# Assessing linearity the easy way: laboratories can comply with new Federal regulations for linearity verification by applying simple calculations and graphs to materials that are readily at hand.

Laboratories can comply with new Federal regulations for linearity
verification by applying simple calculations and graphs to materials
that are readily at hand.

For decades, laboratory method evaluation has traditionally included basic verification of a method's linear range. Recently, in response to Federal legislation, vendors have bombarded laboratorians with extensive information and materials for continued monitoring of reagents and methods to prove the validity of linear range.

Compliance with Federal requirements for linearity verification is a straightforward job: Use available materials and convert data into graphs via simple calculations. This article presents a linearity verification method that has proved efficient and reliable in our laboratory.

Following closely upon the Clinical Laboratory Improvement Amendments (CLIA) of 1988 and the 1990 revision of CLIA '67, the Health Care Financing Administration (HCFA) determined that the "linear reportable range of each quantitative method, if applicable, must be established." (1) Thus, individual laboratories must now routinely monitor reagents and methods to prove that the linear range continues to be valid. To fulfill this requirement, our lab devised a system that is cost-effective and easy to accomplish. It uses materials readily at hand in most laboratories.

According to Beer's Law, applied in quantitative analysis, the concentration of an analyte equals absorbance multiplied by a calibration constant or factor. (2) A direct proportion between absorbance and concentration must be established for a given instrument and method under specific conditions.

Laboratories use standards to establish the calibration constant. Frequently a linear relationship exists only up to a certain concentration or absorbance. When patient values fall within a method's linear range, the may be reported without prior sample dilution.

* Definition. In document EP6-P, "Evaluation of the Linearity of Quantitative Analytical Methods," the National Committee for Clinical Laboratory Standards (NCCLS) defines linearity as follows: "For our purposes linearity is the 'measure of the degree to which a curve approximates a straight line,' Linearity refers to overall system response (i.e., the final analytical answer rather than instrument output). Linearity of a system is measured by tesing levels of an analyte that are known relative to each other. When the system results are plotted against these values, the degree to which the plotted curve conforms to a straight line is a measure of a system's linearity. Conversely, the deviation of the curve from a straight line is a measure of nonlinearity.... Linearity is an attribute of an analytical method that is distinct for accuracy and precicsion." (3)

Measuring linearity requires validation of the entire range through which patient values can be reported from analysis of undiluted specimens. If patient values on initial analysis fall outside the verified range, results may be reported as being greater than the highes value verified or less than the lowest verifiable value.

For analyte concentrations that are above the reportable range, the specimen can be diluted to insure that results from the diluted sample fall within the verified range. This result can be multiplied by the dilution factor and the resultant value reported. In some cases, when a method is validated and linearity studies are used, the linear range found in the laboratory may differ from the linearity published by the manufacturer.

CLIA '88 mandates that calibration,

calibration verification, or recalibration be verified at least every six months or when:

1. Complete change of reagents for a procedure is introduced;

2. Major preventive maintenance or replacement of critical parts take place;

3. Controls begin to reflect an unusual trend;

4. The manufacturer's recommendations specify that verification must take place more frequently; or

5. The laboratory schedule requires more frequent verification.

Linearity verification is not mandated for methods that require calibrations more often than every six months with five or more calibrators plus a zero- or minimum-value calibrator. In such methods, routine calibration of the analyte verifies linearity.

According to CLIA '88, when a linear relationship exists between analyte concentration and instrument reading, at least three points plus a zero or minimum value are required. If a nonlinear relationship exists, at least five points plus a zero or minimum value are required unless the manufacturer requires more point of comparison. Under our laboratory's system, tests (analytes) measured quantitatively in each lab section are divided into those already in compliance and those that require linearity verification.

Material used to verify linearity should have an initial concentration above the upper limit of the current analytical range of each analyte. NCCLS, recommending that the matrix of the verifiers match the matrix of clinically analyzed specimens, lists eight sources of material with which to validate linearity (Figure I). (3)

* QC material. All laboratories, especially those in small hospitals or rural locations, may have difficulty obtaining a sufficient number of patient specimens with analyte values high enough to be used in verifying linearity. An an alternative, such labs might consider using commercial lyophilized quality control material. QC material with different matrices (serum, urine, cerebrospinal fluid) can be used to verify the methods for which results are reported.

