The detection limit Waer quality monitoring data are plagued with levels of chemicals that are too low to be measured precisely c
P. Steven Porter Everglades Research and Education Center Belle Glade, FL 33430 Robert C . Ward Colorado State Universiry Fort Collins, CO 80523 HarryF.BeU IBM Cop. HoDeweN Junction. NY 12533 Water quality management in the United States, having undergone a major legal redirection in 1972, is evolving into an ongoing and routine management effort. Earlier emphasis seemed to be on defining and solving problems rather than operating under the type of continuous control mandated by the 1972 legislation (EL. 92500). This evolution has allowed management to evaluate its information needs. Water quality monitoring provides management with its major source of information about progress toward national water quality goals. However, the inadequacies of monitoring as an information source for water quality management are a concern, having been described (1-5) and discussed in detail (6). Such simple questions as “Is the environment cleaner than it was 15 years ago?” are, in fact, difficultto answer. One reason often cited for management’s inability to answer this question is the lack of monitoring information. Walter A. Lyon, an adjunct professor of civil and urban engineering at the University of Pennsylvania and a witness at the 1983 Congressional hearings on environmental monitoring, testified: “Unquestionably there is a most serious and pervading need for knowledge. . . . Current monitoring does not adequately serve the important purposes of evaluating the progress of national environmental programs . . . and we don’t really know whether we 856 Environ. Sci. Technol., Vol. 22,No. 8, 1988
FlGU
me
a l i i monitoring system
Sample mllection
Sam Fie1b)measurements lingtechniques
I
Laboratory analysis
Jata handling
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Screening and verWation of data Computer hardware Data base management system Stofageandretrieval
Data Analysis Statistical pmcedures with mnespding software Deterministic modeling Water quality index
Rerating . Formats Frequency Distribution
Information utilizatwn Public
Poliimakino . ..~., ~=
Administration Technical
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001M36w881MM2.0856so1.5010 B 1888 American Chemkd Society
are spending this [ S O billion per year] wisely” (6). Statistical analysis of water quality
data, an important aspect of water resource management, depends in part on the integrity of water quality measurements. An active quality assurance effort can often guarantee that such measurements reflect a true state of nature and not some property of the sampling and analysis system. However, many of today’s water quality problems are associated with chemical levels too low to be measured pre+ely. Our discussion will focus on the information needs of water quality management and how these needs are best met for monitoring systems that require many trace-level measurements. We propose that the limit of detection (LOD) or the limit of quantitation (LOQ) not be used to censor data. Although LOD and LOQ aid in the interpretation of individual measurements, they hinder statistical analysis of water quality data. More information is gained when a numerical result and an estimate of measurement precision are reported for every measurement, as opposed to reporting “not detected” or “less than.” This article is not intended to be a review of the issues pertaining to the LOD and related concepts. The reader is referred elsewhere (7-13) for thorough discussions of this topic. statisticalanalysis When measurements less than the LOD are reported as not detected (ND), the data are referred to as censored. Statistical methods for censored data were developed to analyze failure time and survival experiments in which the observations consist of the time for a particular event to occur. For example, one may want to know the average survival time of heart transplant patients. For subjects who survive, it is known only that their survival time is greater than some time r,. Experiments are concluded after a 6 x 4 time or a fixed proportion of failures, producing what is termed type I and type U censored data, respectively. When only the smallest values of an experiment can be observed, the sample is said to be “censored on the right.” When only the largest values can be observed, the sample is “censored on the left.” Water quality data with ND results are type I censored on the left. The level of censoring is determined by the analytical chemist and is based on the confidence with which the analytical signal can be discerned from noise. Samples taken over time may be censored at different levels as changes in analytical technology alter the precision
Statistics are used terpret water quality behavior. They are applied to data records that often contain “nondetects” (NDs), which water quality managers
ndicate the information content of the sample The 95% confidence interval
1 (00for the mean using data of Figure 3 and the method of (Reference41) IS
ifferent censoring levels. Other methods for censored data could have been chosen for this illustram better than the method of Reference form better than the analogous method for censored data will Drobablv be more
Envimn. Sci. Technol., Val. 22. No. 8. 1988 857
