Note: Descriptions are shown in the official language in which they were submitted.
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BIOLOGICAL FLUID ANALYSIS USING DISTANCE OUTLIER DETECTION
BACKGRO~,jND OF THE INVENTION
Spectral analysis is widely used in identifying and quantitating
analytes in a sample of a material. One form of spectral analysis
measures the amount of electromagnetic radiation which is absorbed by a
sample. For example, an infrared spectrophotometer directs a beam of
infrared radiation towards a sample, and then measures the amount of
radiation absorbed by the sample over a range of infrared wavelengths.
An absorbance. spectrum may then be plotted which depicts sample
absorbance as a function of wavelength. The shape of the absorbance
spectrum, including relative magnitudes and wavelengths of peak
absorbances, serves as a characteristic 'fingerprint' of particular analytes
in the sample.
The absorbance spectrum may furnish information useful in
identifying analytes present in a sample: In addition, the absorbance
spectrum can also be of use for quantitative analysis .of the concentration
of individual analytes in the sample. In many instances, the absorbance
of an analyte in a sample is approximately proportional to the
concentration of the analyte in the sample. In those cases where an
absorbance spectrum represents the absorbance of a single analyte in a
sample, the concentration of the analyte may be determined by
comparing the absorbance of the sample to the absorbance of a
reference sample at the same wavelengths, where the reference sample
contains a known concentration of the analyte.
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One fundamental goal of a near-infrared spectroscopic method for
biological fluid analyte concentration measurements such as blood
glucose levels is to collect high quality data. Although great care may be
taken to ensure reliable measurements by consistent sample preparation
and data acquisition, data generated by instrumentation and clinical
reference testing, like all data, are susceptible to the inclusion of errors
from a number of sources. fn large sets of data, it is not uncommon to
have a number of measurements that are extremely deviant from the
expected distribution of measurements, commonly referred to as outliers.
Whether outliers result from statistical errors or systematic errors, outlier
detection identifies samples containing such errors with sufficient
confidence that such samples can be considered unique with respect to
the sampled population. Inclusion of a small number of outliers within a
set of measurements can degrade or destroy a calibration model that
would otherwise be obtained by the measurements.
Referring to the method and apparatus of the present invention,
there are at least four potential sources of error in the chemometric
analysis for biological fluid analyte measurements such as measurements
of blood glucose levels.
A first source of error is related to sample preparation. Blood
serum samples require a great deal of preparation before chemometric
analysis. During this preparation, a number of factors can affect the
sample. For example, the amount of time that blood samples are allowed
to clot may affect sample continuity in terms of fibrinogen content. The
level of clotting also impacts the quality of centrifugation and ultimately
the decanting of serum from cells. Samples prepared for clinical assays
determine the quality of the data used for reference and calibration, so
that great care must be exercised with the samples since this data will
ultimately define the limit of prediction abilities.
A second source of error may result from the spectral
measurement process. For example, the use of a flowcell for sample
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containment during data acquisition is susceptible to problems such as
bubbles in the optical path as well as dilution effects from reference
saline solution carryover. These dilution effects are usually negligible,
' but bubbles in the optical path are not infrequent and have a severe
impact on data quality. In addition, errors produced by mechanical or
electronic problems occurring within the analysis instrumentation can
have important effects on data quality.
A third source of error is also related to the reference tests. Errors
due to out-of-specification instrumental controls and low sample volume
during clinical assays have similar effects to errors related to sample
preparation, described above.
A fourth source of error, and probably the most difficult to identify
and control, relates to sources of the samples, that is, to the individuals
providing the biological fluids. A sample taken from an individual may at
first seem to be quite unique with respect to a previously sampled
population, but may in fact be an ordinary sample when a larger sample
population is considered, that is, a putative unique sample may be only
an artifact of undersampling.
All of these errors, alone or in combination, can lead to a
calculated value of biological fluid analyte concentration that is at great
variance with respect to measurements from samples taken from the
same individual at approximately the same time. These extremely
deviant values, which can be orders of magnitude greater or less than a
predicted mean value, are outliers that should be identified prior to
constructing a model for predicting biological fluid analyte
concentrations.
The removal of outliers from a data set can be accomplished in a
qualitative and subjective sense by graphical inspection of plotted data in
those cases when the dimensionality is low, that is, where the number of
data points associated with each measurement is small. In those
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instances where the number of data points associated with each
measurement is large, however, outlier detection may be more quickly
and efficiently accomplished by a number of automatable procedures
such as residual analysis. However, such procedures are often subject to
a number of errors, or at least subject to errors in interpretation,
especially in the. relatively high dimensional spaces that are typically
associated with multifactorial chemometric analyses.
SUMMARY OF THE INVENTION
To ensure accurate and consistent results, chemometric
applications for biological fluid analyte measurement, such as glucose
concentration determination, require multiple measurements taken from a
number of individual test subjects over a period of time. However, even
with consistent sample preparation and data acquisition, natural
variations in samples and unintended errors can diminish the accuracy of
results. Further, these errors are magnified by the relatively small
number of biological fluid samples that can economically be drawn and
tested. Automated techniques for outlier detection are necessary to
assess the suitability of all acquired samples during both research phase
and in final uses. The quality of data during clinical studies will define
calibration models and the direction of subsequent research thrusts
dependent upon results. In an end use, visual inspection of acquired data
may or may not be possible. Even if inspection of the data is possible,
independent objective methods of determination are needed which are
not susceptible to subjective biases.
In order to' aid in the understanding of the present invention, it can
be stated in essentially summary form that it is directed to a method and
apparatus for measuring biological fluid analyte concentration using
outlier identification and removal based on generalized distances. The
present invention improves the accuracy of biological fluid analyte
concentration determination by identifying outlier values, and identifying
and removing outliers from data before formation of a calibration model.
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The present invention provides a method and apparatus whereby
the concentration of an analyte in a sample of a biological fluid may be
investigated by spectral analysis of electromagnetic radiation applied to
the sample, including collecting calibration data, analyzing the calibration
5 data to identify and remove outliers using the calibration model,
constructing a calibration model, collecting unknown sample data,
analyzing the unknown sample data to identify and remove outliers, and
predicting analyte concentration of non-outliers in the unknown sample
data by using the calibration model.
The analysis of the calibration data set may include data
pretreatment, data decomposition to remove redundant data, and
identification and removal of outliers as having a low probability of class
membership, using generalized distance methods.