Reconstituting the QC material in one-fifth the standard diluent volume causes the analytes to be concentrated about fivefold. This step will usually attain analyte concentrations above manufacturers' claims for analytical range.

Here is a quick way to determine the most effective QC material to use for each verification of analyte linearity. Make a list of each analyte, the current upper limit of the analytical range, the mean value of the QC material with the highest value for the analyte, and the mean QC value multiplied by five. Manufacturers of QC material do not necessarily locate all high concentrates of analytes in abnormal level specimens. It is therefore necessary to review the analyte concentrations of all levels of QC material.

Some lab sections, such as hematology, do not use lyophilized material for quality control. For linearity verification on red blood counts, hemoglobin, white blood counts, and platelet counts, our system uses the following sources of verifier material: for platelet counts, an outdated donor platelet pack; for WBC, harvested buffy coats from patient specimens; and for RBC and hemoglobin, washed RBC concentrates from transfused blood unit pigtails. These verifiers can easily exceed the upper limits of linearity claimed by manufacturers.

* Quantity. Before undertaking verification, prepare enough high-concentration verifier material to use throughout the procedure. To determine the volumes needed for each dilution level, list the sample volume of each analyte. Add the sample volumes and multiply the total by the number of replicates to be used.

Make at least duplicate measurements on each concentration sample. If you are using duplicate measurements, multiply the total sample volume by two; for triplicate measurements, multiply by three. Round the total up or down to the nearest hundred microliters.

You can prepare a fivefold concentration of commercial QC material by diluting the lyophilized material in one-fifth the usual volume for the control. Because these specimens take longer to reconstitute, place them in a refrigerator for at least an hour after adding diluent. For the initial diluent, use one that has been recommended by the manufacturer of the control.

A series of dilutions of the concentrated linearity verifier are used to produce a wide range of concentrations. Initially, more dilutions will be needed to produce a wide range of values for determining linearity or nonlinearity and to establish the widest possible linear range. Once limits of linearity have been established and it has been determined whether the method is linear or nonlinear, only the required number of verifiers (dilutions) are needed to revalidate the method regularly.

A verifier is needed at both the upper and the lower limits of the method's reportable range plus one or two intermediate levels (linear methods). These standard reverification concentrations and dilutions can be marked on the initial study with an asterisk (*) to simplify later studies.

* Diluent. We use deionized water for the quality control material concentrate and saline for platelets and for RBC and WBC concentrates. One text indicates that "the accuracy of the volumetric dilutions is very important, and serial dilutions are not recommended because of the propagation of errors through subsequent samples. Rather, each sample should be prepared by direct dilution from the original high sample or pool." (4) Our laboratory uses the dilutions, samples, and diluent amounts indicated in Table I.

For some analytes, it may be necessary to use other dilutions to obtain the highest possible level of verified linearity, especially if the original or undiluted high sample is above the limits of linearity. The dilutions we use, shown in the column headed "Dilution" in Figure II, are only a suggestion; any that cover a wide range would be appropriate. After the dilutions have been prepared, assay the replicates during a single run or in closely grouped runs.

In the linearity verification form we use (Figures II and IV), the two colums headed "Recovered" list the values obtained as replicates and the mean of each set. Although the anticipated value for the undiluted specimen should be calculable by multiplying the mean of the routine QC value by five, matrix- and reconstitution-related factors may make this method inaccurate.

The column headed "Calculated" lists estimated target values, which are determined as a mean of the calculated target values. Dilutions are usually expressed as a ratio, such as 1:10--one part of the original solution diluted with 10 parts of diluent, for a total of 11 parts.

To calculate target values, multiply the mean of replicates by the total number of parts (in the 1:10 dilution, 11). In a 3:1 dilution, the calculated value is 1.33 (4 divided by 3) multiplied by the replicate mean. Calculations used for each level (dilution) are presented in the box in the top right corner of Figure II.

