Development of Robust Multivariate Calibration Models

Appropriate Data Quality Checks Improve the Reliability of Values Predicted from Milk Mid-Infrared Spectra

Simple Summary

There is a growing interest in using milk mid-infrared (MIR) spectrometry to obtain new phenotypes to assist in the complex management of dairy farms. These predictive values can be erroneous for many reasons, even if the prediction equations used are accurate. Unfortunately, there is no quality protocol routinely implemented to detect those abnormal predictive values in the database recorded by dairy herd improvement (DHI) organizations, except for fat and protein contents. However, for financial and practical reasons, it is unfeasible to adapt the quality protocol commonly used in milk laboratories to improve the accuracy of those traits. So, this study proposes three different statistical methods that would be easy to implement by DHI organizations to detect abnormal values and limit the spectral extrapolation in order to improve the accuracy of MIR-based predictive values.

Abstract

The use of abnormal milk mid-infrared (MIR) spectrum strongly affects prediction quality, even if the prediction equations used are accurate. So, this record must be detected after or before the prediction process to avoid erroneous spectral extrapolation or the use of poor-quality spectral data by dairy herd improvement (DHI) organizations. For financial or practical reasons, adapting the quality protocol currently used to improve the accuracy of fat and protein contents is unfeasible. This study proposed three different statistical methods that would be easy to implement by DHI organizations to solve this issue: the deletion of 1% of the extreme high and low predictive values (M1), the deletion of records based on the Global-H (GH) distance (M2), and the deletion of records based on the absolute fat residual value (M3). Additionally, the combinations of these three methods were investigated. A total of 346,818 milk samples were analyzed by MIR spectrometry to predict the contents of fat, protein, and fatty acids. Then, the same traits were also predicted externally using their corresponded standardized MIR spectra. The interest in cleaning procedures was assessed by estimating the root mean square differences (RMSDs) between those internal and external predicted phenotypes. All methods allowed for a decrease in the RMSD, with a gain ranging from 0.32% to 41.39%. Based on the obtained results, the “M1 and M2” combination should be preferred to be more parsimonious in the data loss, as it had the higher ratio of RMSD gain to data loss. This method deleted the records based on the 2% extreme predictions and a GH threshold set at 5. However, to ensure the lowest RMSD, the “M2 or M3” combination, considering a GH threshold of 5 and an absolute fat residual difference set at 0.30 g/dL of milk, was the most relevant. Both combinations involved M2 confirming the high interest of calculating the GH distance for all samples to predict. However, if it is impossible to estimate the GH distance due to a lack of relevant information to compute this statistical parameter, the obtained results recommended the use of M1 combined with M3. The limitation used in M3 must be adapted by the DHI, as this will depend on the spectral data and the equation used. The methodology proposed in this study can be generalized for other MIR-based phenotypes.

Robust calibration transfer in noninvasive ethanol measurements, Part II: Modification of instrument measurements by incorporation of expert knowledge (MIMIK)

Several calibration transfer methods require measurement of a subset of the calibration samples on each future instrument, which is impractical in some applications. Another consideration is that these methods model inter-instrument spectral differences implicitly rather than explicitly. The present work argues that explicit knowledge of the origins of inter-instrument spectral distortions can benefit calibration transfer during the fabrication and assembly of instrumentation, the formation of the multivariate regression, and its subsequent transfer to future instruments. In Part I of this work, a Fourier transform near-infrared system designed to perform noninvasive ethanol measurements was discussed and equations describing the optical distortions caused by self-apodization, retroreflector misalignment, and off-axis detector field of view were provided and examined using laboratory measurements. The spectral distortions were shown to be nonlinear in the amplitude and wavenumber domains, and thus cannot be compensated by simple wavenumber calibration procedures or background correction. Part II presents a calibration transfer method that combines in vivo data with controlled amounts of optical distortions in order to develop a multivariate regression model that is robust to instrument variation. Evaluation of the method using clinical data showed improved measurement accuracy, outlier detection, and generalization to future instruments relative to simple background correction.

