IUPAC-Consistent Approach to the Limit of Detection in Partial Least-Squares Calibration

ALLEGRINI FRANCO; OLIVIERI ALEJANDRO C.

ANALYTICAL CHEMISTRY

AMER CHEMICAL SOC

Lugar: Washington; Año: 2014 p. 7858 - 7866

0003-2700

There is currently no well-defined procedure for providing the limit of detection (LOD) in multivariate calibration. Defining an estimator for the LOD in this scenario has shown to be more complex than intuitively extending the traditional univariate definition. For these reasons, although many attempts have been made to arrive at a reasonable convention, additional effort is required to achieve full agreement between the univariate and multivariate LOD definitions. In this work, a novel approach is presented to estimate the LOD in partial least-squares (PLS) calibration. Instead of a single LOD value, an interval of LODs is provided, which depends on the variation of the background composition in the calibration space. This is in contrast with previously proposed univariate extensions of the LOD concept. With the present definition, the LOD interval becomes a parameter characterizing the overall PLS calibration model, and not each test sample in particular, as has been proposed in the past. The new approach takes into account IUPAC official recommendations, and also the latest developments in error-in-variables theory for PLS calibration. Both simulated and real analytical systems have been studied for illustrating the properties of the new LOD concept. Analytical chemistry is the science of chemical measurements, and thus it is of fundamental importance to develop appropriate estimators for the figures of merit which are conventionally used to evaluate the quality of the measurements.1−3 Among these figures of merit, one of the most controversial ones has been the limit of detection (LOD).4−7 Its importance lies in the fact that it is a good measure of the quality of a calibration model, because its definition brings together two important analytical concepts: the sensitivity and the precision in the analytical determinations. Currently, the International Union of Pure and Applied Chemistry (IUPAC) adopts the definition given by the International Standardization Organization (document ISO 11843)8 for the capability (or limit) of detection as ?the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) within a stated confidence limit?.9−11 This implies that the LOD is the minimum quantity detectable with a preset probability of false positives (Type I errors) and false negatives (Type II errors).9−11 Regarding LOD estimators, when the analytical signal is univariate and analyte-specific, the recommended detection rule is based on a Neyman-Pearson test that considers false-positive and false-negative errors for the null hypothesis ?there is no analyte? and the alternative hypothesis ?there is analyte?.9 The LOD can be directly estimated from the univariate calibration line, as a simple alternative to the original recommendation, in which the LOD is estimated from the average signal level and standard deviations for repeated