Department of Health Studies and Statistics and Actuarial Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada.
Environ Monit Assess. 1989 Nov;13(2-3):285-94. doi: 10.1007/BF00394234.
When investigating trace substances in ambient water, a proportion of water sample concentrations is usually below limits of detection. In medical and industrial reliability studies, comparisons are often made of time to event data which includes right censored observations indicating only that an observation is greater than a specified value. In this paper consideration is given to the application of non-parametric procedures, widely used in the analysis of time to event data, to water quality data which is left censored.A non-parametric estimate of the cumulative distribution function for left censored water quality data can be generated quite easily. For the comparison of levels of trace substances it is necessary to combine an unconditional likelihood for the proportion of observations below a detection limit with a partial likelihood for the portion of the distribution above the detection limit in order to make use of regression methodology. The details of this are outlined and an example is given which compares levels of toxic substances at the head and mouth of the Niagara river.When comparisons are based on matched pair data, further modifications are necessary. A development paralleling that for time to event data is given. Consideration is also given to model extensions which allow for a dependence between observations at the same location over a period of time.The presentation is introductory and designed to illustrate the potential of some available methodology for use in the analysis of water quality data.
在调查环境水中的痕量物质时，通常会有一部分水样浓度低于检测限。在医学和工业可靠性研究中，通常会对包括右删失观测值的事件时间数据进行比较，这些观测值仅表示观测值大于指定值。本文考虑将广泛应用于事件时间数据分析的非参数程序应用于左删失水质数据。对于左删失水质数据的累积分布函数，可以很容易地生成非参数估计。为了比较痕量物质的水平，有必要将低于检测限的观测比例的无条件似然与检测限以上部分的分布的部分似然结合起来，以便使用回归方法。本文概述了这一点，并给出了一个示例，比较了尼亚加拉河源头和河口的有毒物质水平。当基于匹配对数据进行比较时，需要进一步进行修改。给出了与事件时间数据类似的发展。还考虑了允许在一段时间内对同一位置的观测值之间存在依赖性的模型扩展。本演示文稿是介绍性的，旨在说明一些可用方法在水质数据分析中的应用潜力。
