Assessing the predictive performance of risk-based water quality criteria using decision error estimates from receiver operating characteristics (ROC) analysis.

Field data relating aquatic ecosystem responses with water quality constituents that are potential ecosystem stressors are being used increasingly in the United States in the derivation of water quality criteria to protect aquatic life. In light of this trend, there is a need for transparent quantitative methods to assess the performance of models that predict ecological conditions using a stressor-response relationship, a response variable threshold, and a stressor variable criterion. Analysis of receiver operating characteristics (ROC analysis) has a considerable history of successful use in medical diagnostic, industrial, and other fields for similarly structured decision problems, but its use for informing water quality management decisions involving risk-based environmental criteria is less common. In this article, ROC analysis is used to evaluate predictions of ecological response variable status for 3 water quality stressor-response data sets. Information on error rates is emphasized due in part to their common use in environmental studies to describe uncertainty. One data set is comprised of simulated data, and 2 involve field measurements described previously in the literature. These data sets are also analyzed using linear regression and conditional probability analysis for comparison. Results indicate that of the methods studied, ROC analysis provides the most comprehensive characterization of prediction error rates including false positive, false negative, positive predictive, and negative predictive errors. This information may be used along with other data analysis procedures to set quality objectives for and assess the predictive performance of risk-based criteria to support water quality management decisions.