The construction of a calibration model may utilize principal
component regression, partial least squares, multiple linear regression, or
artificial neural networks, whereby the calibration data set rriay be
reduced to significant factors using principal component analysis or
partial least squares scores, enabling calculation of regression
coefficients and artificial neural network weights.
The unknown sample data may be analyzed using data
pretreatment, followed by projection into the space defined by the
calibration model, and identification and removal of outliers in the
unknown sample data as having a low probability of class membership.
The prediction of analyte concentration of an unknown sample may
include projecting data from the unknown sample into the space defined
by the calibration model, thereby enabling determination of the analyte
concentration.
A first embodiment of the apparatus of the present invention
includes a pump into which a sample is introduced, the pump acting to
circulate the sample through tubing to fill a flowcell, with the pump
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capable of both stopped flow and continuous flow operation. A sample
compartment housing containing the flowcell and a detector is
temperature controlled by a temperature control unit. Light from
relatively broad bandwidth near-infrared source is directed through a
chopper wheel, and the chopped wheel is synchronized by a chopper
synchronization, unit with respect to the detector, facilitating the
apparatus of the present invention to make both light and dark
measurements to substantially eliminate electronic noise. Modulated light
then passes through a monochrometer, allowing variance of the
wavelength of radiation continuously over an appropriate range. The
monochromatic light passes through the flowcell and strikes the detector,
whereby the amount of light transmitted through the sample is measured.
Measurement data is stored in a general purpose programmable computer
having a general purpose microprocessor, available for further processing
according to the present invention. In addition, the computer may also
control operation of the pump, the temperature control unit, the chopper
synchronization unit, the chopper wheel, and the monochrometer.
In a second embodiment of the apparatus of the present invention,
light from the relatively broad bandwidth light source is directed through
the chopper wheel, and thereafter modulated light is passed through a
filter wheel, whereby discrete wavelengths of radiation may be selected
and transmitted to the flowcell.
In a third embodiment of the apparatus of the present invention, a
plurality of narrow bandwidth near-infrared sources, such as a plurality of
laser diodes, is provided to produce near-infrared radiation at a
preselected plurality of wavelengths. Light from a selected narrow
bandwidth near-infrared source may be pulsed by a driver in
synchronization with the detector and directed into the flowcell 1 Q6.
Synchronization of the selected narrow bandwidth near-infrared
source and the detector permits the apparatus to make both light and
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dark measurements, thereby substantially eliminating significant
electronic noise. Selection of each of the set of narrow bandwidth near-
infrared sources for emission of light to be transmitted into the flowcell
may be selected in a convenient order, for instance in order of increasing
or decreasing wavelength, by cpnfiguring the computer to sequentially
pulse each of th,e set of narrow bandwidth near-infrared sources.
In computer implementation of the method and apparatus of the
present invention, variations in the intensity of transmitted light as a
function of wavelength ace converted into digital signals by the detector,
with the magnitude of the digital signals determined by the intensity of
the transmitted radiation at the wavelength assigned to that particular
signal. Thereafter, the digital signals are placed in the memory of the
computer for processing as will be described.
The steps of the method of the present invention include as a first
step collecting data to be used in constructing a calibration model. After
the calibration data have been collected, data pretreatment may be
performed in order to remove or compensate for spectral artifacts such as
scattering (multiplicative) effects, baseline shifts, and instrumental noise.
Pretreatment of the calibration data may be selected from the group of
techniques including calculating nth order derivatives of spectral data,
multiplicative scatter correction, n-point smoothing, mean centering,
variance scaling, and the ratiometric method.
Once data pretreatment, if any, has been performed on the raw
calibration data, a calibration model may be formed. As near-infrared
spectral data variables are highly correlated, to reduce the level of
redundant information present, near-infrared spectral calibration data may
be formed into a nxp matrix representing n samples, .each measured at p
wavelengths. The nxp matrix may be decomposed by principal
component analysis into a set of n, n-dimensional score vectors formed
into a nxn score matrix, and a set of n, p-dimensional loading vectors
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formed into an nxp loading matrix. The score vectors are orthogonal and
represent projections of the n spectral samples into the space defined by
the loading vectors and the major sources of variation.
Principal component analysis generates a set of n eigenvectors and
a set of n eigenvalues, ~I~ s~12 >_ .... Z~1". The eigenvalues represent the
variance explained by the associated eigenvectors and can be divided
into two sets. The first q eigenvalues are primary eigenvalues,
~i~ >~12~,... z~lQ, and account for the significant sources of variations
within the data. The remaining n-q secondary (error) eigenvalues
~Iq+, z~lq+i ~... zan account for residual variance or measurement noise.
The number of primary eigenvalues q may be determined by an
iterative method which compares the q'" eigenvalue's variance to the
variance of the pooled error eigenvalues via an F-test. Further, reduced
eigenvalues may be utilized, which weight the eigenvalues by an amount
proportional to the information explained by the associated eigenvectors.
The q score values for each sample are used to represent the original
data during outlier detection, with the original spectra projected into the
nxq dimensioned principal component subspace defined by loading the
matrix.
Outliers may be identified using generalized distances, such as
Mahalanobis distance or Robust distance. A generalized distance
between a sample and the centroid defined by a set of samples may be
determined using the variance-covariance matrix of the set of samples.
Where the true variance-covariance matrix and the true centroid of a
complete set of samples are unknown, a subset of the complete set may
be used to form an approximate variance-covariance matrix and an
approximate centroid. Further, by using principal component scores to
represent spectral data for each sample, independent variables
maximizing the information content may be obtained, insuring an
invertible approximate variance-covariance matrix. With respect to
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Mahalanobis distance, an approximate centroid may be determined as the
centroid of a multivariate normal distribution of the set of calibration
samples and an approximate variance-covariance matrix of the set of
calibration samples, whereby an approximate Mahalanobis distance. in
units of standard deviations measured between the centroid and each
calibration sample may be found. With respect to Robust distance, by
utilizing a minimum volume ellipsoid estimator (MVE1, robust estimates of
an approximate variance-covariance matrix and an approximate centroid
may be obtained. Alternatively, a projection algorithm may be used to
determine the Robust distance for each calibration sample.
