School of Social and Community Medicine, University of Bristol, Canynge Hall, 39 Whatley Road, Bristol BS8 2PS, UK.
School of Social and Community Medicine, University of Bristol, Canynge Hall, 39 Whatley Road, Bristol BS8 2PS, UK.
Sci Total Environ. 2014 Jul 15;487(100):642-50. doi: 10.1016/j.scitotenv.2014.02.101. Epub 2014 Mar 15.
Concentrations of metabolites of illicit drugs in sewage water can be measured with great accuracy and precision, thanks to the development of sensitive and robust analytical methods. Based on assumptions about factors including the excretion profile of the parent drug, routes of administration and the number of individuals using the wastewater system, the level of consumption of a drug can be estimated from such measured concentrations. When presenting results from these 'back-calculations', the multiple sources of uncertainty are often discussed, but are not usually explicitly taken into account in the estimation process. In this paper we demonstrate how these calculations can be placed in a more formal statistical framework by assuming a distribution for each parameter involved, based on a review of the evidence underpinning it. Using a Monte Carlo simulations approach, it is then straightforward to propagate uncertainty in each parameter through the back-calculations, producing a distribution for instead of a single estimate of daily or average consumption. This can be summarised for example by a median and credible interval. To demonstrate this approach, we estimate cocaine consumption in a large urban UK population, using measured concentrations of two of its metabolites, benzoylecgonine and norbenzoylecgonine. We also demonstrate a more sophisticated analysis, implemented within a Bayesian statistical framework using Markov chain Monte Carlo simulation. Our model allows the two metabolites to simultaneously inform estimates of daily cocaine consumption and explicitly allows for variability between days. After accounting for this variability, the resulting credible interval for average daily consumption is appropriately wider, representing additional uncertainty. We discuss possibilities for extensions to the model, and whether analysis of wastewater samples has potential to contribute to a prevalence model for illicit drug use.
由于灵敏且强大的分析方法的发展，可以非常准确和精确地测量污水中非法药物代谢物的浓度。基于关于母体药物排泄模式、给药途径和使用废水系统的个体数量等因素的假设，可以根据这些测量浓度估算药物的消费水平。在呈现这些“反推”结果时，通常会讨论多个来源的不确定性，但在估计过程中通常不会明确考虑这些不确定性。在本文中，我们通过为涉及的每个参数假设一个分布来演示如何将这些计算置于更正式的统计框架中，该分布基于对支持该分布的证据的审查。然后，通过使用蒙特卡罗模拟方法，很容易将每个参数的不确定性通过反推传播，从而产生每日或平均消费的分布而不是单一估计值。例如，可以用中位数和可信区间来总结。为了演示这种方法，我们使用两种代谢物苯甲酰爱康宁和去甲苯甲酰爱康宁的测量浓度来估计英国一个大城市的可卡因消费。我们还展示了一种更复杂的分析，该分析在贝叶斯统计框架内使用马尔可夫链蒙特卡罗模拟实现。我们的模型允许两种代谢物同时为每日可卡因消费的估计提供信息，并明确允许每天之间的变化。在考虑到这种可变性之后，平均每日消费的可信区间适当变宽，代表了额外的不确定性。我们讨论了模型扩展的可能性，以及废水样本分析是否有可能为非法药物使用的流行模型做出贡献。