I of a method. This multiple censoring also occu~sif analytical results are reported according to ACS “Guidelines for Reporting Data” (7). For example, “not detected” is reported if the analytical response is less than the LOD; “detected” is reported if the analytical response is between the LOD and M Q (the “region of less certain quantitation”); and a numerical result is reported if the analytical response is DNDND ND greater than the LOQ. Water quality data may have very complicated patterns of censoring. The statistical literature contains procedures for censored data that are useful for virtually every problem encountered by water quality managers, including parameter estimation, goodness of fit, regression, and several others. Many of these methods are summarized in books (14-16) that include working examples. Because these methods were developed for failure time and survival analysis, some modification may be necessary to make them usable for data that are type I censored on the lei? (water quality data). Also, many distributions found in survival analysis are not commonly found in water quality data. Reference 17 provides goodness-of-fit tests, parameter estimation, tests for trend, and twosample comparisons using left-censored samples from normally and lognormally distributed populations. Many methods suitable for censored data are sensitive to assumptions about the underlying distribution. Gilliom and Helsel (18) developed means for matching the estimated form of a distribution with a particular estimator (for mean, variance, and median) by using the relative quartile range of the uncensored portion of the sample. They also assessed the performance of a variety of estimators with small samples. Other gocdness-of-fit tests for censored data are described elsewhere (14-16). Gilliom and Helsel (18) also investigated assigning a random number to censored results. Several distributions censored sample can be considered to found in uncensored water quality data be lognormally distributed; d e x r i p were used for purposes of simulation. tions of the method of quantiles and of a For example, when it is thought that graphical method are included. data are normally distributed, normal scores are calculated for results above the LOD and plotted on normal proba- Monitoring information bility paper. A least-squares fit to the Given the many ways that water normal plot is extrapolated into the less quality data with trace-level measurethan or ND region. Extrapolated values ments could be handled, the question becomes: “Which methods, if any, are of less than zero are readjusted to zero. Gilbert and Kinnison (19)describe in able to meet the information needs of detail the use of additional estimators management?” This question can be for samples from lognormally distrib- quite complex, given the variety of stauted populations, including those de- tistical problems in water quality manscribed by Aitchison and Brown (20). agement, yet one simple principle apIn addition, Gilbert and Kinnison pro- plies: Censoring results in a loss of vide guidelines for determining when a information. Data that include NDs 858 Envimn. Sci. Technol.. MI. 22, No. 8. 1988
a
NDNDNDNDNDNDNDND
contain less information than data for which numbers are reported, even if some of those numbers are very imprecise. Information from the point of view of a manager, who must make d e cisions based on water quality measurements, is related to the statistical confidence that can be provided by a given number of observations. More information is provided when an estimate of precision is given for every measurement. It may be useful to consider the problem of information within the context of water quality monitoring, which may be viewed as an information system designed to supply knowledge and understanding about water quality condi-
tions. The flow of information (Figure 1) must be organized and well defined so that no opportunity exists for misinterpretation of objectives from one step to the next. The goals and objectives of the information system must be clearly delineated. The driving force for the flow of information is the fundamental knowledge prcduced by the sampling and analysis portions of the monitoring system. The major objective of sampling is to provide representative portions of the water body for analysis, whereas the aim of an analysis is to reduce uncertainty with respect to the sample to be analyzed, which is equivalent to obtaining information (22). Reducing uncertainty with respect to a sample is bindered by imperfections in the sampling and measurement p m esse% At each step, useful information as well as noise is introduced. Ideally, the noise is removed without meaningful loss of information. In real situations,however, all results contain some noise, and no result preserves all of the information in a sample. Thus water quality monitoring data differ from survival or failure time data, for which methods for censored data were developed. In failure time experiments, numerical responses (failure times) are given precisely and it is presumed that nothing can be said about the failure times of surviving subjects, except that they are greater than the termination time of the experiment. This would hold true for water quality data if censored results were entirely random and numerical responses were entirely deterministic. The presence