Method and apparatus for biological fluid analyte concentration measurement using generalized distance outlier detection

• US 5,606,164 A
• Filed: 01/16/1996
• Issued: 02/25/1997
• Est. Priority Date: 01/16/1996
• Status: Expired due to Term

• Current Assignee: Roche Diabetes Care Inc. (Roche Holding AG)
• Original Assignee: Boehringer Mannheim Corporation
• Inventors: Price, John F., Long, James R.
• Primary Examiner(s): Porta, David P.
• Assistant Examiner(s): Bruce, David Vernon
• Application Number:
  US08/587,017
• Time in Patent Office: 406 Days
• Field of Search: 250/339.01, 250/339.06, 250/339.07, 250/339.09, 250/339.12, 364/413.07, 364/413.08, 364/413.09, 364/413.11
• US Class Current: 250/339.09
• CPC Class Codes: G01J 2003/2866 Markers; Calibrating of scan
• CPC Class Codes: G01N 21/274 Calibration, base line adjustment, drift correction
• CPC Class Codes: G01N 21/359 using near infrared light

Abstract

A method and apparatus for measuring the concentration of an analyte present in a biological fluid is disclosed. The method includes the steps of applying NIR radiation to calibration samples to produce calibration data, analyzing the calibration data to identify and remove outliers, constructing a calibration model, collecting and analyzing unknown samples to identify and remove outliers, and predicting analyte concentration of non-outliers from the calibration model. Analysis of the calibration data includes data pretreatment, data decomposition to remove redundant data, and identification and removal of outliers using generalized distances. The calibration model may utilize principal component regression, partial least squares, multiple linear regression, or artificial neural networks, and reduction using principal component analysis or partial least squares scores. Unknown sample data is analyzed using data pretreatment followed by projection into the calibration model space, and identification and removal of outliers, with prediction of analyte concentration using the calibration model. The apparatus includes a pump which circulates a sample through tubing to fill a flowcell. Light from a NIR source is synchronized with a detector, facilitating light and dark measurements, and passes through a monochrometer and the flowcell and strikes the detector, whereby radiation transmitted through the sample is measured. Measurement data is stored in a general purpose programmable computer also controlling the pump, the detector, synchronization, and the monochrometer. The computer includes a general purpose microprocessor configured with computer program code employing the steps of the method.

Claims

1. 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 n×

p 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 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.

2. The method as set forth in claim 1, wherein:

the step of forming a subspace includes decomposing the matrix by principal component analysis into an n×

n dimensional score matrix and an n×

p dimensional loading matrix, generating by principal component analysis a set of n eigenvectors and a set of n eigenvalues associated with the eigenvectors and arranged in order of decreasing magnitude, dividing the set of eigenvalues into a set of q larger, primary eigenvalues and a set of n-q smaller, error eigenvalues whereby the primary eigenvalues are associated with relatively more significant sources of variations within the set of calibration data and the error eigenvalues are associated with relatively less significant sources of variation within the set of calibration data, and generating the subspace as an n×

q dimensioned principal component subspace from the space defined by the loading matrix; and

the step of constructing a calibration model includes forming a regression coefficient matrix correlating the reduced set of calibration samples with the concentration of the analyte in the reduced set of calibration samples whereby the regression coefficient matrix may be used to predict concentration of the analyte in an unknown sample of the biological fluid given the intensity of the radiation transmitted therethrough at each of the wavelengths.

3. The method as set forth in claims 1 or 2, wherein each of the generalized distances is a Mahalanobis distance determined from the following relationship:

space="preserve" listing-type="equation">MD.sub.i =[(x.sub.i -x)S.sup.-1 (x.sub.i -x).sup.t ].sup.1/2

wherein MD_i is the Mahalanobis distance between an i^th calibration sample x_i and the centroid x of the set of calibration samples, S^-1 is the inverted variance-covariance matrix of the set of calibration data, and (x_i -x)^t is the transpose of (x_i -x).

4. The method as set forth in claims 1 or 2, wherein each generalized distance is a Robust distance determined using an algorithm selected from the group consisting of minimum volume ellipsoid estimator and projection algorithm.

5. The method as set forth in claims 1 or 2, further including the step of pretreating the set of calibration data to remove and compensate for spectral artifacts prior to the step of processing the set of calibration data.

6. The method as set forth in claim 5, wherein the step of pretreating the set of calibration data is performed using an algorithm selected from the group consisting of nth order derivatives, multiplicative scatter correction, n-point smoothing, mean centering, variance scaling, and ratiometric method.

7. The method as set forth in claims 1 or 2, further including the steps of:

forming a ratio of the number of calibration outliers to the number of calibration samples;

determining whether the ratio is greater than a preselected ratio; and

pretreating the set of calibration data to remove and compensate for spectral artifacts prior to the step of processing the set of calibration data if the ratio exceeds the preselected ratio.

8. The method as set forth in claims 1 or 2, wherein the step of identifying calibration outliers includes selecting the magnitude by determining a probability that each member of the set of calibration samples belongs to a class defined by a preselected probability distribution function whereby calibration outliers are identified as calibration samples whose class membership may be rejected at a confidence level greater than a preselected level.

