統計模型於新冠肺炎防疫評估

王威淳

doi:10.6342/NTU202101901

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统计模型於新冠肺炎防疫评估

Statistical Models for Evaluating COVID-19 Pandemic

王威淳 , 博士　　导师：陈秀熙　　

英文 DOI： 10.6342/NTU202101901

新冠肺炎；机器学习；马可夫模型；解封指数；精准监测； COVID-19 ； Machine learning ； Markov model ； Social distancing index ； Precision surveillance

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摘要 │ 参考文献 (159) │ 国际计量

摘要〈TOP〉

背景
面对新冠肺炎大流行下不同高关注变异株 (VOC) 持续出现，急需新颖的统计模型方法了解疾病的流行与影响。因此，本论文的研究目的包括两个部分：第一部分是发展机器学习方法於族群层级防疫作为的评估，结合无监督和监督方式，评估在COVID-19不同波流行之下NPIs作为和疫苗接种对社区疫情爆发的影响；第二部分则是发展一系列随机过程模式估计个人层级从感染、症状前期到症状期的自然进展，并应用於边境控制的精准监测及不同病毒量层级转的转转移以进行流行病学监测。
材料与方法
本论文使用2020年至2022年1月间全球开放式资料进行分析，包括考量疫苗施打情境下解封指数(Social Distancing Index, SDI)、有效再生数等。并利用台湾地区2021年5月至7月的社区感染资料，结合人口学特徵、症状和个人病毒量进行个人层级自然病史统计模型的估计。首先，以易感-感染-传染-恢复(SEIR)模型估计有效再生数(Rt)。结合无监督及监督机器学习方法预测COVID-19的传播式，开发贝氏随机多阶段马可夫模型，估计COVID-19疾病进展，以此为基础进行电脑模拟并提供不同边境控制精准策略的预期结果。最後，发展病毒量导引马可夫模型，以四阶段马可夫回归模式和九阶段离散时间马可夫模型，用於模拟个案在恢复前於不同隐状态(Hidden State)之间与病毒量相关的详细动态转换。
结果
从2021年1月1日到2022年1月22日，全球的流行病至少有三波流行。2021年5月台湾社区流行的实证资料显示NPI手段和检测在前爆发刚开始的两周估计其降低流行的效益达60%，并在2021年6月14日之後增强到超过90%，同时Rt从2021年5月的4.40下降到7月的0.29。
本论文使用的监督机器学习三种（SVM、逻辑斯回归和贝氏网络(Bayesian Network, BN)）中，BN在AUC方面表现最为出色，其次则为逻辑斯回归和SVM。BN将全球流行资料区分为两个群集：疫苗主导群集(群集1)及NPI主导群集(群集2)。
利用台湾2020年3月至2022年1月境外移入个案估计个人层级疾病进展模式，本论文将资料依变异株种类及流行趋势分为7个时期，包括两期D614G、两期Alpha、两期Delta，及近期Omicron。在D614G-1时期，无症状COVID-19的每日发生率估计爲109（每10万人）（95%信赖区间（CI）：98-121），D614G-2时期下降到40（95% CI：30-51），Alpha-1时期回到163（95% CI：141-188），在疫苗广泛接种的Alpha-2、Delta-1和Delta-2时期发生率再次分别下降到117（95% CI。100-135）、97（95%CI：77-120）和112（95%CI：90-134），而最近出现的VOC Omicron期则又使发生率重新上升到317（95%CI：267-371）。若以5天隔离期估算，Omicron将累积最多从症状前期发展到症状期的个案（94%），其次是Delta（74%和80%於两时期）、Alpha VOC（74%和66%於两时期）及D614G（80%和74%於两时期）。
利用隐藏马可夫模式分析台湾地区2021年5月至7月本土个案重覆Ct值变化可将个案分为五种状态：低风险、中风险、高风险、极高风险和康复状态，这五种隐状态对应的放射高斯机率(Emission Probability)分布之平均值分别爲45.0、34.2、29.9、23.8和15.8。其转移机率矩阵则显示病患在病程中不同Ct值变化倾向由低值(转高风险)至高值(较低风险)。
从上述隐藏马可夫模式的结果，我们进一步以Ct值15及25将病毒量分为三层，结合个案症状发生建构四阶段马可夫模式，分析不同病毒量对症状发生的胜算比及对潜伏时间的影响，结果发现中病毒量（15≦Ct<25）和高病毒量（Ct<15）比低病毒量（Ct≧25）的症状发生胜算比分别为3.04（2.43 - 3.61）和10.87（1.69 - 44.90）。中病毒量和高病毒量有较短的潜伏时间。
将病毒量变化视为不同阶段并估计其多阶段病程，结果显示不论在症状前期或症状期，疾病进展朝向高Ct水平（低病毒量）进展的速度比向低Ct水平（高病毒量）方向进展速度快。若比较不同Ct层级由症状前期进展到症状期的速率则发现低Ct水平的患者进展至症状期的速率较高。一旦进入症状期，向高Ct水平进展的速度比症状前期阶段的速率快。
结论
本论文以一系列系统性的新颖统计模型预测社区流行介入措施之效益，估计考量疫苗施打情境下的解封指数，评估遏制措施（包括NPIs、检测和疫苗）的效益，并估计考量病毒变化之个人层级COVID-19疾病自然进展史，期望以科学的方法系统性的提供边境管制实证效益评估和社区监测政策制定的宝贵讯息。