of trace-level measurements in data greatly complicates the design of the data analysis portion of a monitoring system, which follows from consideration of statistical hypotheses that assess whether certain Objectives are Wing met. For example, a goal of the Clean Water Act is to restore and maintain the integrity of the nation’s waters. A particular objective in pursuit of this goal is to enforce water quality srandards in the nations’ rivers. In order to assess progress toward this Objective, statistical hypotheses must be developed. Some questions that come to mind are “What is the probability that water quality will exceed a standard?” and “Is there a trend in a particular water quality variable that could result in a future exceedance?” Methods that address questions of this M~UEwhen data are censored are far more complicated than analogous methods for complete data, both computationally and in the assessment of properties. Complications arise with censored data because the method itself must convert censored results to numerical responses for computations and
because it is nearly impossible to de.-
scribe a method‘s behavior under all the many possible censoring patterns that may arise. Merely providing the numerical response observed in the l a b ratory simplifies both these tasks. More serious, however, is the issue of information. Because the possibility of making a wrong decision increases significantly as analyte concentration declines, information users must be made aware of the uncertainties associated with data that include trace-level determinations (23). This note of caution can provide the impetus for obtaining as much information as possible
frmn a limited number of water quality measurements and utilizing additional information produced by the measure ment system in the deciion-making process. The simple example in Box 1 illustntes the concept of information with respect to the size of a confidence interval. More complex examples can be found in Gilliom et al. (26), who show that power in trend detection is improved when uncermn ‘ results (as op posed to ND)are provided. Porter (17) showed that estimators for the mean of lognormally distributed water quality variables are more e5ciently estimated
Emimn.Sci.Techrol.,MI.Z, No.8. lSee 059
when numerical results rather than censored data are provided. In general, censored data have been shown to contain less information than complete data with respect to many measures of information (e.g., size of confidence interval and variance of estimation) for various statistical criteria (e.g., desired type I and type II error rates). This occurs for any frequency distribution l i l y to be found in water quality data, regardless of the criteria used to censor data. The use of observation error takes this concept a step further.
t a transformation of a water
The analytical signal S is linearly related to
System error System error should be considered in the statistical analyses of monitoring data. Therefore it is desirable from a data analysis viewpoint to express measured concentrations, X,, as
x,
Xm = -k e@p) (1) where X, is the true population concentration and e@,) is the error introduced by the measurement system. The single most important characteristic of any result obtained from one or more analytical measurements is an adequate statement of the uncertainty interval (23). Water quality management attempts to describe the statistical nature of X, given a set of X,. Clearly, near limits of detection, some information about ewp) is necessary. More generally, e@,) should include all sources of error in the monitoring system. Given estimates of the statistical properties of e@,), one can work from X,,, to determine properties of X,. For example, one could estimate analytical signal error and its tragformation by the calibration function (Le., mean and variance of X , for a given, fixed X ); similarly, one could consider the in&ence of other sources of observation error in the monitoring system on X,. Other possibilities include determining the statistical properties of e&) (mean, variance, and distribution) and developing statistical procedures that provide information about X, in contrast to X,. Specific applications are discussed elsewhere (27-34). The problems described by Fuller (27),Hahn (29, J=h (3@,Mee (30, and Mee et al. (32) hinge on the distinction between these two questions: What is the probability that water quality will exceed a standard? and What is the probability that a water quality measurement will exceed a standard? The answers to these two questions generally differ, yet many water quality managers believe they are answering the first question when in fact they are addressing the second. Satterthwaite (34) and Gaylor and Hopper (28) address the problem of es860 Environ. Sci. Technol.. Vol. 22. No.8. 1988
= (S- 4Ybi where 4 and b, are WLS estimates of Bo a Xm
timating the variance of X, from sepaand rate estimates of the variance of X,,, e&). Vecchia et al. (33) consider the special problem posed by calibrated results (those derived from a calibration experiment). Porter (17)attempts to describe the statistical properties of water quality measurements and the influence of those properties on the effectiveness of the methods developed by the au-
thors just mentioned. The box illustrates the approach used in that study.
