Risk Assessment Division, Office of Public Health Science, Food Safety and Inspection Service, USDA, Fort Collins, CO 80526, USA.
Int J Food Microbiol. 2012 Jul 2;157(2):251-8. doi: 10.1016/j.ijfoodmicro.2012.05.014. Epub 2012 May 18.
Every year hundreds of thousands, if not millions, of samples are collected and analyzed to assess microbial contamination in food and water. The concentration of pathogenic organisms at the end of the production process is low for most commodities, so a highly sensitive screening test is used to determine whether the organism of interest is present in a sample. In some applications, samples that test positive are subjected to quantitation. The most probable number (MPN) technique is a common method to quantify the level of contamination in a sample because it is able to provide estimates at low concentrations. This technique uses a series of dilution count experiments to derive estimates of the concentration of the microorganism of interest. An application for these data is food-safety risk assessment, where the MPN concentration estimates can be fitted to a parametric distribution to summarize the range of potential exposures to the contaminant. Many different methods (e.g., substitution methods, maximum likelihood and regression on order statistics) have been proposed to fit microbial contamination data to a distribution, but the development of these methods rarely considers how the MPN technique influences the choice of distribution function and fitting method. An often overlooked aspect when applying these methods is whether the data represent actual measurements of the average concentration of microorganism per milliliter or the data are real-valued estimates of the average concentration, as is the case with MPN data. In this study, we propose two methods for fitting MPN data to a probability distribution. The first method uses a maximum likelihood estimator that takes average concentration values as the data inputs. The second is a Bayesian latent variable method that uses the counts of the number of positive tubes at each dilution to estimate the parameters of the contamination distribution. The performance of the two fitting methods is compared for two data sets that represent Salmonella and Campylobacter concentrations on chicken carcasses. The results demonstrate a bias in the maximum likelihood estimator that increases with reductions in average concentration. The Bayesian method provided unbiased estimates of the concentration distribution parameters for all data sets. We provide computer code for the Bayesian fitting method.
每年都有成千上万甚至上百万的样本被采集和分析，以评估食品和水中的微生物污染。对于大多数商品来说，在生产过程结束时，致病菌的浓度很低，因此需要使用高度敏感的筛选试验来确定感兴趣的生物体是否存在于样本中。在某些应用中，测试呈阳性的样本会进行定量分析。最可能数（MPN）技术是一种常见的定量样品污染水平的方法，因为它能够在低浓度下提供估计值。该技术使用一系列稀释计数实验来推导出感兴趣微生物的浓度估计值。这些数据的一个应用是食品安全风险评估，其中 MPN 浓度估计值可以拟合到参数分布中，以总结潜在暴露于污染物的范围。已经提出了许多不同的方法（例如，替代方法、最大似然和有序统计回归）来将微生物污染数据拟合到分布中，但这些方法的开发很少考虑 MPN 技术如何影响分布函数和拟合方法的选择。在应用这些方法时，经常被忽视的一个方面是数据是代表每毫升微生物的平均浓度的实际测量值，还是代表 MPN 数据的平均浓度的实际估计值。在这项研究中，我们提出了两种将 MPN 数据拟合到概率分布的方法。第一种方法使用最大似然估计器，将平均浓度值作为数据输入。第二种是贝叶斯潜在变量方法，它使用每个稀释度的阳性管数的计数来估计污染分布的参数。对于代表鸡肉胴体中沙门氏菌和弯曲杆菌浓度的两个数据集，比较了两种拟合方法的性能。结果表明，最大似然估计器存在偏差，随着平均浓度的降低而增加。贝叶斯方法为所有数据集提供了污染分布参数的无偏估计。我们提供了贝叶斯拟合方法的计算机代码。
