clustering-segmented autoregressive sigmoid (CSAS) model to explore the space-time pattern of the log-transformed infectious count. Four key characteristics are included in this CSAS model, including unknown clusters, change points, stretched S-curves, and autoregressive terms, in order to understand how this outbreak is spreading in time and in space, to understand how the spread is affected by epidemic control strategies, and to apply the model to updated data from an extended period of time. We propose a nonparametric graph-based clustering method for discovering dissimilarity of the curve time series in space, which is justified with theoretical support to demonstrate how the model works under mild and easily verified conditions. We propose a very strict purity score that penalizes overestimation of clusters. Simulations show that our nonparametric graph-based clustering method is faster and more accurate than the parametric clustering method regardless of the size of data sets. We provide a Bayesian information criterion (BIC) to identify multiple change points and calculate a confidence interval for a mean response. By applying the CSAS model to the collected data, we can explain the differences between prevention and control policies in China and selected countries.