After determining generalized distances for the calibration samples,
the probability of class membership may be determined by a number of
techniques, including evaluation of a chi-squared distribution function or
utilizing Hotelling's T-statistic. Outliers are identified as having
relatively
large generalized distance which results in a relatively low probability of
class membership. Samples whose class membership can be rejected at
a confidence level that is greater than approximately 3-5o may be
considered as outliers. Following identification, outliers in the calibration
samples may be removed. The generalized distances of outliers removed
from the calibration samples may be examined, to determine whether
additional data pretreatment is necessary. In the event that a relatively
large number of outliers have very large generalized distances, further
pretreatment of the calibration data may be indicated. After such
additional pretreatment, the calibration data may again be subjected to
analysis. On the other hand, if relatively large numbers of outliers do not
have very large generalized distances, then additional data pretreatment
may not be appropriate.
A calibration model may then be constructed utilizing any of a
number of techniques, including principal component regression (PCR),
partial least squares (PLS), multiple linear regression (MLR), and artificial
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neural networks (ANN). The calibration model will seek to correlate a set
of independent variables representing absorbance values of n samples
each measured at p wavelengths, with a set of dependent or response
variables representing the concentration of an analyte in each of the n
5 samples, by using a p-dimensional regression coefficient vector. A
calibration model determines regression coefficient vector and is used to
predict the concentration of the analyte in other samples, given only the
absorbances at the p wavelengths.
As noted, near-infrared spectral data variables are highly correlated
10 and while careful selection of the measurement wavelengths may
minimize singularity problems, the spectral regions of interest may suffer
from severe overlap and a high number of wavelengths is needed to
model a multicomponent system. Data compression may be used to
address problems with collinearity to determining regression coefficient
vector, so that redundant data may be reduced down to significant
factors. Principal component regression is one technique that
incorporates a data compression method. The technique of partial least
squares may also be used to address the problem of redundant data.
With respect to both principal component regression and partial
least squares, a determination is made of. the appropriate number of score
vectors or factors to be included in a calibration model that adequately
represents the calibration data. The goal of selecting optimal number of
factors for regression is to obtain parsimonious models with robust
predictive abilities. Including too few factors causes model performance
to suffer due to inadequate information during calibration, while including
too many factors may also degrade performance. Principal components
are normally sorted into an order so that the amount of variation
explained by each principal component monotonically decreases. Later
ordered principal components associated with small eigenvalues may be
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considered as containing measurement noise. By utilizing only the first q
factors and omitting remaining factors, a type of noise rejection may be
incorporated within principal component regression. The number of
principal component analysis or partial least squares scores or factors to
use during the regression step may be determined using the standard
error of prediction, a measure of the error associated with each set of
predictions. By plotting standard error of prediction against the number
of factors used in each of the respective sets of predictions, a piecewise
continuous graphical representation may be obtained and utilized to
determine the number of factors to retain. One criterion for factor
selection is to determine the first local minimum. Another technique for
factor selection uses an F test to compare standard error of prediction
from models using differing numbers of factors.
In certain instances, data being analyzed may not be amenable to
being split into a calibration, training set and a validation, test set. The
reason may be due to a limited number of available samples or that by
splitting data into two sets, one or both of the resulting sets do not
adequately represent the sample population. In such situations, the
iterative technique of leave one out cross validation may be used where,
during each iteration, a sample is excluded from the calibration set and is
used as a test sample. Prediction models using factors determined from
calibration samples are then used to make test sample predictions. The
test sample is then returned to the calibration set and another sample is
excluded. The same process is repeated until all samples have been
excluded from the calibration set and predicted by models generated by
the calibration samples. All predictions are accumulated to give a
standard error of validation.
Subsequent to determining the number of significant factors, the
data set for the calibration model may be reduced to significant factors,
and regression coefficients for the calibration model may be determined.
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After construction of the calibration model, the calibration model may be
applied to data collected from samples where concentration of analytes of
interest
are unknown. The unknown sample data may be appropriately pretreated and then
projected into the principal component space defined by the calibration model.
Next, generalized distances for the unknown sample data set may be found,
using,
for instance, either Mahalanobis or Robust distance as utilized with respect
to the
calibration data, and the probability of class membership may be estimated
using
the techniques described above, including evaluation of a chi-squared
distribution
function or utilizing Hotelling's T-statistic. Outliers in the unknown sample
data
are then identified based upon rejecting class membership at a confidence
level
that is greater than approximately 3-S.sigma.. As the final steps of the
method of
the present invention, in the event that an unknown sample is not an outlier,
the
sample is projected into the space defined by the calibration model, and a
prediction of the concentration of the analyte made. On the other hand, if the
unknown sample is an outlier, the unknown sample may be rejected and no
prediction as to analyte concentration made, although if possible,
remeasurement
of the unknown sample may be made to verify that the sample is an outlier.
With respect to the apparatus of the present invention, the steps previously
described with respect to the method of the present invention may be
configured
on the general purpose microprocessor of the computer by employing computer
program code segments according to each of such steps.
Thus in accordance with one aspect of the invention there is provided an
improved
method for forming a calibration model for use in determining concentration of
an
analyte of a biological fluid of a mammal, comprising the steps of
collecting a set of calibration samples from a plurality of sources of the
biological fluid;
generating near-infrared electromagnetic radiation having a plurality of
wavelengths; irradiating each of the calibration samples with the radiation so
that a
portion of the radiation at each of the wavelengths is transmitted through
each of
the calibration samples;
measuring intensity of the radiation transmitted through each of the
calibration
samples at each of the wavelengths thereby forming a set of calibration data;
processing the set of calibration data, including forming the set of
calibration
data into a nxp matrix defining a space, wherein n is the number of
calibration
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samples and p is the number of wavelengths at which intensity of transmitted
radiation is measured, forming a subspace of the space wherein sources of
relatively greater variations within the set of calibration data are
represented,
projecting the set of calibration data into the subspace, determining a
generalized
distance within the subspace between each calibration sample and a centroid of
a
distribution formed by the set of calibration samples, identifying calibration
outliers as those calibration samples having a generalized distance greater
than a
preselected magnitude, forming a reduced set of calibration samples from
calibration samples remaining after removal of calibration outliers; and
constructing a calibration model from the reduced set of calibration samples
to
predict concentration of the analyte in an unknown sample of the biological
fluid,
wherein the step of constructing a calibration model includes removing
redundant
data from data corresponding to the reduced set of calibration samples.
