Transfer calibration

Of similar significance to the range issue, suitable approaches for calibration transfer must be accepted by regulators for successful implementation of NIR spectroscopy on a large scale within the pharmaceutical industry. Regardless of instrument quality or the utmost discipline and care during method development, calibration transfer will be a reality if a calibration is used over any length of time. 

While method transfer, discussed earlier in this chapter, refers to the process of implementing a newly developed method in a designated laboratory, the term calibration transfer is used in several contexts. One context, in fact, is similar to the usual definition of method transfer. A question that arises when NIR equations are concerned is Can a 

Although today s manufacturers of NIR instruments do provide instruments that are surprisingly consistent and precise from one device to the next, the industrial method development chemist is likely to encounter problems when transferring methods from the laboratory to the production floor on a large scale. The instrumental differences that lead to such problems may or may not be of adequate significance to be identified during fhe insfrumenf qualificahon tests. Appropriate use of reference standards for performance qualificahon can certainly reduce the occurrence of such problems. However, in certain cases, one of the many calibration hansfer algorithms that have been discussed in the literature over the last decade may be required for successful transfer and implementation of a calibrahon. 

Calibrahon fransfer methods can also find wide application for what is also known as calibration maintenance. It must be assumed that the physical process, the instrument, the raw materials, or the produchon personnel will change with time. Any implementahon of a NIR method without these safeguards is not only poor science, but will give NIR a bad reputation when (not if) the equation fails to give a proper predichon. 

A second, and perhaps more important, safeguard is the use of conhol charfs for frend analysis. This plot will show any drift from the median value (nominal value or actual average value) alerting whoever is responsible for calibrahon maintenance before the values actually drift out of accepfance range. It is possible that the reason for fhe driff is fhe process 

Constructing a multivariate model is a time-consuming task that involves various operations including the preparation of a sizeable number of samples, recording their spectra and developing and validating the cali- 

The model can lose its predictive capacity for reasons such as a dramatic change in the nature of the samples. A new calibration model better adjnsted to the new situation must therefore be constructed. In other cases, however, the model can be re-adjnsted (restandardized) in order to ensure a predictive capacity not significantly different from the original one. 

The calibration model may exhibit a decrease in the ability to predict new samples due to changes in the instrumentation. The differences in instmmentation may introduce variability in the spectra. The potential sources of variability include the following  

Replacing the analytical equipment with one of similar, better or rather different characteristics. If both systems are available simultaneously for an adeqnate length of time, then spectra can be recorded on both in order to derive as much information as possible in order to understand the differences and make appropriate corrections to the data to account for them. The original equipment is known as the master and that replacing it as the slave. 

Transferring a calibration to another spectrometer. Becanse the ability to use the master and slave simultaneously may not exist, the amount of nsefnl spectral information may be inadequate. Breakdown of the instrument or end of its service lifetime. Repairing or replacing an instrument may alter spectral responses if the instmments are not perfectly matched. Because this is an unexpected event, spectra recorded prior to the incident are rarely available. 

Consider a process spectroscopy application where all three of the following conditions 

In this situation, it would be ideal to produce a calibration on only one of the analyzers, and simply transfer it to all of the other analyzers. There are certainly cases where this can be done effectively, especially if response variability between different analyzers is low and the calibration model is not very complex. However, the numerous examples illustrated above show that multivariate (chemometric) calibrations could be particularly sensitive to very small changes in the analyzer responses. Furthermore, it is known that, despite the great progress in manufacturing reproducibility that process analyzer vendors have made in the past decade, small response variabilities between analyzers of the same make and 

In such cases, one can retreat to the brute force approach of developing a separate calibration for each analyzer. However, for empirical multivariate calibrations, which require a large number of calibration samples each, this approach can become very laborious. Furthermore, if there is a significant cost associated with the collection, preparation, and analysis of calibration standards, the cost of this instrument-specific calibration approach can become prohibitive. 

A more appealing approach would be to prepare and analyze calibration standards and develop a calibration on a single master analyzer, and then standardize all of the other slave analyzers so that the spectra they produce are the same as those that would have been produced on the master analyzer. This way, in principle, the same calibration could be effectively applied to all of the analyzers, and it would not be necessary to calibrate all of the analyzers separately. 