并列摘要〈TOP〉

Background
In the face of emerging variant of concern (VOC) on COVID-19 pandemic, the development of new epidemic modelling and approach is urgently needed. The objectives of this thesis therefore include two parts. The first part is to apply machine learning approach, combining the unsupervised and supervised methods, to assessing the influence of Non-Pharmaceutical Interventions (NPIs) and vaccine on community-acquired outbreaks given repeated surges of COVID-19 pandemic on population level; the second part is to develop a serial of stochastic process for modelling natural course of infectious process including pre-symptomatic and symptomatic phase for precision surveillance of border control and for modeling the detailed transitions of viral load level for epidemiological surveillance.
Materials and Methods
Open data repository in the period between 2020 and January 2022 were used for analysis. Information on demographic characteristic, symptom, and individual viral load were collected from community. The susceptible-exposed-infected-recovery model was used to estimate the effective productive number (Rt). Machine learning approach combining the unsupervised method and the supervised method was adopted to predict the spread of COVID-19. The four-state Markov model and computer simulation experiments with Bayesian underpinning was developed to model pre-symptomatic disease progression during incubation period to provide precision strategies for border control. The effect of viral-load was considered with two approaches, one regression approach and nine-state discrete-time Markov model approach. Ct-guided Markov model was applied to modelling the detailed dynamic transitions between different hidden states in relation to Ct before recovery.  
Results
The epidemics in the globe had at least three waves of epidemics from January 1st 2021 to January 22th 2022. Fitting the observational data on Taiwan community-acquired outbreak in May 2021, over 60 % of the effectiveness by NPI and testing in the first two weeks was estimated and enhanced to over 90% after June 14 2021. Rt decreased from 4.40 to 0.29 from May 18, 2021 to July 17, 2021.
Among the three supervised ML approach (SVM, logistic regression, and BN) embedded in the hierarchical supervision machine learning, BN demonstrated the superior performance in terms of AUC (87% in cluster 1 and 86% in cluster 2 for training datasets and 75% in cluster 1 and 70% in cluster 2 for validation datasets) followed by logistic regression and SVM. BN classified the global epidemic data into two clusters: the immunity dominant cluster (cluster 1) and the mitigation strategy dominant cluster (cluster 2).
The overall daily rate (per 100,000) of pre-symptomatic COVID-19 cases was estimated as 109 (95% confidence interval (CI): 98-121) in D614G-1 epoch, fell to 40 (95% CI: 30-51) in D614G-2 epoch, resurged to 163 (95% CI: 141-188) in Alpha-1 epoch, declined again to 117 (95% CI: 100-135), 97 (95% CI: 77-120) and 112 (95% CI: 90-134) in Alpha-2, Delta-1, and Delta-2 epoch, respectively, when vaccine was widely administered, and resurged again to 317 (95% CI: 267-371) in the recently emerging VOC Omicron epoch. The probability of progression from pre-symptomatic to symptomatic phase in 5-day quarantine was the highest for Omicron (94%) followed by Delta (74% and 80% in two periods), Alpha VOC (74% and 66% in two periods), followed by D614G (80% and 74% in two periods). 
The mean of Gaussian emission distribution of Ct value for the five hidden states, namely the low risk (state 2), medium risk (state 3), high risk (state 4), extremely high risk (state 5), and the recovery status (state 1) were estimated as 45.0, 34.2, 29.9, 23.8, and 15.8, respectively. The transition probabilities between these five states indicate that dynamic changes of viral load are more likely from the low to the high low Ct level. 
Guided by hidden states of Ct level, the high level of viral shedding was associated with higher proportion of being symptomatic. The odds ratios of medium (15Ct<25) and high level (Ct<15) levels were 3.04 (2.43, 3.61) and 10.87 (1.69, 44.90) than low level (Ct25), respectively. Both medium and high level was associated with shorter incubation time. 
The estimated results show the disease progression towards high Ct level (lower viral shedding) was faster than that towards the detrimental direction in both pre-symptomatic and symptomatic phases. Patients with low Ct level were more likely to develop symptoms compared with high Ct level. Once entering the symptomatic phase, the transition rates towards higher levels of Ct became faster than their counterparts in the pre-symptomatic phase. 
Conclusion
A series of new statistical models with a systematic approach were developed for predicting community-acquired outbreaks with interventions, estimating updated social distancing index, evaluating the effectiveness containment measures (including NPIs, testing, and vaccine), and modelling the occurrence and progression of pre-symptomatic and symptomatic COVID-19 cases in parallel with the evolution of viral shedding. All results provide valuable information for evidence-based policy-making on surveillance of border control and community.

参考文献 ( 159 ) 〈TOP〉

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