In accordance with another aspect of the invention there is provided an
improved
method for determining concentration of an analyte of a biological fluid of a
mammal, comprising the steps of collecting a set of calibration samples from a
plurality of sources of the biological fluid and an unknown sample from an
unknown source of the biological fluid; generating near-infrared
electromagnetic
radiation having a plurality of wavelengths; irradiating each of the
calibration
samples and the unknown sample with the radiation so that a portion of the
radiation at each of the wavelengths is transmitted through each of the
calibration
samples and the unknown sample;
measuring intensity of the radiation transmitted through each of the
calibration
samples at each of the wavelengths thereby forming a set of calibration data
and
through the unknown sample at each of the wavelengths thereby forming a set of
sample data;
processing the set of calibration data, including forming the set of
calibration data
into a nxp matrix defining a space, wherein n is the number of calibration
samples
and p is the number of wavelengths at which intensity of transmitted radiation
is
measured, forming a subspace of the space wherein sources of relatively
greater
variations within the set of calibration data are represented, projecting the
set of
calibration data into the subspace, determining a generalized distance within
the
subspace between each calibration sample and a centroid of a distribution
formed
by the set of calibration samples, identifying calibration outliers as those
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calibration samples having a generalized distance greater than a preselected
magnitude, forming a reduced set of calibration samples from calibration
samples
remaining after removal of calibration outliers;
constructing a calibration model from the reduced set of calibration samples
to predict concentration of the analyte in the unknown sample; and
applying the calibration model to the set of sample data including
projecting the set of sample data into the space defined by the model,
determining
a generalized distance for the unknown sample according to the model, and
predicting concentration of the analyte in the unknown sample according to the
model provided the generalized distance of the unknown sample is not greater
than
the preselected magnitude, wherein
the step of constructing a calibration model includes removing redundant
data from data corresponding to the reduced set of calibration samples.
In accordance with yet another aspect of the invention there is provided an
apparatus for determining concentration of an analyte in an unknown sample of
a
biological fluid of a mammal comprising:
a positioner unit capable of sequentially positioning the unknown sample
and each of a set of calibration samples of the biological fluid collected
from a
plurality of sources;
a radiation emitter capable of emitting near-infrared electromagnetic
radiation at a preselected plurality of wavelengths, said radiation emitter
positioned to sequentially direct radiation of each of the wavelengths into
and
partially through each of the calibration samples and the unknown sample;
a near-infrared electromagnetic radiation detector disposed to sequentially
receive and measure intensity of the radiation transmitted through each of the
calibration samples at each of the wavelengths to form a set of calibration
data and
through the unknown sample to form a set of sample data; and
a computer connected to said detector and having a general purpose
microprocessor configured with computer program code to form the set of
calibration data into a matrix defining a space, form a subspace of the space
wherein sources of relatively greater variations within the set of calibration
data
are represented, project the set of calibration data into the subspace,
determine a
generalized distance within the subspace between each calibration sample and a
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centroid defined by a distribution formed by the set of calibration samples,
identify calibration outliers as those calibration samples having a
generalized
distance greater than a preselected magnitude, form a reduced set of
calibration
samples from calibration samples remaining after removal of calibration
outliers,
construct a calibration model from the reduced set of calibration samples to
predict
concentration of the analyte in the unknown sample, project the set of sample
data
into a space defined by the model, determine a generalized distance for the
unknown sample according to the model, identify the unknown sample as a
sample outlier, and predict concentration of the analyte in the unknown sample
according to the model provided the generalized distance of the unknown sample
is not greater than the preselected magnitude.
In accordance with still another aspect of the invention there is provided an
apparatus for determining concentration of an analyte in an unknown sample of
a
biological fluid of a mammal comprising:
a positioner unit capable of sequentially positioning the unknown sample
and each of a set of calibration samples of the biological fluid collected
from a
plurality of sources, including a flowcell having an input orifice and an
output
orifice, and a pump disposed in fluid connection between said input orifice
and
said output orifice whereby each of the set of calibration samples and the
unknown
sample may be sequentially circulated through said flowcell;
a radiation emitter capable of emitting near-infrared electromagnetic
radiation at a preselected plurality of wavelengths, said radiation emitter
positioned to sequentially direct the radiation of each of the wavelengths
into and
partially through each of the calibration samples and the unknown sample;
a near-infrared electromagnetic radiation detector disposed to sequentially
receive and measure intensity of the radiation transmitted through each of the
calibration samples at each of the wavelengths to form a set of calibration
data and
through the unknown sample to form a set of sample data;
a temperature controller capable of controlling temperature of said
positioner unit and said detector;
a noise reducer coupled to said radiation emitter and said detector, and
capable of reducing noise in measurements of intensity of that portion of the
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radiation transmitted through each of the calibration samples and the
unknown sample; and
a computer connected to said detector and having a general purpose
microprocessor configured with computer program code to form the set of
calibration data into a matrix defining a space, form a subspace of the space
wherein sources of relatively greater variations within the set of calibration
data
are represented, project the set of calibration data into the subspace,
determine a
generalized distance within the subspace between each calibration sample and a
centroid defined by a distribution formed by the set of calibration samples,
identify calibration outliers as those calibration samples having a
generalized
distance greater than a preselected magnitude, form a reduced set of
calibration
samples from calibration samples remaining after removal of calibration
outliers,construct a calibration model from the reduced set of calibration
samples
to predict concentration of the analyte in the unknown sample, project the set
of
sample data into a space defined by the model, determine a generalized
distance
for the unknown sample according to the model, identify the unknown sample as
a
sample outlier, and predict concentration of the analyte in the unknown sample
according to the model provided the generalized distance of the unknown sample
is not greater than the preselected magnitude.
As those skilled in the art will appreciate, the present invention is intended
to
encompass without limitation a range of embodiments that can be better
understood with reference to the drawings and following detailed description
of
the preferred embodiments of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic block diagram of a first preferred embodiment of the
apparatus for biological fluid analyte concentration measurement representing
the
present invention.
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FIG. 2 is a schematic block diagram of a second preferred
embodiment of the apparatus for biological fluid analyte concentration
measurement representing the present invention.
' FIG. 3 is a schematic block diagram of a third preferred
embodiment of the apparatus for biological fluid analyte concentration
measurement representing the present invention.
FIG. 4 is a flowchart representing initial steps of the method for
biological fluid analyte concentration measurement representing the
present invention.
FIG. 5 is a flowchart representing intermediate steps of the method
for biological fluid analyte concentration measurement representing the
present invention.
FIG. 6 is a flowchart representing final steps of the method for
biological fluid analyte concentration measurement representing the
present invention.
FIG. 7 is a scatter plot of principal component 2 versus principal
component 1 of near-infrared spectra from 111 blood glucose samples in
the range of 1580 nm to 1848 nm.
FIG. 8 is a scatter plot of principal component 2 versus principal
component 1 of near-infrared spectra from 1 1 1 blood glucose samples in
the range of 2030 nm to 2398 nm.