s-ry There is a need to analyze water quality data statistically in order to meet the evolving information needs of water quality management. Consequently, a discussion of observation error in monitoring systems and of ana-
lytical error near LODs is needed. A significant improvement in the information content of near-detectionlimit data would occur if one simply reponed the results of all analyses plus an estimate of observation error. The concept of ND is not altered because a confidence interval for X, that overlaps zero is a valid statistical definition of ND. Reporting x, and an estimate of observation error provides more informalion than does ND or simply X,. Reporting X, would improve management responses to water quality statistical hypotheses because such reporting distinguishes between variability caused by natural processes and variability introduced by the monitoring system. The routine reporting of observation error is not common in water quality particularly for monitoring required by regulatory agencies. As noted, the American Chemical Society (3,Kaiser (12), Skogerboe and Koirtyohann (39)*Taylor and Stanley (40), and Wilson (41) have suggested reporting the measurement precision. In addilion, Gilbert and Kinnison (19) suggest that all results be reported 10 facilitate statistical data analysis. The practice may become more prevdent because EPA recently proposed guidelines for regulating drinking-water standards; some of these guidelines are based on the precision of measurements near or at the analytical detection limit (Practical Quantitation Limits). Dowd (42) has suggested that this r e p resents “regulation by analytical chemistry.” It is hoped that discussion will further the dialogue concerning information needs and monitoring objectives between water quality managers and the analysts who generate the data.
Acknowledgment
T h e support of IBM Corporation for P: S. Porter’s Environmental Engineering Graduate Fellowship at Colorado State University is gratefully acknowledged. This article has k e n reviewed for suitability as a n ES&T feature by L. B. Rogers, University of Georgia, Athens, GA
30602.
Referenfes ( I ) Council on Environment Quality; “Final Report of the Interagency Task Force on Environmental Data and Monitoring“; National Technical Information Service: Springfield. VA. 1980. (2) National Academy of Sciences; “Analytical Studies for the U S . Environmental Protection A ency”; National Academ ofsciences: bashingfon. DC. 1977: 4. Accounting Office: “Better (3) Monitoring Techniques Are Needed to Assess the Quality of Rivers and Streams”; Report No. CED-81-30: U.S. General Accounting Office:Washington, DC, 1981; 1981-341-843-635.
(4) General Accounting Offce: “The Nation’s Water: Key Unanswered Questions About the Quality of Rivers a n d Streams”; Report No. GAOIPEMD-866; U.S. General Accountin Office: Washington, DC. 1986: f986-491 -234102. (5) ~ ~ R~~~~~~~ ~ Council; i ..National ~ ~ Water Quality Monitoring and Assessment”; National Academy Press: Wash-
(6) ington, u,s, House DC. 1987. of Re re~entatives, NinetyEighth Congress. 8rst Session; Hearings before the Subcommittee on Natural Resources. Agriculture. Research. and Environment of the Committee an Science and TechnolopNo: 70; “National Environmental onitoring”; U.S. Governmen1 Printing Office: Washington. DC. 1983: 28-186-0. (7) American Chemical Society Committee an Environmental Improvements Anal. Chem. 1983,SS. 2210-18. (8) Clayton, C. A,: Hines. J. W.; Elkins, P D. Anal. Chem. 1987.59, 2506-14. (9) Currie, L. A. And. Chem. IW, 40, 586-93. (IO) Glaser. J . A. et al. Environ. Sei. Technol. 1981. I S , 1426-35. (11) Hubaux, A,: VOS, G. Anol. Chem. 1910, 42. 849-85. (12) Kaiser, H. A n d . Chem. 1970, 42. 26A-
(34) Satterthwaite, E E. 8iOm.Bull. 1986, 2. 110-14. (35) Prudnikov, E. D. Spectrochim. Ana 1981,368. 385-92. (36) Prudnikov, E. D.; Shapkina, Y S . AnaI S I 1984,109, 305-17. (37) arden. 1. S.; Mitchell. D. G.; Mills. ~ W. N. Anol. l Chem. 1980.52, 2310-15. (38) Hinkley, D. V Biomerriko 1969.56, 63539. (39) Skogerboe, R. K.: Koirtyohann. S. R. “Accuracy Assurance in the Analysis of Environmental Samples”; NBS Special Publication 422; National Bureau of Standards: Gaithersburg, MD. 1976; p. 199. (40) Taylor J. K.: Stanley, T. W. “Quality AsSurance for Environmental Measuremenis”; ASTM Special Technical Publication 867. American Society for Testing and Materials: Philadelphia. 1985. (41) Wilson. A. L. Talonlo 1970, 17. 21-30. (42) Dowd, R. M. Environ. Sci. Technol. 1985, 19. 1156.
e
59A.