List these values under "Calculated." The value for Level 6, included to obtain analyte concentration of the diluent, is not used in any further calculations if it is zero or near zero. If it is higher, consult EP6-P for a discussion of how to calculate the target value.

If the target values that have been calculated for each level are reasonably comparable with each other, then the mean of calculated values is used as the target value for Level 1. If they are not reasonably comparable, however, skewedness will prevent the mean of the calculated values from being able to be used as a target value.

To compute target values for all dilutions, divide the mean of calculated values by the total parts of each dilution. For example, in a dilution of 1:10, the mean calculated value (or the Level 1 target value) is divided by 11 to achieve Level 5 target value. For a 3:1 dilution, the target value is divided by 4 (total number of parts) and then multiplied by 3 (the parts of concentrate). Equations for calculating the target value for each level are provided in Figure II.

* Graphing. Since linearity is defined as "the degree to which the plotted curve conforms to a straight line," [3] the next step is to plot the values on linear/linear (square) graph paper. A solid line representing perfect linearity is surrounded above and below by dashed lines representing variance, as seen in the graphs in Figures III and V.

In the examples shown, 10% was arbitrarily chosen as the variance for acceptability of recovered values. A 10% coefficient of variation is commonly accepted as the criterion for satisfactory method variability. Ronald H. Laessig, Ph.D., director of the Wisconsin State Laboratory of Hygiene, Madison, has suggested an admissible variance of 25%. Because the Federal agencies have not defined acceptable variability, each laboratory must determine its own level of acceptable tolerance.

The means of the recovered replicates (Y) are plotted against the target values (X) for each level. As long as the plotted values are within 10% variance (dashed lines), the method is considered linear. Special attention should be paid to the plots to be sure there is no evidence of a nonlinear relationship. For further assurance, a linear regression calculation is used to obtain a value for the slope and intercept of the actual line produced.

* Without a graph. The 10% limits of acceptability can be calculated on the worksheet and not graphed. To do this, multiply the target value for each level by 0.9 for the lower limit (90%) and by 1.1 for the upper limit (110%). If the mean of the replicates for each level then falls within acceptable limits, the recovered result will be found to fall within 10% of the target value.

* Records. Worksheets and graphs can be conveniently stored in a three-ring binder for review by laboratorians and inspectors. The laboratory might select two months of each year--January and July, for example--on which to reconfirm the linearity of appropriate methods.

The methodology described in this article can be included in the initial verification of virtually any new procedure requiring quantitative analysis. Laboratorians must document all the methodologies they use and the conclusions they reach so that others can infer how the information was derived.

Oversight of clinical laboratories by the Federal government will surely continue to intensify. Laboratory managers and supervisors who devise creative solutions and adaptations are likely to achieve the best results. If laboratorians do the early work and develop our own provable standards, we will create the reference points for inspectors who visit us.

[1] Federal Register, p. 9596, vol. 55, no. 50, March 14, 1990.

[2] Tietz, N.W. "Fundamentals of Clinical Chemistry," pp. 105-107. Philadelphia, W.B. Saunders, 1976.

[3] National Committee for Clinical Laboratory Standards. "Evaluation of the Linearity of Quantitative Analytical Methods" (EP6-P), pp. ix, 513, 515-516, vol. 6, no. 18. Villanova, Pa., NCCLS, 1986.

[4] Kaplan, L.A., and Pesce, A.J. "Clinical Chemistry: Theory, Analysis, and Correlation," p. 345. St. Louis, C.V. Mosby, 1984.

General references:

Broddle, R.O. Determining linearity on a micro-computer (Computer Dialog). MLO 19(10): 91-92, October 1987.

Farnham, R. Computer graphs clarify linear regression modules. MLO 23(3): 56-63, March 1991.

Farnham, R. Programming spreadsheet graphics on a PC (Computer Dialog). MLO 23(3): 67-68, March 1991.

Ulstein, H. Impress your inspectors with linearity graphs (Computer Dialog). MLO 22(3): 63-66, March 1990.

The author is administrative director of laboratory services at Baptist Medical Center, Kansas City, Mo.

