疫情初期复杂数据下病死率及其危险因素评估的统计方法研究

It is a significant and urgent researching task to study an accurate and timely assessment of the case fatality rate and risk factors, especially in the early stages, during an outbreak of a novel or emerging infectious disease such as SARS and influenza A (H1N1). If we apply the traditional estimator (cumulative number of deaths / cumulative number of infected cases) before the end of the epidemic, the estimates of case fatality rate are very likely to lead to a seriously bias because of ignoring large numbers of right censored cases (future deaths that have not yet been counted). After SARS, some statistical models of corrected for the lack were developed, however, they fail to deal with the screening of the risk factors, and observed cases data includes complex situations, such as, estimated accuracy correlates highly with competing risks (death and recovery), the left truncation and time-dependent covariates. Therefore, it is a critical and unsolved problem about how to establish some new statistical models (family) to complete the research tasks at the early stages of an outbreak. In view of the facts, this project, based on our group's present researches, survival analysis, competing risks and counting processes theory, plans to develop models of screening for multiple risk factors and covariates specific case fatality rate, and solve the problems of left truncation and time-dependent covariates present as well. The researching processes include mathematical derivations, statistical simulations (sensitivity analysis) and real data analysis, and the development of R package of the model family eventually. The results of this study are expected to be used for shaping and structuring public-health countermeasures of an emerging infectious disease. In addition, the results are not only limited to the case fatality rate study, but also likely to be applied to biology, medicine and other similar complex data.

当一种新发传染病疫情暴发，特别是在初期阶段，准确、及时地评估其病死率和危险因素是一项重要和迫切的研究任务。传统估计法：死亡数/患者数，在疫情未结束时因大量的右删失未被考虑，导致病死率被严重错估。自SARS出现，多个校正此种缺失的统计模型被发展，但均未涉及甄别其危险因素，而且被观察到的患者数据还包含竞争风险（死亡和治愈）、左截断和时协变量等影响估计准确度的复杂情况。此时，如何建立一个新型统计模型（族）去完成疫情初期的研究任务，是一个尚未解决的难题。鉴于此，本课题将在项目组已有的研究基础上，基于生存分析、竞争风险和计数过程等统计理论，经数理推导、统计模拟和流行病实例验证，建立包含多个危险因素的甄别和分群评估模型、解决左截断和时协变量存在的问题，并发展上述模型族的R软件包，以期为重大传染病的防控策略提供决策依据。此研究成果将不仅限于病死率相关研究，更可应用到生物、医学等类似复杂数据的统计分析中。

本课题针对新发传染病疫情爆发，特别是在疫情初期阶段，也就是删失率较高的时期，研究了如何估计其病死率和甄别其危险因素的统计方法。首先，研究基于汇总型数据的病死率估计模型，分析了课题组提出的基于竞争风险的非参数估计方法以及其它几种估计模型，通过模拟研究验证各种方法在不同条件下的精确性和稳定性，并应用到几种疫情数据分析中。其次，针对生存时间及含有有协变量（危险因素）的数据，基于竞争风险理论，结合轮廓似然等统计技术提出了新的半参数估计模型及考虑了变量的筛选问题。再次，左截断存在下病死率或生存率的估计，在原有左截断非参数估计的基础上，进行了一些估计法的矫正，通过模拟研究验证了新的矫正方法有更好的稳健性。同时，研究了在时协变量或风险率非比例下统计推断问题，主要针对组间（如不同治疗法）生存率（或说死亡率）比较的检验法问题开展研究，讨论了新旧多个检验法的性能，也分析了一些固定点、长期的检验方法。最后，额外针对隐形的传染源建立了新的传播动力学模型，及结合病死率及竞争风险概念建立了新的传染病传播模型。