Institute of Medical Biometry and Medical Informatics, University Medical Center, Freiburg, Germany.
Comput Methods Programs Biomed. 2011 Nov;104(2):29-36. doi: 10.1016/j.cmpb.2010.05.007. Epub 2010 Jul 14.
Mathematical modelling of infectious diseases has gained growing attention in epidemiology during the last decades. The major benefits of simulating compartmental models are the prediction of the consequences of potential interventions, a deeper understanding of epidemic dynamics and clinical decision support. The main limitation is however that several parameters are based on uncertain expert guesses (default values) and are not estimated from the study data. In this paper we build a bridge between an extension of the well-known deterministic S-I-R (Susceptible-Infectious-Removed) model which can be described with differential equations and the stochastic counterpart which can be used for statistical inference if outbreak data on an individual level are available. The possibly time-dependent transmission rate as well as the (basic) reproduction number are the main epidemiological parameters of interest. Furthermore, one important type of heterogeneity is considered: individuals may vary due to their susceptibility, i.e., risk factors for infection may be investigated. A SAS computer program is provided to simulate outbreak data for this type of setting. The statistical analysis and typical challenges with epidemic data are discussed. Given data on an individual level, the Cox-Aalen survival model that is based on a multiplicative-additive hazard structure turned out to be a suitable tool for that purpose. The results give valuable information for epidemiologists, statisticians and public health researchers.
在过去几十年的流行病学中，传染病的数学建模得到了越来越多的关注。模拟房室模型的主要好处是可以预测潜在干预措施的后果，可以更深入地了解疫情动态，并为临床决策提供支持。然而，主要的局限性在于，几个参数是基于不确定的专家猜测（默认值），而不是从研究数据中估计出来的。本文在著名的确定性 S-I-R（易感-感染-移除）模型的扩展和随机模型之间架起了一座桥梁，该模型可以用微分方程来描述，如果有个体水平的疫情数据，则可以用于统计推断。可能时变的传播率以及（基本）繁殖数是感兴趣的主要流行病学参数。此外，还考虑了一种重要的异质性类型：个体可能因易感性而有所不同，即可以研究感染的危险因素。为此类设置提供了一个模拟疫情数据的 SAS 计算机程序。讨论了统计分析和疫情数据的典型挑战。对于个体水平的数据，基于乘法加法风险结构的 Cox-Aalen 生存模型是一种合适的工具。结果为流行病学家、统计学家和公共卫生研究人员提供了有价值的信息。