For decades, laboratory method evaluation has traditionally included basic verification of a method's linear range. Recently, in response to Federal legislation, vendors have bombarded laboratorians with extensive information and materials for continued monitoring of reagents and methods to prove the validity of linear range.

Compliance with Federal requirements for linearity verification is a straightforward job: Use available materials and convert data into graphs via simple calculations. This article presents a linearity verification method that has proved efficient and reliable in our laboratory.

Following closely upon the Clinical Laboratory Improvement Amendments (CLIA) of 1988 and the 1990 revision of CLIA '67, the Health Care Financing Administration (HCFA) determined that the "linear reportable range of each quantitative method, if applicable, must be established." (1) Thus, individual laboratories must now routinely monitor reagents and methods to prove that the linear range continues to be valid. To fulfill this requirement, our lab devised a system that is cost-effective and easy to accomplish. It uses materials readily at hand in most laboratories.

According to Beer's Law, applied in quantitative analysis, the concentration of an analyte equals absorbance multiplied by a calibration constant or factor. (2) A direct proportion between absorbance and concentration must be established for a given instrument and method under specific conditions.

Laboratories use standards to establish the calibration constant. Frequently a linear relationship exists only up to a certain concentration or absorbance. When patient values fall within a method's linear range, the may be reported without prior sample dilution.

* Definition. In document EP6-P, "Evaluation of the Linearity of Quantitative Analytical Methods," the National Committee for Clinical Laboratory Standards (NCCLS) defines linearity as follows: "For our purposes linearity is the 'measure of the degree to which a curve approximates a straight line,' Linearity refers to overall system response (i.e., the final analytical answer rather than instrument output). Linearity of a system is measured by tesing levels of an analyte that are known relative to each other. When the system results are plotted against these values, the degree to which the plotted curve conforms to a straight line is a measure of a system's linearity. Conversely, the deviation of the curve from a straight line is a measure of nonlinearity.... Linearity is an attribute of an analytical method that is distinct for accuracy and precicsion." (3)

Measuring linearity requires validation of the entire range through which patient values can be reported from analysis of undiluted specimens. If patient values on initial analysis fall outside the verified range, results may be reported as being greater than the highes value verified or less than the lowest verifiable value.

For analyte concentrations that are above the reportable range, the specimen can be diluted to insure that results from the diluted sample fall within the verified range. This result can be multiplied by the dilution factor and the resultant value reported. In some cases, when a method is validated and linearity studies are used, the linear range found in the laboratory may differ from the linearity published by the manufacturer.

CLIA '88 mandates that calibration,

Table I Creating the dilution: Selected examples Dilution Sample Diluent Undiluted 400[mu]l 0[mu]l 3:1 300[mu]l 100[mu]l 1:1 200[mu]l 200[mu]l 1:4 100[mu]l 400[mu]l 1:10 100[mu]l 1000[mu]l Total volume of verifier concentrate 1100[mu]l

calibration verification, or recalibration be verified at least every six months or when:

1. Complete change of reagents for a procedure is introduced;

2. Major preventive maintenance or replacement of critical parts take place;

3. Controls begin to reflect an unusual trend;

4. The manufacturer's recommendations specify that verification must take place more frequently; or

5. The laboratory schedule requires more frequent verification.

Linearity verification is not mandated for methods that require calibrations more often than every six months with five or more calibrators plus a zero- or minimum-value calibrator. In such methods, routine calibration of the analyte verifies linearity.

According to CLIA '88, when a linear relationship exists between analyte concentration and instrument reading, at least three points plus a zero or minimum value are required. If a nonlinear relationship exists, at least five points plus a zero or minimum value are required unless the manufacturer requires more point of comparison. Under our laboratory's system, tests (analytes) measured quantitatively in each lab section are divided into those already in compliance and those that require linearity verification.

Material used to verify linearity should have an initial concentration above the upper limit of the current analytical range of each analyte. NCCLS, recommending that the matrix of the verifiers match the matrix of clinically analyzed specimens, lists eight sources of material with which to validate linearity (Figure I). (3)

* QC material. All laboratories, especially those in small hospitals or rural locations, may have difficulty obtaining a sufficient number of patient specimens with analyte values high enough to be used in verifying linearity. An an alternative, such labs might consider using commercial lyophilized quality control material. QC material with different matrices (serum, urine, cerebrospinal fluid) can be used to verify the methods for which results are reported.

