A key component of site characterization is the statistical analysis of contaminant concentrations in soil, water and air samples. Such analysis can pose challenges due to the presence of nondetects or left-censored observations, which are measurements smaller than a detection limit. Censored values should be accounted for because they do not imply the absence of contamination, but the insufficient accuracy of the measuring instruments. Indeed, trace levels of hazardous pollutants can pose risks to the human health and the environment. Even if an environmental investigation achieves a representative sample of concentration data according to sound analytical protocols and data validation procedures, improper statistical analyses that do not properly accommodate censored observations may not represent actual site conditions. Obviously, remedial designs based on a distorted view of the contamination condition could be ineffective and not sustainable environmentally and economically.
The main goal of this research is to scrutinize the impact of left-censored values on site characterization outcomes. To this end, we explore different statistical methods (i) to estimate descriptive statistics, (ii) to quantify uncertainty around estimates, and (iii) to examine potential dependencies across observations due to clustering as an inherent part of sampling techniques. Substituting censored values with an arbitrarily selected constant is commonly practiced by both practitioners and researchers. In contrast, there are a number of parametric and non-parametric methods that can be used to draw inferences from censored data, and therefore, provide a more realistic insight into a contamination problem. Parametric methods, such as maximum likelihood and regression-based procedures, estimate descriptive statistics through fitting a parametric distribution to data. Due to the right-skewed shape of concentration data, gamma, Weibull, and lognormal distributions are the most plausible parametric models, with the latter being the most commonly used in environmental studies. Non-parametric procedures such as the Kaplan-Meier method, however, do not require any distributional assumption.
This study employs a comprehensive data simulation exercise, in which the true underlying distribution is known, to evaluate the performance of parametric and non-parametric estimators based on a large number of scenarios differing in censoring percent, sample size, and data skewness. This research also highlights the importance of investigating the robustness of parametric methods against model misspecifications. Using simulated data, we elucidate how substituting censored observations provides biased estimates and why it should be avoided even for data with a small percentage of censoring. We found that the maximum likelihood method based on the lognormality assumption is highly sensitive to data skewness, sample size, and censoring percentage. While the lognormal maximum likelihood method is mainly used in environmental studies, our findings point out that caution should be exercised in assuming a lognormal density distribution of data. Instead, we recommend the maximum likelihood estimator based on a gamma distribution, regression-based methods (using either a lognormal or gamma distribution), and the Kaplan-Meier technique. With respect to quantifying the uncertainty around estimates for real concentration data, in which the true structure of data is unknown, we evaluate the performance of parametric and non-parametric estimators employing a bootstrapping technique. The conclusions drawn from bootstrapping of real data are in accordance with those inferred from the simulated data.
An important part of this research investigates the presence of correlation, associated with sampling techniques, among concentration observations. We provide statistical and conceptual backgrounds as well as motivations for mixed effects models that are able to accommodate dependence across data points while accounting for censored observations. Standard statistical methods assume that samples of concentration data are independent. However, in environmental site characterization studies, this assumption is likely to be violated because concentration observations collected, for example, from the same borehole are presumably correlated. This can in turn affect sample size determination procedures. We therefore employ a mixed effects model to capture potential dependencies and between group variability in data. The relevance of the estimated between-borehole variability is explained in terms of determining the optimal number of boreholes as well as samples to be collected from each borehole. Our proposed mixed effects model also provides insights into the vertical extent of contamination that can be useful in designing remediation strategies.
The findings of this doctoral research help increase the awareness of the scientific community as well as practitioners, exposure assessors, and policy-makers about the importance of censored observations. Aiming at unification of the field, this thesis contributes to literature by improving our understanding of the comparative aspects of different statistical methods in the context of site characterization studies. It thus offers considerable promise as a guideline to researchers, practitioners, and decision-makers.
| Date | 22 Nov 2016 |
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| Original language | American English |
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| Awarding Institution | - École de technologie supérieure
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| Supervisor | Jean-Sébastien Dubé (Supervisor) |
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