FIG. 9 is a scatter plot of principal component 3 versus principal
component 2 of near-infrared spectra from 1 1 1 blood glucose samples in
the range of 2030 nm to 2398 nm.
FIG. 10 is a bar graph of calculated Mahalanobis distances for 103
blood glucose samples in the range of 1 100 nm to 2398 nm taken from
data depicted in FIGS. 7-9.
FIG. 1 1 is a scatter plot of predicted blood glucose concentrations
from 103 samples using data derived from 2030 nm to 2398 nm,
generated from a partial least squares model optimized with twelve
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factors attaining a standard error of validation of 64.10 mg/dL versus
actual blood glucose concentrations.
FIG. 12 is a scatter plot of predicted blood glucose concentrations
from 100 samples using data derived from 2030 nm to 2398 nm, -
generated from a partial least squares model optimized with eight factors
attaining a standard error of validation of 27.43 mg/dL versus actual
blood glucose concentrations.
FIG. 13 is a bar graph of calculated Mahalanobis distances for 100
blood glucose samples in the range of 1580 nm to 1848 nm taken from
data depicted in FIGS. 7-9.
FIG. 14 is a bar graph of calculated Mahalanobis distances for 100
blood glucose samples in the range of 2030 nm to 2398 nm taken from
data depicted in FIGS. 7-9.
FIG. 15 is a scatter plot of predicted blood glucose concentrations
from 95 samples using data derived from 2030 nm to 2398 nm,
generated from a partial least squares model optimized with eight factors
attaining a standard error of validation of 26.97 mg/dL versus actual
blood glucose concentrations.
FIG. 16 is a table representing a summary of outlier detection
results for 11 1 blood glucose samples over the spectral ranges 1580 nm
to 1848 nm and 2030 nm to 2398 nm utilizing the present invention, and
indicating possible causes of sample error.
FIG. 17 is a graph of the standard error of prediction versus the
numbers of factors used during regression.
pESCRIPTION OF THE PREFERRED EMBODIMENTS
The following portion of the specification, taken in conjunction
with the drawings, sets forth the preferred embodiments of the present
invention. The embodiments of the invention disclosed herein are the
best modes contemplated by the inventors for carrying out their invention
in a commercial environment, although it should be understood that
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various modifications can be accomplished within the parameters of the
present invention.
Referring now to the drawings for a detailed description of the
" present invention, reference is first made to FIG. 1, depicting a first
5 preferred embodiment of an apparatus for biological fluid analyte
concentration measurement. In apparatus 100, a biological fluid sample
may be introduced into pump 102 which circulates the sample through
tubing 104 to fill flowcell 106. Pump 102 may be capable of both
stopped flow and continuous flow operation. Sample compartment 108
10 contains flowcell 106 and detector 1 10, and is temperature controlled by
temperature control unit 1 12. Light from relatively broad bandwidth
near-infrared source 1 14 is directed through chopper wheel 116.
Chopper wheel 1 16 is synchronized by chopper synchronization unit 1 18
with respect to detector 116, facilitating apparatus 100 to make both
15 light and dark measurements to substantially eliminate electronic noise.
Modulated light then passes through monochrometer 120, allowing
continuous variance of the wavelength of radiation over an appropriate
range. The monochromatic light passes through flowcell 106 and strikes
detector 110. Detector 1 10 measures the amount of light transmitted
through the sample. Measurement data is then stored in general purpose
programmable computer 124 having a general purpose microprocessor,
where the data will be available for further processing as will be
described. In addition, computer 124 may also control operation of
pump 102, temperature control unit 1 12, chopper synchronization
unit 118, chopper wheel 116, and monochrometer 120.
In a second embodiment of apparatus 100 as depicted in FIG. 2,
light from relatively broad bandwidth source 1 14 is directed through
chopper wheel 1 16, and thereafter the modulated light is passed through
filter wheel 130 whereby discrete wavelengths of radiation may be
selected and transmitted to flowcell 106.
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16
In a third embodiment of apparatus 100 of the present invention as
depicted in FIG. 3, a plurality of narrow bandwidth near-infrared
sources 134, such as a plurality of laser diodes, is provided to produce
near-infrared radiation at a preselected plurality of wavelengths. Light
from a selected narrow bandwidth near-infrared source 134 may be
pulsed by driver 138 in synchronization with detector 1 10 and directed
into flowcell 106. Synchronization of the selected narrow bandwidth
near-infrared source 134 and detector 110 permits apparatus 100 to
make both light and dark measurements, thereby substantially eliminating
electronic noise. Selection of each of the set of narrow bandwidth near-
infrared sources 134 for emission of light to be transmitted into flowcell
106 may be selected in a convenient order, for instance in order of
increasing or decreasing wavelength, by configuring computer 124 to
sequentially pulse each of the set of narrow bandwidth near-infrared
sources.
Referring to FIGS. 1-3, in computer implementation of the
apparatus and method of the present invention, variations in the intensity
of transmitted light as a function of wavelength are converted into digital
signals by the detector, with the magnitude of the digital signals
determined by the intensity of the transmitted radiation at the wavelength
assigned to that particular signal. Thereafter, the digital signals are
placed in the memory of computer 124, for processing as will be
described.
As symbolically depicted in FIG. 4, step 1 in the method of the
present invention refers to collecting data to be used in performing
calibration and thereafter constructing a calibration model. After the
calibration data have been collected, data pretreatment of step 2 may be
performed, as it is often necessary to pretreat raw spectral data prior to
data analysis or calibration model building in order to remove or
compensate for spectral artifacts such as scattering (multiplicative)
CA 02228844 2004-05-20
17
effects, baseline shifts, and instrumental noise. Pretreatment of the
calibration data may be selected from the group of techniques including
calculating nth order derivatives of spectral data, multiplicative scatter
correction, n-point smoothing, mean centering, variance scaling, and tk~e
ratiometric method.
Once data pretreatment, if any, has been performed on the raw
calibration data, steps directed towards forming a calibration model may
be taken. With reference to step 3 as depicted in FIG. 4, near-infrared
spectral data variables are highly correlated. To reduce the level of
redundant information present, near-infrared spectral calibration data may
be formed into a nxp matrix X representing n samples, each measured at
p wavelengths, and may be decomposed by principal component analysis
into a set of n, n-dimensional score vectors formed into a nxn score
matrix T, and a set of n, p-dimensional loading vectors formed into an
nxp loading matrix L, with
X=TL ~ .