(13) Long. G. L.; Winefordner. J. D. Anal. Chem. 1983,55, 712A-724A. (14) Cox. D. R.; Oakes. D. Analysis ofsurvivo1 Data: Chapman and Hall: New York, 1984. (15) Miller, R. G . Survival Anoiysis: wiley: New Yark, 1981. (16) Kalbfleisch. J . ; F’rentice. R. L. The Stotirriral Analysis of Failure Time Dora: Wiley: New York. 1980. (17) porter. p. S. Ph.D. Thesis. Colorado State University. 1986. (18) Gilliom, R. J.; Helsel. D. R. “Estimation of Distributional parameters for ten. sored Trace-Level Water Quality Data”; U S Geological Survey open file report 84-729. 1984. (19) Gilbert, R. 0.; Kinnison. R. R. Health
(20) Phvs. Aitchison, 1981.40, J , ;377-90. Brown. Lognormal Distribution: Cambridge at
R %even I S an U.S.SLY an professor in the lnsriture of Food and Agriculrural Sciences at the Univer.siry of Florida. He earnedhis 8,s. and M.S. degreesfrom the Universiry of Illinois and his Ph.D. from Colorado Sfare University; all degrees are in envimmenral engineering. He has worked as a consulranr fo industry in the areas of hazardous-wasre management. water quality monitoring, and wastewater freatment. He is currently conducting research on waferqua~~rymonitor~ngsysrems and the effectsofagriculturalpracrices on wafer quali? in
the University Press: Cambridge, U.K., 1957. (21) ward, R. c.; McBride. G . B. “Design of Water Quality Monitoring Systems in New Zealand”; Publication No. 8 : Water Quality Centre. Ministry of Works and Development: Hamilton, New Zealand. 1986. (22) Massart. D. L.;Dijkstra, A,; Kaufman. rL.o Evaluarion r o ~Methodr and Oprimizorion Anal~licol oflnbo-
durcs: Elsevier: New York. 1978; Vol. I . (23) Ro ers. L. B. J. Chem. Educ. 1986, 63, 3-%. (24) schmee, J . ; Gladstein. D.; ~~l~~~ w. Terhnomerrics. 1985.27. 119-28. (25) American Society for Testing and Materials; Annual Book of ASTM Standards: American Society for Testing and Materiais: Philadelphia. 1983: p. 354. (26) Gilliom. R. 1 . ; Hirsch, R. M.: Gilroy, E. J. Environ. Sci. Technol. 1984, 18. 530-35. (27) ~ ~ [ w,l A. ~ ~M~~~~~~~~~~ , E~~~~ Models: Wiley: New York, 1987. (28) Gaylor. D. w.; Hopper, E N. Technometrim 1969, 11. 691-706. (29) Hahn, G . J . J . Quo[. Techno/. 1982, 14, 117-21. (30) Jaech. 1. L. J. Q d Technol. 1984, 16. 69-73. (31) Mee, R. W. J. Qual. Technol. 1984, 16. 74-80. (32) Mee. R. w.: Owen. D. B.; Shyu, J. J. Qual. Technol. 1986, 18, 29-40. (33) Vecchia, D. F, el J , Quo(. ~&,,,,l,, in press.
Robert C. Ward (1) i s p r f ~ i w cillv die o,vricultural and dremical enyineeriny depnrrment and associme dean in the College of Engineering at Colorado State Unimrsiry. He is the of more than 70 and a rexrbook on water quality monitoring and of the Moni. toring Newark Design Short Course, conducred annually since 1979.
Hany E BeU (r) is a senior scientist in I B M k General Technology Division, lo-
caredin HopewelIJuncrion, Nl! Heholdsa B.S. degree in chemisrr rom N i z a berhtown College and a P l d : in analytical chemistryfrom the University of Delaware. He has been employed 1967. His current responsib groundwarer.moniroring nework and starisrical merhods f o r the analysis of environmenral monitoring data.
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