Brookmeyer R, Blades N, Hugh-Jones M, Henderson D A
Department of Biostatistics, Johns Hopkins University School of Public Health, Baltimore, MD 21205, USA.
Biostatistics. 2001 Jun;2(2):233-47. doi: 10.1093/biostatistics/2.2.233.
An outbreak of anthrax occurred in the city of Sverdlovsk in Russia in the spring of 1979. The outbreak was due to the inhalation of spores that were accidentally released from a military microbiology facility. In response to the outbreak a public health intervention was mounted that included distribution of antibiotics and vaccine. The objective of this paper is to develop and apply statistical methodology to analyse the Sverdlovsk outbreak, and in particular to estimate the incubation period of inhalational anthrax and the number of deaths that may have been prevented by the public health intervention. The data available for analysis from this common source epidemic are the incubation periods of reported deaths. The statistical problem is that incubation periods are truncated because some individuals may have had their deaths prevented by the public health interventions and thus are not included in the data. However, it is not known how many persons received the intervention or how efficacious was the intervention. A likelihood function is formulated that accounts for the effects of truncation. The likelihood is decomposed into a binomial likelihood with unknown sample size and a conditional likelihood for the incubation periods. The methods are extended to allow for a phase-in of the intervention over time. Assuming a lognormal model for the incubation period distribution, the median and mean incubation periods were estimated to be 11.0 and 14.2 days respectively. These estimates are longer than have been previously reported in the literature. The death toll from the Sverdlovsk anthrax outbreak could have been about 14% larger had there not been a public health intervention; however, the confidence intervals are wide (95% CI 0-61%). The sensitivity of the results to model assumptions and the parametric model for the incubation period distribution are investigated. The results are useful for determining how long antibiotic therapy should be continued in suspected anthrax cases and also for estimating the ultimate number of deaths in a new outbreak in the absence of any public health interventions.
1979年春，俄罗斯斯维尔德洛夫斯克市爆发了炭疽疫情。此次疫情是由于军事微生物设施意外释放出的孢子被吸入所致。针对此次疫情，开展了一项公共卫生干预措施，包括分发抗生素和疫苗。本文的目的是开发并应用统计方法来分析斯维尔德洛夫斯克疫情，特别是估计吸入性炭疽的潜伏期以及公共卫生干预措施可能预防的死亡人数。可用于分析此次共同来源疫情的数据是报告死亡病例的潜伏期。统计问题在于潜伏期被截断了，因为一些人的死亡可能已被公共卫生干预措施阻止，因此未被纳入数据。然而，不知道有多少人接受了干预，也不知道干预措施的效果如何。构建了一个考虑截断效应的似然函数。该似然函数被分解为一个样本量未知的二项似然函数和潜伏期的条件似然函数。这些方法得到了扩展，以考虑干预措施随时间逐步实施的情况。假设潜伏期分布服从对数正态模型，估计中位数和平均潜伏期分别为11.0天和14.2天。这些估计值比之前文献中报道的要长。如果没有公共卫生干预措施，斯维尔德洛夫斯克炭疽疫情的死亡人数可能会增加约14%；然而，置信区间较宽（95%置信区间为0 - 61%）。研究了结果对模型假设和潜伏期分布参数模型的敏感性。这些结果对于确定疑似炭疽病例应持续进行抗生素治疗的时长以及估计在没有任何公共卫生干预措施的情况下新疫情中的最终死亡人数很有用。