(1)
In most spectroscopic applications, p > n, so that decomposition may be
considered decomposing matrix X of rank n into a sum of n rank 1
matrices. The score vectors represent projections of the n spectral
samples in X into the space defined by the loading vectors. The score
matrix T represents the major sources of variation found within X, and
the column vectors in T are orthogonal.
Referring to steps 4 and 5 as depicted in FIG. 4, principal
component analysis generates a set of n eigenvectors and a set of n
eigenvalues, ~I~ z~tz z ... s~l". The eigenvalues represent the variance
explained by the associated eigenvectors. The eigenvalues may be
divided into two sets. The first q eigenvalues are primary-eigenvalues
a~ zaz Z ... z~lQ and account for the significant sources of variations within
the data. The remaining n-q secondary, or error, eigenvalues
~Iq+~ z~lq+z ~ ... z~1" account for residual variance or measurement noise.
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18
With reference to steps 6 and 7 of FIG. 4, the number of primary
eigenvalues q may be determined by an iterative method which compares
the qt" eigenvalue's variance to the variance of the pooled error
eigenvalues via an F-test,
F(1,n-q) = n~g (n-q) . (2)
j=q+i
In addition, reduced eigenvalues which weight the eigenvalues by an
amount proportional to the information explained by the associated
eigenvectors may be utilized with the reduced eigenvalue defined as
q (n-q+s) (P-q+1) ~ (3)
so that equation 2 may be expressed as
n
(p-j+1) (n-j+1)
A
F ( 1, n-q) _ ~=g+~
(p-q+1 ) ( n-q+1 )
~j
j=Q+i
The it" sample in the principal component subspace is represented by the
q score values of t,. The q score values for each sample are used to
represent the original data during outlier detection. In doing so, the
original spectra are projected into the nxq dimensioned principal
component subspace defined by loading matrix L.
As depicted symbolically in steps 8 and 9 of FIG. 4, outliers may
be identified using generalized distances, such as Mahalanobis distance
or Robust distance. A generalized distance between a centroid ,u of a set
of samples and the it" sample x; may be determined from
D~= f (xi-~,) f'-1 (xi-Et) tl 1~2 (5)
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19
where f is the variance-covariance matrix of the set of samples. Where
the true variance-covariance matrix and the true centroid of a complete
set of samples are not determinable, a subset of the complete set of
samples may be used to form an approximate variance-covariance matrix
and an approximate centroid. In addition, by using principal component
scores to represent spectral data for each sample, independent variables
are orthogonal thus maximizing the information content and insuring an
invertible approximate variance-covariance matrix.
Generalized distances may be Mahalanobis distances as described
in step 10a of FIG. 4, with an approximate centroid x determined as the
centroid of a multivariate normal distribution of the set of calibration
samples and an approximate variance-covariance matrix of the set of
calibration samples S. Approximate Mahalanobis distances MD, in
units of standard deviations measured between the centroid and an ,tn
calibration sample x; may thus be determined from
~j= ~ (Xiy S 1 (Xi_~ t~ 1/2
(6)
where
9
~ (Xi-x~ t (Xi-x~ (7)
i'1
(g'-1)
With respect to Robust distance as depicted in step 10b of FIG. 4,
by utilizing a minimum volume ellipsoid estimator (MVE), robust estimates
of the approximate variance-covariance matrix SRobust and the approximate
centroid xRobust may be obtained, with Robust Distances RD, for the i'U'
calibration sample determined from
-1 r i/a
Vii- ~ (Xi xRobust) 'SRobust (Xi-XRobust)
i8)
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Alternatively, a projection algorithm may be used to determine the Robust
distance RD; for the 1'" calibration sample from
5 RD.=max( I (xjvg-L (xlvg, . . . , xnvg)
1
~Z(XlVg, . . . ,xnv9) (9) _
for g=1,...,n and where a scale of a minimum volume ellipsoid is given
10 by
Z(XlVg, . . .,XnVg)=(1+~ ~) (XjVg-X -2Vg) (10)
and a location of a minimum volume ellipsoid is given by
(xw9+X _ nv9) (1 1 )
L (XlVg, . . . , XnVg) = 2
2
x; a p-dimensional vector representing the r''t' calibration sample, and vg is
a p-dimensional vector representing the gt'' calibration sample defined by
v g=xg-M
( 12)
where M is a p-dimensional vector such that the r~'' component of M is
given by the median of a set formed by the rah component of each of the
n vectors x; . For each value of g= 1,...,n, index j used in equations 10
and 1 1 is determined from
xwg-x _ 2 v~=mini 2 +1vg-xlv~, x 2 +2vg-xav9'., . . . , xavg-x n vg )
2 (13)
where x,vg ~ x2vg <_ x3vg <_ ... _< x"vg.
After determining the generalized distances for the calibration
samples, referring to step 1 1 shown in FIG. 4, the probability of class
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21
membership may be determined by a number of techniques, including
evaluation of a chi-squared distribution function or utilizing Hotelling's T-
statistic. As depicted in step 12, outliers are identified as having
- relatively large generalized distance which results in a relatively low
probability of class membership. Generally speaking, samples whose
class membership can be rejected at a confidence level in the range of
approximately 3-5Q may be considered as outliers. Following
identification, outliers in the calibration samples may be removed as
depicted in step 13. Further, as indicated in step 14, the generalized
1 O distances of outliers removed from the calibration samples may be
examined to determine whether additional data pretreatment is
necessary. In the event that a relatively large number of outliers have
very large generalized distances, further pretreatment of the calibration
data may be indicated. If such further pretreatment of the calibration
data is indicated, then after such pretreatment, the calibration data will
again be subjected to the steps previously described beginning at step 2.
On the other hand, if relatively large numbers of outliers do not have very
large distances, then additional data pretreatment may not be
appropriate.
Thereafter, as indicated by step 15 shown in FIG. 5, a calibration
model may be constructed utilizing any of a number of techniques,
including principal component regression (PCR), partial least squares
(PLS), multiple linear regression (MLR), and artificial neural networks
(ANN). The calibration model will seek to correlate a set of independent
variables representing absorbance values of n samples measured at p
wavelengths, symbolically represented by the nxp matrix X, with a set of
dependent or response variables representing the concentration of an
analyte in each of the n samples, symbolically represented by vector y. y
is an n-dimensional vector, or alternatively, may be considered to be an
nx7 matrix. After mean centering X and y, the relationship between X
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22
and -y may be expressed as
y=Xb+e
(14)
where b represents a p-dimensional regression coefficient vector (px7
matrix) and E is an n-dimensional vector (nx 7 matrix) representing errors
in y. The calibration model determines vector b, using
b= (X'X) -1X'y'.
