具有联系人追踪的HIV：近似贝叶斯计算的案例研究
HIV with contact-tracing: a case study in Approximate Bayesian Computation
摘要：
缺失数据是流行病学中经常出现的问题，其中可能部分观察到感染过程。近似贝叶斯计算，替代数据填补方法，如马尔可夫链蒙特卡罗集成，提出了在流行病学模型的推断。这是一种完全依赖于数值模拟的无可能性方法。ABC包括计算模拟和观察到的汇总统计量之间的距离，并根据该距离对模拟进行加权。我们提出了一个原始的扩展ABC路径值汇总统计，对应的累计检测次数作为时间的函数。对于一个标准的房室模型，成功的，传染病和被感染的个人（SIR），我们证明了后验分布得到的ABC和MCMC是相似的。在一个完善的SIR模型非常适合在古巴的艾滋病毒接触者追踪数据，我们进行了比较ABC与完整的和装箱的检测时间。对于古巴的数据，我们评估了检测系统的效率，并预测了艾滋病毒/艾滋病疾病的演变。特别地，发现未检测到的感染性个体的百分比为40%的量级。
英文摘要：
Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on numerical simulations. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detections as a function of time. For a standard compartmental model with Suceptible, Infectious and Recovered individuals (SIR), we show that the posterior distributions obtained with ABC and MCMC are similar. In a refined SIR model well-suited to the HIV contact-tracing data in Cuba, we perform a comparison between ABC with full and binned detection times. For the Cuban data, we evaluate the efficiency of the detection system and predict the evolution of the HIV-AIDS disease. In particular, the percentage of undetected infectious individuals is found to be of the order of 40%.
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