Laboratoire des Techniques de l'Ingénierie Médicale et de la Complexité, Université Grenoble 1, 38706 La Tronche, France.
Biostatistics. 2010 Oct;11(4):644-60. doi: 10.1093/biostatistics/kxq022. Epub 2010 May 10.
Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian computation (ABC), an alternative to data imputation methods such as Markov chain Monte Carlo (MCMC) 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%.
数据缺失是流行病学中一个常见的问题，在这个问题中，感染过程可能部分可见。近似贝叶斯计算（ABC）是一种替代数据插补方法（如马尔可夫链蒙特卡罗（MCMC）积分）的方法，用于在流行病学模型中进行推断。它是一种无似然的方法，仅依赖于数值模拟。ABC 包括计算模拟和观察到的汇总统计数据之间的距离，并根据该距离对模拟进行加权。我们提出了一种对路径值汇总统计数据的原始 ABC 扩展，对应于随时间累积的检测次数。对于具有易感者、感染者和恢复者的标准隔室模型（SIR），我们表明 ABC 和 MCMC 获得的后验分布相似。在一个非常适合古巴 HIV 接触者追踪数据的精细 SIR 模型中，我们在具有完整和分组检测时间的 ABC 之间进行了比较。对于古巴数据，我们评估了检测系统的效率并预测了 HIV-艾滋病的发展。特别是，发现未被检测到的传染性个体的百分比约为 40%。