This method is probably the simplest of the software-based standardization approaches.73,74 It is applied to each X-variable separately, and requires the analysis of a calibration set of samples on both master and slave instruments. A multivariate calibration model is built using the spectra obtained from the master instrument, and then this model is applied to the spectra of the same samples obtained from the slave instrument. Then, a linear regression of the predicted Y-values obtained from the slave instrument spectra and the known Y-values is performed, and the parameters obtained from this linear regression fit are used to calculate slope and intercept correction factors. In this 

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Several approaches have been investigated recently to achieve this multivariate calibration transfer. All of these require that a small set of transfer samples is measured on all instruments involved. Usually, this is a small subset of the larger calibration set that has been measured on the parent instrument A. Let Z indicate the set of spectra for the transfer set, X the full set of spectra measured on the parent instrument and a suffix Aor B the instrument on which the spectra were obtained. The oldest approach to the calibration transfer problem is to apply the calibration model, b, developed for the parent instrument A using a large calibration set (X ), to the spectra of the transfer set obtained on each instrument, i.e. and Zg. One then regresses the predictions (=Z b ) obtained for the parent instrument on those for the child instrument yg (=Z b ), giving... 

For PyMS to be used for (1) routine identification of microorganisms and (2) in combination with ANNs for quantitative microbiological applications, new spectra must be comparable with those previously collected and held in a data base.127 Recent work within our laboratory has demonstrated that this problem may be overcome by the use of ANNs to correct for instrumental drift. By calibrating with standards common to both data sets, ANN models created using previously collected data gave accurate estimates of determi-nand concentrations, or bacterial identities, from newly acquired spectra.127 In this approach calibration samples were included in each of the two runs, and ANNs were set up in which the inputs were the 150 new calibration masses while the outputs were the 150 old calibration masses. These associative nets could then by used to transform data acquired on that one day to data acquired at an earlier data. For the first time PyMS was used to acquire spectra that were comparable with those previously collected and held in a database. In a further study this neural network transformation procedure was extended to allow comparison between spectra, previously collected on one machine, with spectra later collected on a different machine 129 thus calibration transfer by ANNs was affected. Wilkes and colleagues130 have also used this strategy to compensate for differences in culture conditions to construct robust microbial mass spectral databases. 

M. L. Magee, J. T. On mass spectrometer instrument standardization and interlaboratory calibration transfer using neural networks. Anal. Chim. Acta 1997,384, 511-532. 

Conspicuous by its absence is the question of calibration transfer, even though we consider it unsolved in the general sense, in that there is no single recipe or algorithm that is pretty much guaranteed to work in all (or at least a majority) of cases. Nevertheless, not only are many people working on the problem (so that it is hardly unaddressed ), but there have been many specific solutions developed over the years, albeit for particular calibration models on particular instruments. So we do not need to beat up on this one by ourselves. 

Even worse, there are no fundamental studies dealing with the relationship of the algorithm s behavior to the underlying physics, chemistry, mathematics, or instrumental effects. It is not difficult to see that the calibration transfer problem breaks down into... 

Calibration transfer, n - a method of applying a multivariate calibration developed on one instrument to data measured on a different instrument, by mathematically modifying the calibration model or by a process of instmment standardization. 

Standardization The instrument response function can vary from analyzer to analyzer. If calibration transfer is to be achieved across all instrument platforms it is important that the instrument function is characterized, and preferably standardized [31]. Also, at times it is necessary to perform a local calibration while the analyzer is still on-line. In order to handle this, it is beneficial to consider an on-board calibration/standardization, integrated into the sample conditioning system. Most commercial NIR analyzers require some form of standardization and calibration transfer. Similarly, modem FTIR systems include some form of instrument standardization, usually based on an internal calibrant. This attribute is becoming an important feature for regulatory controlled analyses, where a proper audit trail has to be established, including instrument calibration. 

J. Gislason, H. Chan, and M. Sardashti, Calibration Transfer of chemometric models based on process nuclear magnetic resonance spectroscopy, Appl. Spectrosc., 55(11), 1553-1560 (2001). 

Concurrent with the selection of transfer standards is the selection of the optimal strategy deciding whether to use calibration transfer or instrument standardization, assigning the master and slave instruments, and selecting a suitable transfer algorithm. Some commonly used algorithms for calibration transfer and instrument standardization are discussed below. 

This method can be considered a calibration transfer method that involves a simple instrument-specific postprocessing of the calibration model outputs [108,113]. It requires the analysis of a subset of the calibration standards on the master and all of the slave instmments. A multivariate calibration model built using the data from the complete calibration set obtained from the master instrument is then applied to the data of the subset of samples obtained on the slave instruments. Optimal multiplicative and offset adjustments for each instrument are then calculated using linear regression of the predicted y values obtained from the slave instrument spectra versus the known y values. 