Robustness of near-infrared calibration models for the prediction of milk constituents during the milking process

The robustness of in-line raw milk analysis with near-infrared spectroscopy (NIRS) was tested with respect to the prediction of the raw milk contents fat, protein and lactose. Near-infrared (NIR) spectra of raw milk (n = 3119) were acquired on three different farms during the milking process of 354 milkings over a period of six months. Calibration models were calculated for: a random data set of each farm (fully random internal calibration); first two thirds of the visits per farm (internal calibration); whole datasets of two of the three farms (external calibration), and combinations of external and internal datasets. Validation was done either on the remaining data set per farm (internal validation) or on data of the remaining farms (external validation). Excellent calibration results were obtained when fully randomised internal calibration sets were used for milk analysis. In this case, RPD values of around ten, five and three for the prediction of fat, protein and lactose content, respectively, were achieved. Farm internal calibrations achieved much poorer prediction results especially for the prediction of protein and lactose with RPD values of around two and one respectively. The prediction accuracy improved when validation was done on spectra of an external farm, mainly due to the higher sample variation in external calibration sets in terms of feeding diets and individual cow effects. The results showed that further improvements were achieved when additional farm information was added to the calibration set. One of the main requirements towards a robust calibration model is the ability to predict milk constituents in unknown future milk samples. The robustness and quality of prediction increases with increasing variation of, e.g., feeding and cow individual milk composition in the calibration model.

Framework for multivariate selectivity analysis, part II: experimental applications

In Part I of this paper, a framework for multivariate selectivity was introduced that is both calculable from first principles and experimentally tractable. In this part, we employ the proposed selectivity framework for analyzing both in vitro and in vivo near-infrared experimental data. Two in vitro data sets are used to compare different methods for estimating selectivity and to demonstrate the benefits obtained from validation data with expanded interferant concentration ranges. The in vitro data also demonstrate that the experimentally estimated selectivities provide insights into the properties of the calibration models that are difficult or impossible to infer by other means. The merits of the proposed selectivity function are further demonstrated using a complex in vivo application: the noninvasive measurement of ethanol in humans. Results indicate that in vivo calibration model sensitivity, selectivity, and concentration correlations can be systematically interrogated using the proposed selectivity framework and judicious use of experimental measurements. These analyses not only provide selectivity and sensitivity information, but also the variance components of the total MSEP, which is invaluable information for both method development and analytical method characterization.

Comparison of methods for transfer of calibration models in near-infared spectroscopy: a case study based on correcting path length differences using fiber-optic transmittance probes in in-line near-infrared spectroscopy

This article addresses problems related to transfer of calibration models due to variations in distance between the transmittance fiber-optic probes. The data have been generated using a mixture design and measured at five different probe distances. A number of techniques reported in the literature have been compared. These include multiplicative scatter correction (MSC), path length correction (PLC), finite impulse response (FIR), orthogonal signal correction (OSC), piecewise direct standardization (PDS), and robust calibration. The quality of the predictions was expressed in terms of root mean square error of prediction (RMSEP). Robust calibration gave good calibration transfer results, while the other methods did not give acceptable results.

Parent and harvest year effects on near-infrared reflectance spectroscopic analysis of olive (Olea europaea L.) fruit traits

The influence of parent and harvest year on the determination of oil, moisture, oleic acid, and linoleic acid contents in intact olive fruit was studied by near-infrared spectroscopy (NIRS). Spectral data from 400 to 1700 nm were recorded on 437 fruit samples collected in 1996 and 1997 from seedling plants derived from three different female parents. Partial least squares models were developed using samples for each year and for each female parent separately and were validated against the other groups. Calibration models were accurate enough to predict all constituents in new samples from a different female parent but were not transferable across years. However, a calibration equation of sufficient accuracy was obtained from the combined data set (r values of 0.94, 0.93, 0.84, and 0.88 and RMSECV values of 1.33, 1.88, 4.73, and 2.91 for oil, moisture, oleic acid, and linoleic acid contents, respectively). These results demonstrate the utility of NIRS as a selection tool in olive breeding programs.

Adaptable multivariate calibration models for spectral applications

Multivariate calibration techniques have been used in a wide variety of spectroscopic situations. In many of these situations, spectral variation can be partitioned into separate classes. For example, suppose that multiple spectra are obtained from each of a number of different objects wherein the level of the analyte of interest varies within each object over time. In such situations, the total spectral variation observed across all measurements has two distinct general sources of variation: intraobject and interobject. One might want to develop a global multivariate calibration model that predicts the analyte of interest accurately both within and across objects, including new objects not involved in developing the calibration model. However, this goal might be hard to realize if the interobject spectral variation is complex and difficult to model. If the intraobject spectral variation is consistent across objects, an effective alternative approach might be to develop a generic intraobject model that can be adapted to each object separately. This paper contains recommendations for experimental protocols and data analysis in such situations. The approach is illustrated with an example involving the noninvasive measurement of glucose using near-infrared reflectance spectroscopy. Extensions to calibration maintenance and calibration transfer are discussed.