Estimating a Representative Value and Proportion of True Zeros for Censored Analytical Data with Applications to Contaminated Site Assessment

摘要

This paper demonstrates a maximum likelihood (ML)-based approach to derive representative ("best guess") contaminant concentrations from data with censored values (e.g., less than the detection limit). The method represents an advancement over existing techniques because it is capable of estimating the proportion of measurements that are true zeros and incorporating varying levels of censorship (e.g., sample specific detection limits, changes through time in method detection). The ability of the method to estimate the proportion of true zeros is validated using precipitation data. The stability and flexibility of the method are demonstrated with stochastic simulation, a sensitivity analysis, and unbiasedness analysis including varying numbers of significant digits. A key aspect of this paper is the application of the statistical analysis to real site rock core contaminant concentration data collected within a plume at two locations using high resolution depth-discrete sampling. Comparison of the representative values for concentrations at each location along the plume center-line shows a larger number of true zeros and generally lower concentrations at the downgradient location according to the conceptual site model, leading to improved estimates of attenuation with distance and/or time and associated confidence; this is not achievable using deterministic methods. The practical relevance of the proposed method is that it provides an unproved basis for evaluating change (spatial, temporal, or both) in environmental systems.