Analyzing censored water quality data using a non-parametric approach

In the analysis of water quality data, samples with concentrations reported below the limit of detection (LOD) are referred to as Type I censored on the left. A variety of procedures have been proposed for estimating descriptive statistics from left-censored data. Usually, the estimation is carried out by either replacing the LOD with a constant between 0 and the LOD, or assuming the data follow a normal or lognormal distribution. In this paper, a simple transformation is proposed to convert multiple left-censored water quality data to right-censored data. The transformed cumulative distribution is similar to a survival function, and enables use of survival analysis techniques for left-censored data. In particular, the product limit method (Kaplan-Meier estimator) is applied to estimate descriptive statistics from the transformed data. The performance of the Kaplan-Meier estimator is compared with maximum likelihood, probability plotting, and substitution methods by Monte Carlo simulations. The Kaplan-Meier estimator performs as well as or better than these more familiar methods. Finally, the Kaplan-Meier estimator is used to analyze some priority pollutant data collected in sediment from the central basin of Puget Sound.