Estimation of descriptive statistics for multiply censored water quality data

Helsel, Dennis R.; Cohn, Timothy A.

doi:10.1029/wr024i012p01997

Cited by 312 publications

(260 citation statements)

References 13 publications

(15 reference statements)

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“…Commonly, a value of ½ the minimum reporting value is substituted for these values when calculating the mean or other summary statistics from such data. However, this leads to substantial bias on any subsequently calculated statistical values (Singh and Nocerino 2002) and represents a significant loss of information (Helsel and Cohn 1988). Despite the clear limitations of such data substitution, it is specified in the European QA/QC Directive (EC 2009) as an appropriate data manipulation.…”

Section: Assessment: the Use Of Monitoring Data And Wqgs To Support Dmentioning

confidence: 99%

Water quality guidelines for chemicals: learning lessons to deliver meaningful environmental metrics

Merrington

Grist

et al. 2013

Environ Sci Pollut Res

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Many jurisdictions around the globe have well developed regulatory frameworks for the derivation and implementation of water quality guidelines (WQGs) or their equivalent (e.g. environmental quality standards, criteria, objectives or limits). However, a great many more still do not have such frameworks and are looking to introduce practical methods to manage chemical exposures in aquatic ecosystems. There is a potential opportunity for learning and sharing of data and information between experts from different jurisdictions in order to deliver efficient and effective methods to manage potential aquatic risks, including the considerable reduction in the need for aquatic toxicity testing and the rapid identification of common challenges. This paper reports the outputs of an international workshop with representatives from 14 countries held in Hong Kong in December 2011. The aim of the workshop and this paper was to identify 'good practice' in the development of WQGs to deliver to a range environmental management goals. However, it is important to broaden this consideration to cover often overlooked facets of implementable WQGs, such as demonstrable field-validation (i.e., does the WQG protect what it is supposed to?), fit for purpose of monitoring frameworks (often an on-going cost) and finally how are these monitoring data used to support management decisions in a manner that is transparent and understandable to stakeholders. It is clear that regulators and the regulated community have numerous pressures and constraints on their resources. Therefore the final section of this paper addresses potential areas of collaboration and harmonisation. Such approaches could deliver a consistent foundation from which to assess potential chemical aquatic risks, including, for example, the adoption of bioavailability-based approaches for metals, whilst reducing administrative and technical burdens in jurisdictions.

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Section: Assessment: the Use Of Monitoring Data And Wqgs To Support Dmentioning

confidence: 99%

Water quality guidelines for chemicals: learning lessons to deliver meaningful environmental metrics

Merrington

Grist

et al. 2013

Environ Sci Pollut Res

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“…PPR fills in missing observations and zeros using estimates of the missing observations obtained by a regression of the observed values against their normal scores or another appropriate variate. The method was formalized by Gilliom and Helsel [1986] and was later studied by Helsel and Cohn [1988] and Kroll and Stedinger [1996]. This method also appears in the statistical literature where it has been applied to normal samples [David, 1980].…”

Section: Probability Plot Regressionmentioning

confidence: 99%

Log Pearson type 3 quantile estimators with regional skew information and low outlier adjustments

Griffis

Stedinger

Cohn

2004

Water Resources Research

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[1] The recently developed expected moments algorithm (EMA) [Cohn et al., 1997] does as well as maximum likelihood estimations at estimating log-Pearson type 3 (LP3) flood quantiles using systematic and historical flood information. Needed extensions include use of a regional skewness estimator and its precision to be consistent with Bulletin 17B. Another issue addressed by Bulletin 17B is the treatment of low outliers. A Monte Carlo study compares the performance of Bulletin 17B using the entire sample with and without regional skew with estimators that use regional skew and censor low outliers, including an extended EMA estimator, the conditional probability adjustment (CPA) from Bulletin 17B, and an estimator that uses probability plot regression (PPR) to compute substitute values for low outliers. Estimators that neglect regional skew information do much worse than estimators that use an informative regional skewness estimator. For LP3 data the low outlier rejection procedure generally results in no loss of overall accuracy, and the differences between the MSEs of the estimators that used an informative regional skew are generally modest in the skewness range of real interest. Samples contaminated to model actual flood data demonstrate that estimators which give special treatment to low outliers significantly outperform estimators that make no such adjustment.

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“…In the parametric ML method, the parameters are estimated by maximizing the likelihood function, which is a product of the probability density function (PDF) for the measurements greater than the LOD and the cumulative distribution function (CDF) for the measurements less than the LOD (Fisher,1925;Cohen, 1959Cohen, , 1961Finkelstein and Verma, 2001). Probability plot-based methods [also known as regression on order statistics (ROS) or log-probit regression (LPR)] computes the mean and standard deviation by fitting a linear regression of the log-transformed data versus their normal scores on a normal or lognormal probability plot (Kroll and Stedinger, 1996;Helsel and Cohen, 1988;Gilliom and Helsel, 1986). The LPR method was generally comparable to the ML method in most simulation studies, although its variant (the robust LPR) might show slight improvement over the ML under a simulated mixed distribution (Gilliom and Helsel, 1986).…”

Section: Introductionmentioning

confidence: 99%

A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data

Huynh

Quick

Ramachandran

et al. 2015

ANNHYG

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Classical statistical methods for analyzing exposure data with values below the detection limits are well described in the occupational hygiene literature, but an evaluation of a Bayesian approach for handling such data is currently lacking. Here, we first describe a Bayesian framework for analyzing censored data. We then present the results of a simulation study conducted to compare the β-substitution method with a Bayesian method for exposure datasets drawn from lognormal distributions and mixed lognormal distributions with varying sample sizes, geometric standard deviations (GSDs), and censoring for single and multiple limits of detection. For each set of factors, estimates for the arithmetic mean (AM), geometric mean, GSD, and the 95th percentile (X 0.95 ) of the exposure distribution were obtained. We evaluated the performance of each method using relative bias, the root mean squared error (rMSE), and coverage (the proportion of the computed 95% uncertainty intervals containing the true value). The Bayesian method using non-informative priors and the β-substitution method were generally comparable in bias and rMSE when estimating the AM and GM. For the GSD and the 95th percentile, the Bayesian method with non-informative priors was more biased and had a higher rMSE than the β-substitution method, but use of more informative priors generally improved the Bayesian method's performance, making both the bias and the rMSE more comparable to the β-substitution method. An advantage of the Bayesian method is that it provided estimates of uncertainty for these parameters of interest and good coverage, whereas the β-substitution method only provided estimates of uncertainty for the AM, and coverage was not as consistent. Selection of one or the other method depends on the needs of the practitioner, the availability of prior information, and the distribution characteristics of the • 56Ann. Occup. Hyg., 2016, Vol. 60, No. 1, 56-73 doi:10.1093/annhyg/mev049 Advance Access publication 24 July 2015 measurement data. We suggest the use of Bayesian methods if the practitioner has the computational resources and prior information, as the method would generally provide accurate estimates and also provides the distributions of all of the parameters, which could be useful for making decisions in some applications.

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Estimation of descriptive statistics for multiply censored water quality data

Cited by 312 publications

References 13 publications

Water quality guidelines for chemicals: learning lessons to deliver meaningful environmental metrics

Water quality guidelines for chemicals: learning lessons to deliver meaningful environmental metrics

Log Pearson type 3 quantile estimators with regional skew information and low outlier adjustments

A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data

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