Citation:

SINGH, A. AND J. M. NOCERINO. STATISTICAL METHODS FOR ENVIRONMENTAL APPLICATIONS USING DATA SETS WITH BELOW DETECTION LIMIT OBSERVATIONS AS INCORPORTED IN PROUCL 4.0. Presented at 26th Annual EPA Quality Assurance Conference, Cincinnati, OH, June 11 - 14, 2007.

Impact/Purpose:

The overall objectives of this task are to: 1) provide ORD state-of-the-science technical support and assistance to Regional staff; 2) facilitate the evaluation and application of site characterization technologies at Superfund and RCRA sites; and 3) improve communication among Regions and ORD laboratories.

Description:

Nondetect (ND) or below detection limit (BDL) results cannot be measured accurately, and, therefore, are reported as less than certain detection limit (DL) values. However, since the presence of some contaminants (e.g., dioxin) in environmental media may pose a threat to human health and the environment, even at trace levels, the NDs cannot be ignored or deleted from subsequent statistical analyses. Using data sets with NDs and multiple DLs, practitioners need to compute reliable estimates of the population mean, standard deviation, and various upper limits, including the upper confidence limit (UCL) of the population mean, the upper prediction limit (UPL), and the upper tolerance limit (UTL). Exposure assessment, risk management, and cleanup decisions at potentially impacted sites are often made based upon the mean concentrations and the UCLs of the means of the contaminants of potential concern (COPCs), whereas background evaluations and comparisons require the computations of UPLs and UTLs to estimate background threshold values (BTVs) and other not-to-exceed values. The 95% UCLs are used to estimate the exposure point concentration (EPC) terms or to verify the attainment of cleanup levels; and upper percentiles, UPLs, and UTLs are used for screening of the COPCs, to identify polluted site areas of concern and hot spots, and also to compare site concentrations with those of the background.

Even though methods exist in the literature to estimate the population mean and the standard deviation for data sets with NDs, no specific guidance with a theoretical justification is available on how to compute appropriate UCLs, UPLs, and other limits based upon data sets with NDs and multiple DLs. The main objective of this paper is to present defensible statistical methods that can be used to compute appropriate estimates of environmental parameters, EPC terms, BTVs, and other not-to-exceed values based upon data sets with NDs. This paper describes both parametric and nonparametric methods to compute UCLs, UPLs, and UTLs based upon data sets with NDs having multiple DLs. Some of the methods considered include: the maximum Likelihood Estimation (MLE) method, the regression on order statistics (ROS) methods, and the Kaplan-Meier (KM) method. Based upon our findings, it is recommended to avoid the use of ad hoc UCL methods based upon Student's t-statistic on ML estimates. It is also suggested to avoid the use of the DL/2 method on data sets even with low (<5%-10%) censoring intensities. It is shown that, just like for uncensored data sets, for highly skewed data sets with NDs, one should use the Chebyshev inequality based UCLs (e.g. using KM estimates) to provide an adequate coverage for the population mean.

Several of these methods have been incorporated into the ProUCL 4.0 software package. ProUCL 4.0 makes some recommendations based upon the results and findings of Singh, Maichle, and Lee (EPA 2006). Some examples to elaborate on the issues of distortion of the various statistics and upper limits by outliers and by the use of a lognormal model to accommodate those outliers will be discussed using ProUCL 4.0.

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