9. The method as set forth in claim 8, wherein the probability distribution function is formed using an algorithm selected from the group consisting of chi-squared distribution function evaluation and Hotelling'"'"'s T-statistic evaluation.

10. The method as set forth in claim 8, wherein the preselected level is in the range of approximately 3 to 5 standard deviations as defined by the probability distribution function.

24. The method as set forth in claims 1, 2, 11 or 12, wherein the step of constructing a calibration model includes removing redundant data from data corresponding to the reduced set of calibration samples.

25. The method as set forth in claims 1, 2, 11 or 12, wherein the step of constructing a calibration model is performed using an algorithm selected from the group consisting of principal component regression, partial least squares, multiple linear regression, and artificial neural networks.

26. The method as set forth in claims 1, 2, 11 or 12, wherein the step of constructing a calibration model is performed using an algorithm selected from the group consisting of principal component regression, partial least squares, and multiple linear regression, and includes selecting an optimal number of score vectors to use in the calibration model whereby redundant data may be removed from data corresponding to the reduced set of calibration samples.

27. The method as set forth in claim 26 wherein the step of selecting the optimal number of score vectors includes:

constructing n preliminary calibration models, each preliminary calibration model using a different number of score vectors selected from a range of 1 through n;

determining a standard error of prediction for each of the preliminary calibration models; and

comparing the standard error of prediction for the preliminary models to determine the optimal number of score vectors.

28. The method as set forth in claim 27 wherein comparing the standard error of prediction is performed using an algorithm selected from the group consisting of F-test and local minimum determination.

11. 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 n×

p 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 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, identifying the unknown sample as a sample outlier provided the generalized distance of the unknown sample is greater than the preselected magnitude, 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.

12. The method as set forth in claim 11, wherein:

the step of forming a subspace includes decomposing the matrix by principal component analysis into an n×

n dimensional score matrix and an n×

p dimensional loading matrix, generating by principal component analysis a set of n eigenvectors and a set of n eigenvalues associated with the eigenvectors and arranged in order of decreasing magnitude, dividing the set of eigenvalues into a set of q larger, primary eigenvalues and a set of n-q smaller, error eigenvalues whereby the primary eigenvalues are associated with relatively more significant sources of variations within the set of calibration data and the error eigenvalues are associated with relatively less significant sources of variation within the set of calibration data, and generating the subspace as an n×

q dimensioned principal component subspace from the space defined by the loading matrix; and

the step of constructing a calibration model includes forming a regression coefficient matrix correlating the reduced set of calibration samples with the concentration of the analyte in the reduced set of calibration samples whereby the regression coefficient matrix may be used to predict concentration of the analyte in an unknown sample of the biological fluid given the intensity of the radiation transmitted therethrough at each of the wavelengths.

13. The method as set forth in claims 11 or 12, wherein each of the generalized distances of the set of calibration samples is a Mahalanobis distance determined from the following relationship:

space="preserve" listing-type="equation">MD.sub.i =[(x.sub.i -x)S.sup.-1 (x.sub.i -x).sup.t ].sup.1/2

wherein MD_i is the Mahalanobis distance between an i^th calibration sample x_i and the centroid x of the set of calibration samples, S^-1 is the inverted variance-covariance matrix of the set of calibration data, and (x_i -x)^t is the transpose of (x_i -x), and wherein the generalized distance of the unknown sample according to the model is a Mahalanobis distance determined from the following relationship;

space="preserve" listing-type="equation">MD.sub.sample =[(x.sub.sample -x.sub.model)S.sup.-1 (x.sub.sample -x.sub.model).sup.t ].sup.1/2

wherein MD_sample is the Mahalanobis distance between the unknown sample and the centroid x_model of the model S^-1_model is the inverted variance-covariance matrix of the model, and (x_sample -x_model)^t is the transpose of (x_sample -x_model).

14. The method as set forth in claims 11 or 12, wherein each of the generalized distances of the set of calibration data is a Robust distance determined using an algorithm selected from the group consisting of minimum volume ellipsoid estimator and projection algorithm.

15. The method as set forth in claims 11 or 12, further including the steps of:

forming a ratio of the number of calibration outliers to the number of calibration samples;

determining whether the ratio is greater than a preselected ratio;

pretreating the set of calibration data to remove and compensate for spectral artifacts prior to the step of processing the set of calibration data if the ratio exceeds the preselected ratio; and

pretreating the sample data to remove and compensate for spectral artifacts prior to the step of applying the calibration model to the sample data if the ratio exceeds the preselected ratio.

16. The method as set forth in claims 11 or 12, further including the steps of:

pretreating the set of calibration data to remove and compensate for spectral artifacts prior to the step of processing the set of calibration data; and

pretreating the sample data to remove and compensate for spectral artifacts prior to the step of applying the calibration model to the sample data.

17. The method as set forth in claim 16, wherein the steps of pretreating the set of sample data and pretreating the set of calibration data are each performed using an algorithm selected from the group consisting of nth order derivatives, multiplicative scatter correction, n-point smoothing, mean centering, variance scaling, and ratiometric method.

