Transfer of calibration models

The development of a calibration model is a time consuming process. Not only have the samples to be prepared and measured, but the modelling itself, including data pre-processing, outlier detection, estimation and validation, is not an automated procedure. Once the model is there, changes may occur in the instrumentation or other conditions (temperature, humidity) that require recalibration. Another situation is where a model has been set up for one instrument in a central location and one would like to distribute this model to other instruments within the organization without having to repeat the entire calibration process for all these individual instruments. One wonders whether it is possible to translate the model from one instrument (old or parent or master. A) to the others (new or children or slaves, B). 

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 

This yields an estimate for the bias (intercept) a and slope b needed to correct predictions yg from the new (child) instrument that are based on the old (parent) calibration model, b. The virtue of this approach is its simplicity one does not need to investigate in any detail how the two sets of spectra compare, only the two sets of predictions obtained from them are related. The assumption is that the same type of correction applies to all future prediction samples. Variations in conditions that may have a different effect on different samples cannot be corrected for in this manner. 

All other approaches try and relate the child spectra to the parent spectra. In the patented method of Shenk and Westerhaus [41 Sh], in its simplest form, one first applies a wavelength correction and then a correction for the absorbance. Each wavelength channel i of the parent instrument is linked to a nearby wavelength channel j(i) in the child instrument, namely the one to which it is maximally correlated. Then, for each pair of wavelengths, i for the parent and j i) for the child, a simple linear regression is carried out, linking the pair of measured absorbances 

In this way the child spectrum is transformed into a spectrum as if measured on the parent instrument. In a more refined implementation one establishes the highest correlating wavelength channel through quadratic interpolation and, subsequently, the corresponding intensity at this non-observed channel through linear interpolation. In this way a complete spectrum measured on the child instrument can be transformed into an estimate of the spectrum as if it were measured on the parent instrument. The calibration model developed for the parent instrument may be applied without further ado to this spectram. The drawback of this approach is that it is essentially univariate. It cannot deal with complex differences between dissimilar instruments. 

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The above example, of course, is relatively abstract and academic , and as such perhaps not of too much interest to the majority. Another example, with more practical application, is transfer of calibration models from one instrument to another. This is an endeavor of enormous current practical importance. Witness that hardly a month passes without at least one article on that topic in one or more of the analytical or spectroscopic journals. Yet all those reports are the same Effect of Data Treatment ABC Combined with Algorithm XYZ Compared to Algorithm UVW or some such they are all completely empirical studies. In themselves there is nothing wrong with that. The problem is that there is nothing else. There are no critical reviews summarizing all this work and extracting those aspects that are common and beneficial (or common and harmful, for that matter). 

This leads us to the other hand, which, it should be obvious, is that we feel that Chemometrics should be considered a subfield of Statistics, for the reasons given above. Questions currently plaguing us, such as How many MLR/PCA/PLS factors should I use in my model , Can I transfer my calibration model (or more importantly and fundamentally How can I tell if I can transfer my calibration model ), may never be answered in a completely rigorous and satisfactory fashion, but certainly improvements in the current state of knowledge should be attainable, with attendant improvements in the answers to such questions. New questions may arise which only fundamental statistical/probabilistic considerations may answer one that has recently come to our attention is, What is the best way to create a qualitative (i.e., identification) model, if there may be errors in the classifications of the samples used for training the algorithm ... 

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). 

Data preprocessing is important in multivariate calibration. Indeed, the relationship between even basic procedures such as centring the columns is not always clear, most investigators following conventional methods, that have been developed for some popular application but are not always appropriately transferable. Variable selection and standardisation can have a significant influence on the performance of calibration models. 

This standardization approach consists of transferring the calibration model from the calibration step to the prediction step. This transferred model can be applied to new spectra collected in the prediction step in order to compute reliable predictions. An important remark is that the standardization parameters used to transfer calibration models are exactly the same as the ones used to transfer NIR spectra. Some standardization methods based on transferring spectra yield a set of transfer parameters. For instance, the two-block PLS algorithm yields a transfer matrix, and each new spectrum collected in the prediction step is transferred by simply multiplying it by the transfer matrix. For these standardization methods, the calibration model can be transferred from the calibration step to the prediction step using the same transfer matrix. It should be pointed out that all standardization methods yielding a transfer matrix (direct standardization, PDS, etc.) could be used in order to transfer the model from the calibration to the prediction step. For instrument standardization, the transfer of a calibration model from the master instrument to the slave instruments enables each slave instrument to compute its own predictions without systematically transferring the data back to the master instrument. 

While these models simulate the transfer of lead between many of the same physiological compartments, they use different methodologies to quantify lead exposure as well as the kinetics of lead transfer among the compartments. As described earlier, in contrast to PBPK models, classical pharmacokinetic models are calibrated to experimental data using transfer coefficients that may not have any physiological correlates. Examples of lead models that use PBPK and classical pharmacokinetic approaches are discussed in the following section, with a focus on the basis for model parameters, including age-specific blood flow rates and volumes for multiple body compartments, kinetic rate constants, tissue dosimetry,... 

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. 

There are other mysteries in NIR (and other applications of chemometrics) that nonlinearity can also explain. For example, as indicated above, one is the difficulty of transferring calibration models between instruments, even of the same type. Where would our technological world be if a manufacturer of, say, rulers could not reliably transfer the calibration of the unit of length from one ruler to the next ... 

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. 

It is worth noting that these standards could be a subset of the same standards used to develop the calibration model for the property of interest. In this case, there are several sample selection strategies available for identifying the transfer standards from the complete set of calibration samples [107-111]. 

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. 

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]. 

R.D. Guenard, C.M. Wehlberg, R.J. Pell and D.M. Haaland, Importance of prediction outlier diagnostics in determining a successful inter-vendor multivariate calibration model transfer, Appl. Spectrosc., 61, 747 (2007). 

A host of mathematical techniques for standardizing calibration models to facilitate their transfer is available. These generally focus on the coefficients of the model, the spectral response or the predicted values. ... 

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... 

Bro, R. and Ridder, C. (2002) Notes on Calibration of Instruments (Spectral Transfer), http // www.models.kvl.dk/users/rasmus/presentations/calibrationtransfer/calibrationtransfer.pdf. 

The constitutive equations use a thermodynamic framework, that in fact embodies not only purely mechanical aspects, but also transfers of masses between the phases and diffusion of matter through the extrafibrillar phase. Since focus is on the chemo-mechanical couplings, we use experimental data that display different salinities. The structure of the constitutive functions and the state variables on which they depend are briefly motivated. Calibration of material parameters is defined and simulations of confined compression tests and of tree swelling tests with a varying chemistry are described and compared with available data in [3], The evolution of internal entities entering the model, e.g. the masses and molar fractions of water and ions, during some of these tests is also documented to highlight the main microstructural features of the model. 

The previously discussed standardization methods require that calibration-transfer standards be measured on both instruments. There may be situations where transfer standards are not available, or where it is impractical to measure them on both instruments. In such cases, if the difference between the two instruments can be approximated by simple baseline offsets and path-length differences, preprocessing techniques such as baseline correction, first derivatives, or MSC can be used to remove one or more of these effects. In this approach, the desired preprocessing technique is applied to the calibration data from the primary instrument before the calibration model is developed. Prediction of samples from the primary or secondary instrument is accomplished simply by applying the identical preprocessing technique prior to prediction. See Section 5.9 for a brief overview of preprocessing methods and Chapter 4 for a more detailed discussion. A few methods are briefly discussed next. 

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