title: An investigation of the impact of left-censored soil contamination data on the uncertainty of descriptive statistical parameters.
abstract: Left-censored concentration data are frequently encountered because measuring instruments cannot detect concentrations below the instrument detection limit. For statistical analysis of left-censored data, the environmental literature mainly refers to the following methods: maximum likelihood estimator, regression on order statistics using log-normal and gamma assumption (rROS and GROS, respectively), and Kaplan-Meier. A number of simulation experiments examined the performance of these methods in terms of bias and/or mean square error. However, no matter which method is adopted, some uncertainty is introduced into outcomes because all that is known about a left-censored observation is that the concentration falls between 0 and the detection limit. The data used in the present study come from analysis of soil samples collected for a site characterization in Montreal, Canada. Employing nonparametric bootstrap, the authors quantify the uncertainty and bias in the mean and standard deviation estimates obtained by the maximum likelihood estimation (under log-normal, Weibull, and gamma distributions), rROS, GROS, and Kaplan-Meier methods. First, the authors demonstrate that the highest uncertainty is associated with the maximum likelihood estimator under log-normality and Weibull assumptions, whereas a gamma assumption leads to estimates with less uncertainty. Second, the authors show that although an increase in sample size improves the uncertainty, it reduces the bias only in the rROS, GROS, and Kaplan-Meier methods. Finally, comparing percentage uncertainty in the mean of contaminant data, the authors illustrate that adopting an inappropriate estimator results in large uncertainties. Environ Toxicol Chem 2016;35:2623-2631. © 2016 SETAC.
authors.affiliation: Department of Construction Engineering, École de technologie supérieure, Montréal, Quebec, Canada. niloofar.shoari.1@ens.etsmtl.ca.|Department of Statistics, Texas A&M University, College Station, Texas, USA. niloofar.shoari.1@ens.etsmtl.ca.
authors.forename: Niloofar
authors.initials: N
authors.lastname: Shoari
authors.affiliation: Department of Construction Engineering, École de technologie supérieure, Montréal, Quebec, Canada.
authors.forename: Jean-Sébastien
authors.initials: JS
authors.lastname: Dubé
mesh_terms: D002170:Canada; D003627:Data Interpretation, Statistical; D004784:Environmental Monitoring / Q000706:statistics & numerical data*; D016013:Likelihood Functions; D057230:Limit of Detection; D018401:Sample Size; D012987:Soil / Q000737:chemistry* / Q000592:standards; D012989:Soil Pollutants / Q000032:analysis*; D035501:Uncertainty
chemical_list: D012987:Soil; D012989:Soil Pollutants
keywords: Contaminants; Hazard/risk assessment; Left-censored; Nonparametric bootstrap; Soil contamination; Uncertainty