Reconstituting the QC material in one-fifth the standard diluent volume causes the analytes to be concentrated about fivefold. This step will usually attain analyte concentrations above manufacturers' claims for analytical range.

Here is a quick way to determine the most effective QC material to use for each verification of analyte linearity. Make a list of each analyte, the current upper limit of the analytical range, the mean value of the QC material with the highest value for the analyte, and the mean QC value multiplied by five. Manufacturers of QC material do not necessarily locate all high concentrates of analytes in abnormal level specimens. It is therefore necessary to review the analyte concentrations of all levels of QC material.

Some lab sections, such as hematology, do not use lyophilized material for quality control. For linearity verification on red blood counts, hemoglobin, white blood counts, and platelet counts, our system uses the following sources of verifier material: for platelet counts, an outdated donor platelet pack; for WBC, harvested buffy coats from patient specimens; and for RBC and hemoglobin, washed RBC concentrates from transfused blood unit pigtails. These verifiers can easily exceed the upper limits of linearity claimed by manufacturers.

* Quantity. Before undertaking verification, prepare enough high-concentration verifier material to use throughout the procedure. To determine the volumes needed for each dilution level, list the sample volume of each analyte. Add the sample volumes and multiply the total by the number of replicates to be used.

Make at least duplicate measurements on each concentration sample. If you are using duplicate measurements, multiply the total sample volume by two; for triplicate measurements, multiply by three. Round the total up or down to the nearest hundred microliters.

You can prepare a fivefold concentration of commercial QC material by diluting the lyophilized material in one-fifth the usual volume for the control. Because these specimens take longer to reconstitute, place them in a refrigerator for at least an hour after adding diluent. For the initial diluent, use one that has been recommended by the manufacturer of the control.

A series of dilutions of the concentrated linearity verifier are used to produce a wide range of concentrations. Initially, more dilutions will be needed to produce a wide range of values for determining linearity or nonlinearity and to establish the widest possible linear range. Once limits of linearity have been established and it has been determined whether the method is linear or nonlinear, only the required number of verifiers (dilutions) are needed to revalidate the method regularly.

A verifier is needed at both the upper and the lower limits of the method's reportable range plus one or two intermediate levels (linear methods). These standard reverification concentrations and dilutions can be marked on the initial study with an asterisk (*) to simplify later studies.

* Diluent. We use deionized water for the quality control material concentrate and saline for platelets and for RBC and WBC concentrates. One text indicates that "the accuracy of the volumetric dilutions is very important, and serial dilutions are not recommended because of the propagation of errors through subsequent samples. Rather, each sample should be prepared by direct dilution from the original high sample or pool." (4) Our laboratory uses the dilutions, samples, and diluent amounts indicated in Table I.

For some analytes, it may be necessary to use other dilutions to obtain the highest possible level of verified linearity, especially if the original or undiluted high sample is above the limits of linearity. The dilutions we use, shown in the column headed "Dilution" in Figure II, are only a suggestion; any that cover a wide range would be appropriate. After the dilutions have been prepared, assay the replicates during a single run or in closely grouped runs.

In the linearity verification form we use (Figures II and IV), the two colums headed "Recovered" list the values obtained as replicates and the mean of each set. Although the anticipated value for the undiluted specimen should be calculable by multiplying the mean of the routine QC value by five, matrix- and reconstitution-related factors may make this method inaccurate.

The column headed "Calculated" lists estimated target values, which are determined as a mean of the calculated target values. Dilutions are usually expressed as a ratio, such as 1:10--one part of the original solution diluted with 10 parts of diluent, for a total of 11 parts.

To calculate target values, multiply the mean of replicates by the total number of parts (in the 1:10 dilution, 11). In a 3:1 dilution, the calculated value is 1.33 (4 divided by 3) multiplied by the replicate mean. Calculations used for each level (dilution) are presented in the box in the top right corner of Figure II.

