D.Luc Massart

Comparison between the direct trilinear decomposition and the multivariate curve resolution-alternating least squares methods for the resolution of three-way data sets

Abstract Direct trilinear decomposition (DTD) and multivariate curve resolution-alternating least squares (MCR-ALS) methods are two of the most representative three-way resolution procedures. The former, non-iterative, is based on the resolution of the generalized eigenvector/eigenvalue problem and the latter, iterative, is focused on the optimization of initial estimates by using data structure and chemical constraints. DTD and MCR-ALS have been tested on a variety of three-way simulated data sets having common sources of variation in real response profiles, such as signal shift, broadening or shape distortions caused by noise. The effect of these factors on the resolution results has been evaluated through the analysis of several parameters related to the recovery of both qualitative and quantitative information and to the quality of the overall data description. Conclusions inferred from the simulated examples help to clarify the performance of both methods on a real example and to provide some general guidelines to understand better the potential of each method.

Inter-laboratory studies in analytical chemistry

Inter-laboratory studies are performed with different aims and consequently require different evaluation methods and statistical treatment. The review considers method-performance studies (collaborative trials), laboratory-performance studies (proficiency tests), collaborative bias evaluation, inter-laboratory evaluation of to-be standard methods as well as certification studies for reference materials. Besides the classical evaluation methods using outlier tests, robust statistics and graphical methods are taken into account.

Comparison of different approaches to estimate the uncertainty of a liquid chromatographic assay

A measurement result cannot be properly interpreted without knowledge about its uncertainty. Several concepts to estimate the uncertainty of a measurement result have been developed. Here, four different approaches for uncertainty estimation are compared on the example of the RP-high-performance liquid chromatography (HPLC) assay for tylosin for veterinary use: the guide to the expression of uncertainty in measurement (GUM) approach, which derives the uncertainty of a measurement result by combining the uncertainties related to the uncertainty sources of the measurement process; the top-down approach, which uses the reproducibility estimate from an inter-laboratory study as uncertainty estimate; an approach recently presented by Barwick and Ellison, which combines precision, trueness and robustness data to obtain an uncertainty estimate of the measurement result and finally a further approach, which directly estimates the measurement uncertainty from a robustness test. The comparison shows that the different approaches lead to comparable uncertainty estimates.

Comparison of alternative measurement methods

A procedure to compare the performance (precision and bias) of an alternative measurement method and a reference method has been extensively described. It is based on ISO 5725-6 which has been adapted to the intralaboratory situation. This means that the proposed approach does not evaluate the reproducibility, but considers the (operator+instrument+time)-different intermediate precision and/or the time-different intermediate precision. A 4-factor nested design is used for the study. The calculation of different variance estimates from the experimental data is carried out by ANOVA. The Satterthwaite approximation is included to determine the number of degrees of freedom associated with the compound variances. Taken into account the acceptable bias, the acceptable ratio between the precision parameters of the two methods, the significance level α and the probability β to wrongly accept an alternative method with an unacceptable performance, the formulae to determine the number of measurements required for the comparison are given. For the evaluation of the bias, in addition to the point hypothesis testing, the interval hypothesis testing is also included as an alternative. Two examples are given as an illustration of the proposed approach.

Robust regression and outlier detection in the evaluation of robustness tests with different experimental designs

Abstract Robustness tests are usually based on an experimental design approach. As designed experiments generally lead to a large variability among the results, erroneous results are often not readily detected. As a consequence, the ordinary least squares (OLS) estimates of the effects of the robustness test can be biased. Here, two robustness tests are studied, which both contain a suspicious result. Moreover, simulated datasets are considered to examine the influence of the extent of the outlier as well as the influence of multiple outliers. On the one hand, different methods are applied to inspect the results of the experiments for outliers: the half-normal plot of the OLS residuals, the normal probability plot of the effects and a method, which is based on experimental design reconstruction. On the other hand, two robust regression methods are applied to calculate the effects with a minimum influence of possible outliers. The different methods are compared and it is evaluated under which circumstances they can be applied.

Derivation of system suitability test limits from a robustness test on an LC assay with complex antibiotic samples

A System Suitability Test (SST) is a test to verify the adequate working of the equipment used for analytical measurements. In pharmaceutical analysis, SSTs are performed at least at the beginning of a series of routine analyses. The most generally applied SST considers the precision of the analysis, i.e. the repeatability standard deviation must not exceed a predefined value. Additionally, a SST can also consider responses indicative for the quality of the technique used, e.g. resolutions between peaks or peak asymmetry in high performance liquid chromatography. The system is then only declared suitable if the response is within given limits. However, it is not always evident how to define the SST limits to be fulfilled for a newly developed method. Robustness tests have been proposed as a starting point in a strategy to deduce these limits. Here, it is examined how such a strategy can be applied for complex samples of microbial origin.

Intersite transfer of industrial calibration models

Two instrument standardisation methods, the piecewise direct standardisation and a method based on neural networks, are compared for the transfer of industrial near-infrared powder spectra between two sites. Some important issues that can affect transfer, such as influence of signal preprocessing or representativity of standardisation samples are discussed in detail. Particularities and limitations specific to each transfer method are outlined. In particular, it is shown that both methods lead to different reconstruction results in the presence of structured background noise.

Knowledge-based computer system for the detection of matrix interferences in atomic absorption spectrometric methods

A knowledge-based computer system which assists with the detection of matrix interferences during the validation of atomic absorption spectrometry (AAS) is described. The system compares the slopes of a standard addition line and an aqueous calibration line. An experimental design is proposed which guarantees that the probability of not detecting important interferences (β-error) is acceptably low. To permit a detection of interferences by the comparison of curved calibration lines, a linearization is proposed. The system is developed in a Windows environment and is one module of a more complete hypertext system for the final validation of AAS methods.

Influence of precision, sample size and design on the beta error of linearity tests

The beta error of two linearity tests for the detection of lack-of-fit to a straight line calibration model based on small sample size (6≤n≤10) has been evaluated namely, the ANOVA lack-of-fit to the first degree model and the test of significance of b2, the second degree coefficient from the second degree model fitted through the data. For these investigations different models, designs and measurement precisions were considered by means of simulations. The effect of heteroscedasticity was also evaluated. The results obtained indicated that the test of significance of b2 in general performs better than the ANOVA test. The designs with three concentration levels (measurements positioned at both extremes and at concentration in the middle of the calibration range) give the best results. Heteroscedasticity and low measurement precision increase the probability that lack-of-fit is not detected. Two means to predict the beta error for the test of significance of b2 are proposed: (i) prediction derived from the plots of the beta error versus the ratio of the deviation from linearity (expressed as the average relative prediction error) to the measurement precision (expressed as %RSD at the concentration in the middle of the calibration range) and (ii) prediction using the formula. The formula to determine the sample size that allows the detection of a certain deviation from linearity with a specified beta error is also given.