The GLS method was mentioned earher, as a preprocessing method that down-weights multivariate directions in the data that correspond to known interfering effects. However, it can also be used in a calibration transfer context, where directions in the data that correspond to instrumental differences are down-weighted. The use of GLS weighting for cahbration transfer is discussed in reference [116]. 

Orthogonal signal correction (OSC) This method explicitly uses y (property or analyte) information in calibration data to develop a general filter for removing any y-irrelevant variation in any subsequent x data [118]. As such, if this y-irrelevant variation includes inter-instrument effects, then this method performs some degree of calibration transfer. The OSC model does not exphcitly handle x axis shifts, but in principle can handle these to some extent. It has also been shown that the piecewise (wavelength-localized) version of this method (POSC) can be effective in some cases [119]. 

Multiway methods For analyzer data where a single sample generates a second order array (ex. GC/MS, LC/UV, excitation/emission fluorescence), multiway chemometric modehng methods, such as PARAFAC (parallel factor analysis) [121,122], can be used to exploit the second order advantage to perform effective calibration transfer and instrument standardization. 

J. Workman and J. Coates, Multivariate calibration transfer the importance of standardizing instrumentation. 

E. Bouveresse, D.L. Massart and P. Dardenne, Calibration transfer across near-infrared spectroscopic instruments using Shenk s algorithm effects of different standardisation samples. Anal. Chim. Acta, 297, 405 16 (1994). B.G. Osborne and T. Feam, Collaborative evaluation of universal cahbrations for the measurement of protein and moisture in flour by near-infrared reflectance, /. Food TechnoL, 18, 453 60 (1983). 

Y. Wang and B.R. Kowalski, Calibration transfer and measurement stabihty of near-infrared spectrometers, Appl. Spectrosc., 46, 764-771 (1992). 

Standardizing the predicted values is a simple, useful choice that ensures smooth calibration transfer in situations (a) and (b) above. The procedure involves predicting samples for which spectra have been recorded on the slave using the calibration model constructed for the master. The predicted values, which may be subject to gross errors, are usually highly correlated with the reference values. The ensuing mathematical relation, which is almost always linear, is used to correct the values subsequently obtained with the slave. 

Alternative mathematical methods such as artificial neural networks (ANN), maximum likelihood PCA and positive matrix factorization have also proved effective for calibration transfer, but are much more complex than the previous ones and are beyond the scope of this chapter. For more information about this topic see Chapter 12. 

Ideally, an on-line analyzer will be calibrated before it is installed in the process. It may be possible to accomplish this by calibrating it off-line with process grab samples and/or synthetic samples. It may be possible to install the analyzer in a lab-scale reactor, or in a semi-works or pilot plant. It may be possible to transfer to the on-line analyzer a method developed on an off-line analyzer or on another on-line analyzer (e.g. at a different plant site). However, sometimes none of these are possible and the analyzer will need to be calibrated on-line. The challenges of on-line model development (calibration) and validation, as well as approaches to dealing with them, are discussed below. For information related to calibration transfer issues, please see Chapter 12 of this book. 

Sjoblom, J., Svensson, O., Josefson, M., Kullberg, H., and Wold, S. (1998) An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra. Chemom. Intell. Lab. Syst. 44, 229-244. 

There are several other chemometric approaches to calibration transfer that will only be mentioned in passing here. An approach based on finite impulse response (FIR) filters, which does not require the analysis of standardization samples on any of the analyzers, has been shown to provide good results in several different applications.81 Furthermore, the effectiveness of three-way chemometric modeling methods for calibration transfer has been recently discussed.82 Three-way methods refer to those methods that apply to A -data that must be expressed as a third-order data array, rather than a matrix. Such data include excitation/emission fluorescence data (where the three orders are excitation wavelength, emission wavelength, and fluorescence intensity) and GC/MS data (where the three orders are retention time, mass/charge ratio, and mass spectrum intensity). It is important to note, however, that a series of spectral data that are continuously obtained on a process can be constructed as a third-order array, where the three orders are wavelength, intensity, and time. 

Workman, J. and Coates, J., Multivariate Calibration Transfer The Importance of Standardizing Instrumentation Spectroscopy 1993, 8(9), 36—12. 

Wang, Y. and Kowalski, B.R., Calibration Transfer and Measurement Stability of Near-Infrared Spectrometers Appl. Spectrosc. 1992, 46, 764-771. 

Bouveresse, E., Massart, D.L. and Dardenne, P., Calibration Transfer Across Near-Infrared Spectroscopic Instruments using Shenk s Algorithm Effects of Different Standardisation Samples Anal. Chim. Acta 1994, 297, 405—116. 

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