Analyzing the spatial distribution of PCB concentrations in soils using below-quantification limit data

Abstract

Polychlorinated biphenyls (PCBs) are highly toxic environmental pollutants that can accumulate in soils. We consider the problem of explaining and mapping the spatial distribution of PCBs using a spatial data set of 105 PCB-187 measurements from a region in the north of France. A large proportion of our data (35%) fell below a quantification limit (QL), meaning that their concentrations could not be determined to a sufficient degree of precision. Where a measurement fell below this QL, the inequality information was all that we were presented with. In this work, we demonstrate a full geostatistical analysis-bringing together the various components, including model selection, cross-validation, and mapping-using censored data to represent the uncertainty that results from below-QL observations. We implement a Monte Carlo maximum likelihood approach to estimate the geostatistical model parameters. To select the best set of explanatory variables for explaining and mapping the spatial distribution of PCB-187 concentrations, we apply the Akaike Information Criterion (AIC). The AIC provides a trade-off between the goodness-of-fit of a model and its complexity (i.e., the number of covariates). We then use the best set of explanatory variables to help interpolate the measurements via a Bayesian approach, and produce maps of the predictions. We calculate predictions of the probability of exceeding a concentration threshold, above which the land could be considered as contaminated. The work demonstrates some differences between approaches based on censored data and on imputed data (in which the below-QL data are replaced by a value of half of the QL). Cross-validation results demonstrate better predictions based on the censored data approach, and we should therefore have confidence in the information provided by predictions from this method.