(15)
Knowledge of b is used to predict the concentration of the analyte, y, in
unknown samples, given only absorbances at each of the p wavelengths.
Referring to step 16, the determination of (X t~'' may be difficult
as collinearity is inherent in spectroscopic data. As described, near-
infrared spectral data variables are highly correlated. While careful
selection of the measurement wavelengths may minimize singularity
problems, the spectral regions of interest may suffer from severe overlap
and a high number of wavelengths is needed to model a multicomponent
system. Data compression may be used to address problems with
collinearity to determining regression coefficient vector b, so that
redundant data may be reduced down to significant factors.
Principal component regression is one technique to determine
vector b that incorporates a data compression method. The first step in
principal component regression is to perform principal component
analysis on the calibration data as formed into matrix X. The score matrix
T represents the major sources of variation found within X, and the
column vectors in T are orthogonal: As a result, in the next step in
principal component regression, T is used in place of X whereby an
approximate value of b is found using
b= (T'T) -1T'y
(16)
as (TTY is invertible.
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23
The techniques ofi partial least squares may also be used to
address the problem of redundant data. One difference between partial
least squares and principal component regression is the way in which the
score matrix T and the loading matrix L are generated. As described, in
principal component regression,, using non-linear iterative partial least
squares (NIPALS), loading vectors are extracted one at a time in the order
of their contribution to the variance in X. As each loading vector is
determined, it is removed from X and the next loading vector is
determined. This process is repeated until n loadings have been
determined. In partial least squares, concentration, y block, information
is used during iterative decomposition of X. With concentration
information incorporated into L, T values are related to concentration as
well as placing useful predictive information into earlier factors as
compared to principal component regression.
With respect to both principal component regression and partial
least squares, determination must be made of the appropriate number of
score vectors or factors to be included in a calibration model that
adequately represents the calibration data. The goal of selecting optimal
number of factors for regression is to obtain parsimonious models with
robust predictive abilities. Including too few factors causes model
performance to suffer due to inadequate information during calibration.
Including too many factors may also degrade performance. Principal
components are normally sorted into an order so that the amount of
variation explained by each principal component monotonically
decreases. Later ordered principal components associated with small
eigenvalues may be considered as containing measurement noise. By
utilizing only the first q factors and omitting the remaining factors, a type
of noise rejection may be incorporated within principal component
regression. The number of principal component analysis or partial least
squares scores or factors, q, to use during the regression step may be
CA 02228844 2004-05-20
24
determined as follows. In the case of matrix X with rank n, n preliminary
calibration models are built. Each preliminary calibration model uses a
different number of score vectors selected from the range of 1 through n
score vectors. Predictions are then made form the n preliminary
calibration models using the standard error of prediction technique.The
standard error of prediction (SEP) is a measure of the error associated
with each set of predictions and is given by
n
(yj_~i,k) 2 (17)
SEP(k) = i=1
n-1
where the number of test set samples is given by n and
j? j =y+ ( XL j ) bi .
(181
By plotting standard error of prediction against the number of factors
(score vectors) used, denoted by k, in each of the respective sets of
predictions, a piecewise continuous graphical representation such as FIG.
17 may be obtained and utilized to determine the number of factors to
retain. One criterion for factor selection is to determine the first local
minimum. Applying a first local minimum criterion to the data graphed in
FIG. 17, eight factors would be selected for the calibration model. A
general interpretation of FIG. 17 is that significant information is being
incorporated into the calibration model in factors one through six. As
factors seven and eight are included, subtleties in the data are included.
For factors nine through fifteen, variations or measurement noise specific
to the calibration set are being modeled, so errors increase. Another
technique for factor selection uses an F test to compare standard error of
prediction from models using differing numbers of factors. An F test
factor optimization would find that the standard error of prediction using an
eight factor model does not vary significantly from the standard error of
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prediction of a six factor model, whereby six factors is seen to be
optimal.
In certain instances, data being analyzed may not be amenable to
being split into a calibration, training set and a validation, test set. The
5 reason may be due to a limited number of available samples or that by
splitting data into two sets, one or both of the resulting sets do not
adequately represent the sample population. The technique of leave one
out cross validation may be used in such a situation. Leave one out
cross validation is an iterative process, where during each iteration, a
10 sample is excluded from the calibration set and is used as a test sample.
Prediction models using 1 through n-7 factors determined from n-7
calibration samples are then used to make test sample predictions. The
test sample is then returned to the calibration set and another sample is
excluded. The same process is repeated until all n samples have been
15 excluded from the calibration set and predicted by models generated by
the n-7 calibration samples. All predictions are accumulated to give the
standard error of validation (SEV) given by
n
2
(19)
(Y1 Wci~ t,k)
20 SEV(k) _ ==1
n-1
where the subscript (iJ represents the i''h leave one out iteration which
leaves out the i''h sample, with the standard error of validation then
treated as standard error of prediction.
25 Referring to step 17, as depicted in FIG. 5, after determining the
number of significant factors, data for the calibration model may be
reduced to significant factors, and regression coefficients for the
calibration model may be determined.
After construction, the calibration model as described above may
be applied to data collected from samples where concentration of
CA 02228844 2004-05-20
26
analytes of interest are unknown, symbolically indicated in FIG. 6 as step
18. The unknown sample data may be appropriately pretreated as
indicated at step 19, with similar techniques to those described above
with respect to pretreatment techniques capable of use with calibration
data. Upon completion of pretreatment, the sample data may be
projected into the principal component space that was previously defined
by the calibration model, as indicated in step 20. In step 21, generalized
distances for the unknown sample is found using the generalized
distance, such as Mahalanobis or Robust distances, that was utilized
with respect to the calibration data. The probability of class membership
may be estimated using the techniques described above, including
evaluation of a chi-squared distribution function or utilizing Hotelling's T-
statistic. Referring next to step 22, unknown sample outliers may then be
identified based upon rejecting class membership at a confidence level
that is in the approximate range of 3-5Q. In the event that an unknown
sample is not an outlier, as in step 23a, the unknown sample may be
projected into the space defined by the calibration model; and a
prediction of the concentration of the analyte may be made. However, if
the unknown sample is an outlier, as in step 23b, the unknown sample
should be rejected and no prediction as to analyte concentration is made,
although if possible, remeasurement of the unknown sample may be
made for reanalysis to verify that the unknown sample is indeed an
outlier.
