Practical quantitation limits

Gibbons, Robert D.; Grams, Nancy; Jarke, Frank H.; Stoub, Kenneth P.

doi:10.1016/0169-7439(92)80003-m

Cited by 16 publications

(29 citation statements)

References 6 publications

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“…Here we select the smallest value of X such that the LCL > 0. Second, we can also use the method to obtain a quantification limit (see Currie 1968Currie , 1995Gibbons, Grams, Jarke, and Stoub 1992;Gibbons, Coleman, and Maddalone 1997). In this case we seek the true concentration for which the confidence interval is sufficiently small to provide a reliable quantitative determination.…”

Section: Discussionmentioning

confidence: 99%

Confidence Regions for Random-Effects Calibration Curves With Heteroscedastic Errors

Bhaumik

Gibbons

2005

Technometrics

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We construct confidence bounds for a random-effects calibration curve model. An example application is analysis of analytical chemistry data in which the calibration curve contains measurements y for several values of known concentration x in each of q laboratories. Laboratory is considered a random effect in this design, and the intercept and slope of the calibration curve are allowed to have laboratory-specific values.Here we (a) develop an appropriate interlaboratory calibration curve for heteroscedastic data of the type commonly observed in analytical chemistry; (b) compute a point estimate for an unknown true concentration X when corresponding measured concentrations Y 1 , Y 2 , . . . , Y q are provided from q laboratories (i.e., a subset of the original q laboratories used to calibrate the model, where 1 ≤ q ≤ q); (c) compute the asymptotic mean and variance of the estimate; and (d) construct a confidence region for X. We then illustrate the methods are using both simulated and typical interlaboratory calibration data. Other relevant applications of the general approach are highlighted.

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Section: Discussionmentioning

confidence: 99%

Confidence Regions for Random-Effects Calibration Curves With Heteroscedastic Errors

Bhaumik

Gibbons

2005

Technometrics

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“…A more direct, operational, definition has been proposed by Adams et al (24) who defined L Q as the concentration at which the relative standard deviation is 10%. Gibbons has shown how to apply this results-oriented definition for the linear calibration case when variance stabilizing transformations are required (25). However, work in the area of non-linear calibration is at the stage where correct estimation and characterization of the calibration function is still of interest (26).…”

Section: Quantitationmentioning

confidence: 99%

“…If there were eight concentration levels, a zero concentration standard, and a blank without antibody to check for non-specific binding, with each analysis done in triplicate, then 30 analyses would be needed for the calibration curve. The estimation of quantitation limits for linear response functions by Gibbons et al, (25) suggested 50 to 100 determinations in order to avoid complex measurement error components in the calculation. This is certainly possible for a 96-well plate format or where large numbers of samples are run in highly controlled conditions, but rather formidable for field analysis of a few samples or immunoassay formats accommodating few standards.…”

Section: Limitations and Barriersmentioning

confidence: 99%

Maximizing Information from Field Immunoassay Evaluation Studies

Gerlach

Emon

1996

ACS Symposium Series

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The U.S. Environmental Protection Agency (EPA) and other regulatory agencies are beginning to accept data from environmental immunoassay field evaluation studies. This paper focuses on practical problems and suggested solutions to a variety of statistical and data analysis issues related to analytical method evaluation problems encountered with environmental immunoassays. We propose that multiple estimates of performance parameters be obtained from independent parts of an evaluation whenever possible, and that confidence intervals or range estimates are better descriptors of expected performance than point estimates. Methods for minimizing false negative and false positive rates are discussed and guidance is provided when calculating confidence intervals of small rates and proportions. Examples using nonlinear calibration curves and limits of detection demonstrate the importance of understanding experimental design and variance sources when interpreting field evaluation results. Experimental factors and scientific assumptions must match statistical assumptions in order to produce results which correctly characterize an evaluation.The EPA's Characterization Research Division -Las Vegas has been active in several field evaluation studies of immunoassay test kits at Superfund and other hazardous waste sites. These studies are an important phase in building confidence in the environmental analysis community for this new methodology. One feature of many of the field immunoassays is their relative ease of use. However, easy-to-use methods do not necessarily generate easy-to-understand data sets. Each evaluation also tends to have many phases which generate a number of sets of data. Our experience in developing and evaluating environmental immunoassays has resulted in improved understanding of many aspects of immunoassay method validation. Our review of data packages sub-

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“…To obtain the limit of detection for concentration, a simple linear transformation on

{\overset{LOD}{true}}_{Y}

is performed [13], to obtain:

{\overset{LOD}{true}}_{X} = \frac{3 {({\hat{σ}}^{2} + {\hat{σ}}_{β_{0}}^{2})}^{1 ∕ 2}}{{\overset{β}{true}}_{1}}

…”

Section: Introductionmentioning

confidence: 99%

Change‐point models to estimate the limit of detection

May

Chu

Ibrahim

et al. 2013

Statistics in Medicine

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In many biological and environmental studies, measured data is subject to a limit of detection. The limit of detection is generally defined as the lowest concentration of analyte that can be differentiated from a blank sample with some certainty. Data falling below the limit of detection is left-censored, falling below a level that is easily quantified by a measuring device. A great deal of interest lies in estimating the limit of detection for a particular measurement device. In this paper we propose a change-point model to estimate the limit of detection using data from an experiment with known analyte concentrations. Estimation of the limit of detection proceeds by a two-stage maximum likelihood method. Extensions are considered that allow for censored measurements and data from multiple experiments. A simulation study is conducted demonstrating that in some settings the change-point model provides less biased estimates of the limit of detection than conventional methods. The proposed method is then applied to data from an HIV pilot study.

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Practical quantitation limits

Cited by 16 publications

References 6 publications

Confidence Regions for Random-Effects Calibration Curves With Heteroscedastic Errors

Confidence Regions for Random-Effects Calibration Curves With Heteroscedastic Errors

Maximizing Information from Field Immunoassay Evaluation Studies

Change‐point models to estimate the limit of detection

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