Limits of detection and decision. Part 3

Abstract It has been shown that the MARLAP (Multi-Agency Radiological Laboratory Analytical Protocols) for estimating the Currie detection limit, which is based on ‘critical values of the non-centrality parameter of the non-central t distribution’, is intrinsically biased, even if no calibration curve or regression is used. This completed the refutation of the method, begun in Part 2. With the field cleared of obstructions, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system (CMS) having heteroscedastic, Gaussian measurement noise and using weighted least squares (WLS) processing, was then derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, “hockey stick” and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.

[1]  P.W.J.M. Boumans,et al.  A tutorial review of some elementary concepts in the statistical evaluation of trace element measurements , 1978 .

[2]  L. A. Currie,et al.  LIMITS FOR QUALITATIVE DETECTION AND QUANTITATIVE DETERMINATION. APPLICATION TO RADIOCHEMISTRY. , 1968 .

[3]  Mocak,et al.  A STATISTICAL OVERVIEW OF STANDARD ( IUPAC AND ACS ) AND NEW PROCEDURES FOR DETERMINING THE LIMITS OF DETECTION AND QUANTIFICATION : APPLICATION TO VOLTAMMETRIC AND STNPPING TECHNIQUES , 2004 .

[4]  Agustin G. Asuero,et al.  Fitting Straight Lines with Replicated Observations by Linear Regression. III. Weighting Data , 2007 .

[5]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[6]  P.W.J.M. Boumans,et al.  Atomic emission detection limits; more than incidental analytical figures of merit! - A tutorial discussion of the differences and links between two complementary approaches— , 1991 .

[7]  Joel Tellinghuisen,et al.  Statistical Error Propagation , 2001 .

[8]  Lloyd A. Currie,et al.  Detection and quantification limits: origins and historical overview , 1997 .

[9]  B. Altschuler,et al.  Statistical Measures of the Lower Limit of Detection of a Radioactivity Counter , 1963 .

[10]  Graham R. Wood,et al.  Comparison of two common estimators of the ratio of the means of independent normal variables in agricultural research , 2006, Adv. Decis. Sci..

[11]  E. S. Pearson,et al.  ON THE USE AND INTERPRETATION OF CERTAIN TEST CRITERIA FOR PURPOSES OF STATISTICAL INFERENCE PART I , 1928 .

[12]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[13]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[14]  Analysis of interferents by means a D-optimal screening design and calibration using partial least squares regression in the spectrophotometric determination of Cr(VI). , 2007, Talanta.

[15]  P. Moschopoulos,et al.  The distribution of the sum of independent gamma random variables , 1985 .

[16]  L. A. Currie,et al.  Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995) , 1995 .

[17]  Lloyd A. Currie,et al.  Detection in Analytical Chemistry: Importance, Theory, and Practice , 1987 .

[18]  Volker Thomsen,et al.  Limits of Detection in Spectroscopy , 2003 .

[19]  Eric R. Ziegel,et al.  Statistical Methods for Detection and Quantification of Environmental Contamination , 2003, Technometrics.

[20]  P. Boumans.  Detection limits and spectral interferences in atomic emission spectrometry , 1994 .

[21]  J. D. Winefordner,et al.  Limit of detection. A closer look at the IUPAC definition , 1983 .

[22]  D. B. Owen,et al.  Confidence intervals for the coefficient of variation for the normal and log normal distributions , 1964 .

[23]  E. Voigtman,et al.  Statistical properties of limit of detection test statistics. , 2003, Talanta.

[24]  C. Andrew. Clayton,et al.  Detection limits with specified assurance probabilities , 1987 .

[25]  Erik Nielsen,et al.  Statistics for analytical chemistry , 1987 .

[26]  P. Boumans,et al.  Detection limit including selectivity as a criterion for line selection in trace analysis using inductively coupled plasma-atomic emission spectrometry (ICP-AES)—a tutorial treatment of a fundamental problem of AES , 1987 .

[27]  R. Fisher.  036: On a Distribution Yielding the Error Functions of Several Well Known Statistics. , 1924 .

[28]  H. Kaiser,et al.  Zum Problem der Nachweisgrenze , 1965 .

[29]  G. Scollary,et al.  A statistical overview of standard (IUPAC and ACS) and new procedures for determining the limits of detection and quantification: Application to voltammetric and stripping techniques (Technical Report) , 1997 .

[30]  D. E. Coleman,et al.  Regulation – From an industry perspective or: Relationships between detection limits, quantitation limits, and significant digits , 1997 .

[31]  Lloyd A. Currie,et al.  DETECTION : INTERNATIONAL UPDATE, AND SOME EMERGING DI-LEMMAS INVOLVING CALIBRATION, THE BLANK, AND MULTIPLE DETECTION DECISIONS , 1997 .

[32]  Andre. Hubaux,et al.  Decision and detection limits for calibration curves , 1970 .

[33]  The Distribution of the Estimated Coefficient of Variation , 1931 .

[34]  H. Kaiser.  Zur Definition der Nachweisgrenze, der Garantiegrenze und der dabei benutzten Begriffe , 1966 .

[35]  A. G. Asuero,et al.  Fitting Straight Lines with Replicated Observations by Linear Regression: Part II. Testing for Homogeneity of Variances , 2004 .

[36]  R. Gibbons,et al.  Weighted least-squares approach to calculating limits of detection and quantification by modeling variability as a function of concentration. , 1997, Analytical chemistry.

[37]  Leonard Oppenheimer,et al.  Determining the lowest limit of reliable assay measurement , 1983 .