18. The method as set forth in claims 11 or 12, wherein the step of identifying calibration outliers includes selecting the magnitude by determining a probability that each member of the set of calibration samples belongs to a class defined by a preselected probability distribution function whereby calibration outliers are identified as calibration samples whose class membership may be rejected at a confidence level greater than a preselected level, and wherein the step of identifying a sample outlier includes determining whether probability of class membership of the unknown sample may be rejected at a confidence level greater than the preselected level, according to the model.

19. The method as set forth in claim 18, wherein the probability distribution function is formed using an algorithm selected from the group consisting of chi-squared distribution function evaluation and Hotelling'"'"'s T-statistic evaluation.

20. The method as set forth in claim 18, wherein the preselected level is in the range of approximately 3 to 5 standard deviations as defined by the probability distribution function.

21. The method as set forth in claim 12, wherein the unknown sample and each of the calibration samples includes a second analyte having concentration within a preselected range.

22. The method as set forth in claim 21, wherein the second analyte is triglycerides.

23. The method as set forth in claim 22, wherein the second analyte is total protein.

29. The method as set forth in claims 2 or 12, wherein the step of dividing the set of eigenvalues includes determining the number of primary eigenvalues q by an iterative method which compares variance of the q^th eigenvalue to the variance of the pooled error eigenvalues using an F-test.

30. The method as set forth in claim 29, wherein the step of determining the number of primary eigenvalues q includes weighing the eigenvalues by an amount proportional to information explained by associated eigenvectors to produce a set of reduced eigenvalues.

31. 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 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 provided the generalized distance of the unknown sample is greater than the preselected magnitude, 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.

32. The apparatus of claim 31, wherein said positioner unit comprises:

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.

33. The apparatus of claim 31, further comprising a temperature controller capable of controlling temperature of said positioner unit and said detector.

34. The apparatus of claim 31, wherein each of the generalized distances is a Mahalanobis distance determined from the following relationship:

space="preserve" listing-type="equation">MD.sub.i =[(x.sub.i -x)S.sup.-1 (x.sub.i -x).sup.t ].sup.1/2

wherein MD_i is the Mahalanobis distance between an i^th calibration sample and the centroid x of the set of calibration samples, S^-1 is the inverted variance-covariance matrix of the set of calibration data, and (x_i -x)^t is the transpose of (x_i -x).

35. The apparatus of claim 31, wherein each generalized distance is a Robust distance determined using an algorithm selected from the group consisting of minimum volume ellipsoid estimator and projection algorithm.

36. The apparatus of claim 31, further comprising 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 radiation transmitted through each of the calibration samples and the unknown sample.

40. The apparatus of claims 36, 38, or 39, wherein:

said radiation emitter includes a relatively broad bandwidth near-infrared electromagnetic radiation source and a monochrometer disposed between said source and said positioner unit; and

said noise reducer includes a chopper disposed between said source and said monochrometer whereby radiation from said source may be alternatively blocked from transmission to said monochrometer, and a synchronizer operably connected to said chopper and said detector whereby signals produced in said detector when radiation from said source is blocked by said chopper may be subtracted from signals produced in said detector when radiation from said source is not blocked by said chopper.

41. The apparatus of claims 36, 38, or 39, wherein:

said radiation emitter includes a relatively broad bandwidth near-infrared electromagnetic radiation source and a filter wheel disposed between said source and said positioner unit; and

said noise reducer includes a chopper disposed between said source and said monochrometer whereby radiation from said source may be alternatively blocked from transmission to said monochrometer, and a synchronizer operably connected to said chopper and said detector whereby signals produced in said detector when radiation from said source is blocked by said chopper may be subtracted from signals produced in said detector when radiation from said source is not blocked by said chopper.

42. The apparatus of claims 36, 38, or 39, wherein:

said radiation emitter includes a plurality of relatively narrow bandwidth near-infrared electromagnetic radiation sources connected to said computer whereby said sources may be activated in a preselected sequential order; and

said noise reducer includes a pulse driver operably connected to each of said sources and said detector whereby signals produced in said detector when radiation from set of sources is not pulsed by said driver may be subtracted from signals produced in said detector when radiation from said sources is pulsed by said driver.

37. 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 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 provided the generalized distance of the unknown sample is greater than the preselected magnitude, 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.

38. The apparatus of claim 37, wherein each of the generalized distances is a Mahalanobis distance determined from the following relationship:

space="preserve" listing-type="equation">MD.sub.i =[(x.sub.i -x)S.sup.-1 (x.sub.i -x).sup.t ].sup.1/2

wherein MD_i is the Mahalanobis distance between an i^th calibration sample and the centroid x of the set of calibration samples, S^-1 is the inverted variance-covariance matrix of the set of calibration data, and (x_i -x)^t is the transpose of (x_i -x).

39. The apparatus of claim 37, wherein each generalized distance is a Robust distance determined using an algorithm selected from the group consisting of minimum volume ellipsoid estimator and projection algorithm.