Use of Censored Multiple Regression to Interpret Temporal Environmental Data and Assess Remedy Progress

Abstract

Many methods to evaluate temporal trends in monitoring data focus on univariate techniques that account for changes in the response variable (e.g., concentration) by means of a single variable, namely time. When predictable site-specific factors, such as groundwater-surface water interactions, are associated with or may cause concentration changes, univariate methods may be insufficient for characterizing, estimating, and forecasting temporal trends. Multiple regression methods can incorporate additional explanatory variables, thereby minimizing the amount of unexplained variability that is relegated to the “error” term. However, the presence of sample results that are below laboratory reporting limits (i.e., censored) prohibits the direct application of the standard least-squares method for multiple regression. Maximum likelihood estimation (MLE) for multiple regression analysis can enhance temporal trend analysis in the presence of censored response data and improve characterizing, estimating, and forecasting of temporal trends. Multiple regression using MLE (or censored multiple regression) was demonstrated at the U.S. Department of Energy Hanford Site where analyte concentrations in groundwater samples are negatively correlated with the stage of the nearby Columbia River. Incorporating a time-lagged stage variable in the regression analysis of these data provides more reliable estimates of future concentrations, reducing the uncertainty in evaluating the progress of remediation toward remedial action objectives. Censored multiple regression can identify significant changes over time; project when maxima and minima of interest are likely to occur; estimate average values and their confidence limits over time periods relevant to regulatory compliance; and thereby improve the management of remedial action monitoring programs.