A simple approach to uncertainty propagation in preprocessed multivariate calibration

Abstract

A simple approach is described to estimate the confidence limit for the concentrations predicted by multivariate calibration when preprocessing techniques such as orthogonal signal correction or net analyte calculation are applied. It involves reconstructing the unpreprocessed data using the extracted spectral factors and those employed for prediction in order to correctly estimate the sample leverages. Monte Carlo simulations carried out by adding random noise to both concentrations and analytical signals for theoretical binary mixtures are in excellent agreement with the calculations. Experimental multicomponent examples were studied by a similar Monte Carlo approach, and the obtained variances are also in agreement with the calculated values. Implications concerning the limits of detection in the latter cases are also discussed.

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

“…12. In contrast to the previous case, here the factor, which dominates the concentration variance, is the uncertainty in analyte calibration concentrations [98]. Analogous to the univariate case, error-propagation expressions indicate that in the latter case the concentration uncertainty is strongly dependent on the sample leverage.…”

“…A literature survey shows that deriving formulas using the method of error propagation has been a major research topic. When employing first-order multivariate data, most publications are concerned with standard (i.e., linear) PLSR [22,23,[82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101] 8 The limit of detection is the analyte level that with sufficiently high probability (1 -β) will lead to a correct positive detection decision. The detection decision amounts to comparing the prediction ĉ with the critical level (L c ).…”

“…Additional selected examples involving the use of error-propagation for estimating concentration uncertainties and limit of detection are the spectrofluorometric determination of the antibiotic tetracycline in human serum [98,145] and the spectrophotometric analysis of bromhexine in a decongestant syrup [98,165]. In the former case, the analyte signal is completely overlapped by the stronger and intrinsically variable fluorescence bands of human serum, see Fig.…”

“…Therefore, several first-order multivariate models based on PLS regression were employed. A detailed analysis of the various uncertainty sources present in this system led to the conclusion that the dominating factor in estimating prediction uncertainties was the instrumental uncertainty for unknown samples, rather than the calibration modeling parameters [98]. The error propagation approach was compared with Monte Carlo simulations based on noise addition, and also with an empirical approach involving replicate analysis of spiked samples.…”

“…These three approaches were also successfully applied to the estimation of the limit of detection. The empirical approach included the analysis of samples of progressively decreasing analyte concentration [98,145].…”