ABSTRACT Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.

中文翻译：

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用于将随机流行病模型拟合到患病率数据的有效数据增强

摘要 随机流行病模型描述了疾病在人群中传播时流行病的动态。通常，在一组离散时间仅观察到一小部分病例。由于缺乏关于流行病时间演变的完整信息，导致了复杂的潜变量问题，其中流行病的状态空间规模随着人口规模的增加而变大。这使得即使对于中等规模的人群，对缺失数据进行分析整合也是不可行的。我们提出了一种数据增强马尔可夫链蒙特卡罗（MCMC）框架，用于随机流行病模型参数的贝叶斯估计，其中测量值随着受试者级别的疾病史而增强。在我们的 MCMC 算法中，我们根据数据提出每个新的受试者级路径，使用时间非均匀连续时间马尔可夫过程，其速率由其他个体的感染历史确定。该方法是通用的，并且可以应用于广泛的流行病模型，只需对模型动态和/或排放分布进行最小的修改。我们在多个随机流行病模型的背景下提出我们的算法，其中数据是二项式采样的患病率计数，并将我们的方法应用于英国寄宿学校流感爆发的数据。本文的补充材料可在线获取。