With respect to the apparatus of the present invention, it will be
understood that the steps previously described with respect to the
method of the present invention may be configured on the general
purpose microprocessor of computer 124 by employing computer
program code segments according to each of such steps.
In use, the method and apparatus of the present invention was
applied to blood glucose concentration data obtained from samples from
CA 02228844 2004-05-20
27
111 individuals. Six of the samples did not have enough serum to collect
a near-infrared spectrum, so that vectors of zeros were used to fill their
position within the data matrix in order to maintain succession number
integrity during data manipulation. The six samples and the associated
reference tests were omitted from future analyses. Two other samples
were associated,with reference test errors and were omitted, leaving 103
samples in the data set.
Potential outliers were identified through visual inspection of two
dimensional and three dimensional scatter plots of principal component
scores. FIGS. 7-9 depict separate principal component analyses of two
spectral regions performed. Vectors of zeros, indicated by reference
numeral 200, lie far from the main group of data, as expected. The near-
infrared spectra of three samples, indicated by reference numerals 23,
67, and 83, each exhibited indications of interference due to bubbles in
the optical path of the flowcell. As shown in FIGS. 7-9, such
interference was present across the spectrum utilized as shown by
distance of samples 23, 67, and 83 from the main group. In FIG. 7,
samples 28 and 44 are seen to be potential outliers, as are samples 3
and 4 in FIG. 8. In FIG. 9, samples 3, 4, and 44 are potential outliers.
Mahalanobis distances were calculated for the 103 samples, as
shown in FIG. 10, wherein samples 23, 67, and 83 are seen to have
Mahalanobis distances much greater than the other samples. Further, in
FIGS. 10, 13, and 14, omitted samples are depicted as having zero
Mahalanobis distance. A number of additional samples appear in FIG. 10
to be outlier candidates, including samples 3, 4, and 44. The data were
subjected to further analyses, as will be described, with samples 23, 67,
and 83 omitted, leaving 100 samples in the data set.
The detrimental impact of including outlier samples in a data set is
illustrated in FIGS. 1 1 and 12. FIG. 1 1 depicts a scatter plot of predicted
blood glucose concentrations from 103 samples using data derived from
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28
2030 nm to 2398 nm generated from a partial least squares model
optimized with twelve factors attaining a standard error of validation of
64.10 mg/dL versus actual blood glucose concentrations. With samples
23, 67, and 83 removed, FIG. 12 depicts a scatter plot of predicted '
blood glucose concentrations from 100 samples using data derived from
2030 nm to 2398 nm, generated from a partial least squares model
optimized with eight factors attaining a standard error of validation of
27.43 mg/dL versus actual blood glucose concentrations. With gross
outliers eliminated, the partial least squares technique utilized in the
method of the present invention was able to make better predictions and
use a less complex model, that is, a model using fewer factors. The
sample depicted in FIG. 1 1 having a predicted value of approximately
750 mg/dL corresponded to sample indicated by reference numeral 83. If
sample 83 in FIG. 11 is ignored and the remaining samples in FIG. 11 are
compared with those in FIG. 12, it is apparent that there is a wider
spread of data about the identity line in FIG. 1 1. These results illustrate
the influence of a relatively small number of outliers in seriously
degrading the overall performance of a calibration model.
Two spectral regions of the 100 samples were tested separately
for outliers, with Mahalanobis distances for each of the regions shown in
FIG. 13 and 14. Nine samples were flagged as possible outliers in the
1580 nm to 1848 nm region, and six samples were flagged in the 2030
nm to 2398 nm region as possible outliers. As is apparent from
comparison of FIGS. 13 and 14, the flagged samples were different in
the two spectral regions. Outliers may be selected to be those flagged
samples that are excluded from class membership in either or both
spectral ranges, at a confidence level selected to be in the range of 3-5Q.
Four of the samples rejected were also identified as possible outliers from
the principal component score plots, FIGS. 7-9. Identification of the fifth
sample required examination in the higher dimensional space associated
with Mahalanobis distances.
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FIG. 16 sets forth a summary of 95 samples representing both
major spectral regions examined using the method and apparatus of he
present invention, and shows that blood glucose concentration
predictions using the 95 and 100 sample data sets and the same spectral
regions yielded very similar results. A slight reduction in prediction error
to SEV of 26.97 mg/dL with respect to the 100 sample set depicted in
FIG.12 resulted for the 95 sample set depicted in FIG. 15 for the 2030
nm to 2398 nm region, with the difference representing approximately a
1 % reduction in error. An F-test at the 95% confidence level did not find
1 O this a significant difference. Comparison of the partial least squares
results from other spectral regions with various forms of data
preprocessing yielded similar findings.
If a Mahalanobis distance threshold of 3.0 is used to determine
outliers, a set of 89 samples results. Utilizing a partial least squares
technique, leave-one-out validation on the set of 89 samples resulted in
an SEV of 27.95 mg/dL, a slight increase over the 100 and 95 sample
sets. It was separately determined that the six samples omitted in the 89
sample set with respect to the 95 sample set corresponded to samples
having a high triglyceride concentration, a high total protein value, or
both. The presence of the six outliers constituted an artifact of
undersampling, that is, if a greater number of representative samples
with high triglyceride or total protein concentrations were present in the
original set of samples, samples having high triglyceride or total protein
concentrations would be less likely to be flagged as outliers.
Sensitivity of outlier detection to triglyceride or any other analyte
which affects spectral response may be advantageous, however.
Spectral data may be partitioned such that samples with high
triglycerides form a first calibration set while samples with low
triglycerides form a second calibration set, so that new samples may be
tested with the method and apparatus of the present invention to
CA 02228844 2004-05-20
determine whether the first or second calibration set is representative of
the new sample; thus allowing the selection of a prediction model
determined from "similar" calibration spectra.
The present invention having been described in its preferred
5 embodiments, it is clear that it is susceptible to numerous modifications
and embodiments within the ability of those skilled in the art and without
the exercise of the inventive faculty. As will be appreciated by those
skilled in the art, the method and apparatus of the present invention
encompass alternative biological fluid analyte measurement techniques,
10 including biological fluid analyte concentrations derived using light
reflectance, light transmission, and other techniques used in conjunction
with invasive, non-invasive, and in-vivo biological fluid analyte
measurement techniques. In addition, measurements of biological fluid
analytes may also include triglycerides, cholesterol, and serum proteins,
15 with outlier detection using the method and apparatus of the present
invention.