List these values under "Calculated." The value for Level 6, included to obtain analyte concentration of the diluent, is not used in any further calculations if it is zero or near zero. If it is higher, consult EP6-P for a discussion of how to calculate the target value.

If the target values that have been calculated for each level are reasonably comparable with each other, then the mean of calculated values is used as the target value for Level 1. If they are not reasonably comparable, however, skewedness will prevent the mean of the calculated values from being able to be used as a target value.

To compute target values for all dilutions, divide the mean of calculated values by the total parts of each dilution. For example, in a dilution of 1:10, the mean calculated value (or the Level 1 target value) is divided by 11 to achieve Level 5 target value. For a 3:1 dilution, the target value is divided by 4 (total number of parts) and then multiplied by 3 (the parts of concentrate). Equations for calculating the target value for each level are provided in Figure II.

* Graphing. Since linearity is defined as "the degree to which the plotted curve conforms to a straight line," [3] the next step is to plot the values on linear/linear (square) graph paper. A solid line representing perfect linearity is surrounded above and below by dashed lines representing variance, as seen in the graphs in Figures III and V.

In the examples shown, 10% was arbitrarily chosen as the variance for acceptability of recovered values. A 10% coefficient of variation is commonly accepted as the criterion for satisfactory method variability. Ronald H. Laessig, Ph.D., director of the Wisconsin State Laboratory of Hygiene, Madison, has suggested an admissible variance of 25%. Because the Federal agencies have not defined acceptable variability, each laboratory must determine its own level of acceptable tolerance.

The means of the recovered replicates (Y) are plotted against the target values (X) for each level. As long as the plotted values are within 10% variance (dashed lines), the method is considered linear. Special attention should be paid to the plots to be sure there is no evidence of a nonlinear relationship. For further assurance, a linear regression calculation is used to obtain a value for the slope and intercept of the actual line produced.

* Without a graph. The 10% limits of acceptability can be calculated on the worksheet and not graphed. To do this, multiply the target value for each level by 0.9 for the lower limit (90%) and by 1.1 for the upper limit (110%). If the mean of the replicates for each level then falls within acceptable limits, the recovered result will be found to fall within 10% of the target value.

* Records. Worksheets and graphs can be conveniently stored in a three-ring binder for review by laboratorians and inspectors. The laboratory might select two months of each year--January and July, for example--on which to reconfirm the linearity of appropriate methods.

The methodology described in this article can be included in the initial verification of virtually any new procedure requiring quantitative analysis. Laboratorians must document all the methodologies they use and the conclusions they reach so that others can infer how the information was derived.

Oversight of clinical laboratories by the Federal government will surely continue to intensify. Laboratory managers and supervisors who devise creative solutions and adaptations are likely to achieve the best results. If laboratorians do the early work and develop our own provable standards, we will create the reference points for inspectors who visit us.

[1] Federal Register, p. 9596, vol. 55, no. 50, March 14, 1990.

[2] Tietz, N.W. "Fundamentals of Clinical Chemistry," pp. 105-107. Philadelphia, W.B. Saunders, 1976.

[3] National Committee for Clinical Laboratory Standards. "Evaluation of the Linearity of Quantitative Analytical Methods" (EP6-P), pp. ix, 513, 515-516, vol. 6, no. 18. Villanova, Pa., NCCLS, 1986.

[4] Kaplan, L.A., and Pesce, A.J. "Clinical Chemistry: Theory, Analysis, and Correlation," p. 345. St. Louis, C.V. Mosby, 1984.

General references:

Broddle, R.O. Determining linearity on a micro-computer (Computer Dialog). MLO 19(10): 91-92, October 1987.

Farnham, R. Computer graphs clarify linear regression modules. MLO 23(3): 56-63, March 1991.

Farnham, R. Programming spreadsheet graphics on a PC (Computer Dialog). MLO 23(3): 67-68, March 1991.

Ulstein, H. Impress your inspectors with linearity graphs (Computer Dialog). MLO 22(3): 63-66, March 1990.

The author is administrative director of laboratory services at Baptist Medical Center, Kansas City, Mo.

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Author: | Hunter, Lynda |
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Publication: | Medical Laboratory Observer |

Date: | Jun 1, 1991 |

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