QNT Linearity

QNT Linearity

Quantitative Linearity (LIN)

Overview

Other Names - Linearity, Lin, Reportable Range Experiment, Analytical Range Experiment, Range Verification, Working Range Experiment

Linearity experiments assess a method's ability to accurately measure analyte concentrations across a specified range, ensuring consistent precision and trueness throughout.

Definitions

🗣️
**Cualia Support Docs Definitions (Public)**

Name
Definition
Deming Variance Ratio (vr)

Quantifies the agreement between two measurement methods, considering measurement errors. A maximum allowable difference from 1 is standard. VR=Var(X)+Var(Y)Var(X−Y)VR = \frac{Var(X) + Var(Y)}{Var(X - Y)} Var(X)Var(X) = Variance of X Var(Y)Var(Y) = Variance of Y

Eligible (Sample and Results)

Samples that provide the necessary information for statistical calculations to be performed. Usually this is possessing both an actual and expected result.

Experiment

A sampling of results that are statistically analyzed and interpreted in the evaluation of testing performance.

Level(s)

A reference Level within a range to determine performance around that value.

Linearity (Lin) Experiment

Linearity is an MV experiment to establish the correlation between Reference and Actual Results

Method Validation

A systematic process to evaluate whether the performance of a medical Test meets quality goals to be used for medical testing.

Method Verification

A systematic process to evaluate whether the performance of a medical Test meets quality goals set by a validation. Performance evaluations may usually be found in a manufacturer insert.

Passing Bablok Correlation Coefficient (r)

Measures the strength and direction of the linear relationship between two measurement methods using Passing Bablok regression. A minimum absolute value of 0.95 is standard for strong correlation. r=Cov(X,Y)Var(X)+Var(Y)r = \frac{Cov(X, Y)}{Var(X) + Var(Y)} Cov(X,Y)Cov(X, Y) = Covariance of X and Y Var(X)Var(X) = Variance of X Var(Y)Var(Y) = Variance of Y

Pearson Correlation Coefficient (r)

Measures the strength and direction of a linear relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation. r=Cov(X,Y)σXσYr = \frac{Cov(X, Y)}{\sigma_X \sigma_Y} Cov(X,Y)Cov(X, Y) = Covariance of X and Y σXσ_X = Standard Deviation of X σYσ_Y = Standard Deviation of Y Cov(X,Y)=1n−1∑i=1n(xi−xˉ)(yi−yˉ)Cov(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y}) nn = Number of data points xix_i = Individual data point of variable XyiXy_i = Individual data point of variable Y xˉ\bar{x} = Mean of variable X yˉ\bar{y} = Mean of variable Y

R-squared (R²) Coefficient

R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, with higher values indicating a better fit. Usually >0.95 is considered statistical correlation. R2=1−∑i=1n(yi−y^i)2∑i=1n(yi−yˉ)2R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}i)^2}{\sum{i=1}^{n} (y_i - \bar{y})^2} R2R^2 = Coefficient of determination yiy_i = Observed value y^i\hat{y}_i= Predicted value yˉ\bar{y} = Mean of observed values nn = Sample size

Range Verified

Range of values from lowest to highest that was measured within a group of samples.

Replicate

Multiple tests on the same sample to assess precision and repeatability, conducted within a run or across multiple runs.

Reportable Range

Analytical range at which a method's results is verified. A Linearity experiment is used to determine this range. Reportable range means the span of test result values over which the laboratory can establish or verify the accuracy of the instrument or test system measurements response.

Result(s)

A value or determination collected by measurement or calculation.

Sample Correlation Coefficient (R)

The sample correlation coefficient (R) quantifies the strength and direction of the linear relationship between two variables based on sample data. A min value of 0.95 is standard. R=r2R = \sqrt{r^2} r2r^2 = Coefficient of Determination

Sample(s)

Individual specimens collected for testing representing the source. In MV experiments with Runs, this can refer to to the number of concentration levels used.

Slope

A statistically calculated line in the notation of Y = mx + b that represents the linear relationship between two datasets. y=mx+by = mx + b m=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} b=∑y−m∑xnb = \frac{\sum y - m \sum x}{n} m: The slope of the line, which indicates how much y changes for a unit change in x. b: The y-intercept of the line, which is the value of y when x=0. n: The number of data points or observations in the dataset. x: The independent variable values in the dataset. y: The dependent variable values in the dataset.

Spearman Rank Correlation Coefficient (p)

Measures the strength and direction of a monotonic relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation. p=1−6∑di2n(n2−1)p = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} did_i= Difference between ranks of X and Y nn = Number of pairs

Test/Analytical Measurement Range (AMR)

Range between the lowest and highest concentrations of an analyte that a test can accurately measure without dilution or concentration.

What is Linearity?

Linearity experiments validate a method's ability to accurately and consistently measure analyte concentrations across its specified analytical range, referred to as the reportable range or analytical measurement range (AMR). These experiments apply a calibration equation to determine how well the method maintains accuracy and precision at various concentration levels, confirming the instrument's performance throughout the designated range.

The experiments also assess the method's overall trueness across the AMR by examining how closely the test results match the expected concentrations. This comprehensive testing ensures that the method meets its performance criteria and can be reliably used for precise analytical measurements in scientific and clinical applications.

Experiment Settings and Acceptance Criterias

1. Define Acceptance Criterias

Levels: The number of levels throughout a range that require testing.

Replicates per Level: Number of replicates to be performed at each level or concentration.

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Regression Type - Calculates a correlation value to assess the relationship between two data sets. This value can be set to be greater than or less than a cutoff value in order to determine experiment passing.

Range Extension (%): An added range to for the lowest and highest actual results that will be appended to fulfill the test range. This is for when a test range has a range of 5 to 40, it is very difficult to achieve sample testing at exact 5 and 40.

Example: for a test range of 5 to 40 with a 5% range extension, if the highest measure result is 38 then 1.9 (38 x 0.05) will be contributed to the ranges determined by actual testing but will not exceed the actual test range. For example low and high results of 6 and 36 will achieve a final verified test range of 5 to 37.8.

Sample Selection

Choose a representative set samples that reflect the diversity and variability expected in routine testing. Ensure samples cover the full range of analyte concentrations and conditions relevant to the test.

It is recommended that most of the samples come from the true population. Some manufacturer products such as commercial kits and controls may be used. These may often be necessary for particularly difficult to obtain concentrations and conditions.

Testing Samples

Measure each sample on a reference method (expected) and on your new instrumentation (actual). Record the results, label and source either in the Cualia app or on your own platform. Include the label and the source.

Use the Cualia MV App

Make sure the data is entered into the experiment with the right acceptance criterias.

Preparation Checklist

Analyzer is set up in Cualia → AnalyzersAnalyzers
Tests are set up in the analyzer → Quantitative TestsQuantitative Tests and Qualitative TestsQualitative Tests
The initial MV details are prepared → MV Overview and DetailsMV Overview and Details

General Experiment Recommendations: Dos and Don’ts

❌
Don’t: Enter private patient information, identifiers or data into Cualia.
❌
Don’t: Rush Through an MV: Sometimes an MV can take months waiting for the right samples to come through. Based on our experience, the most time consuming part of an MV is finding out after days after measurements and painstakingly entering in the data to find that something was done incorrectly and the cycle must be repeated.
❌
Don’t: Rely too much on controls, calibrators and spiked samples: The goal of an MV is not to pass inspection but to truly evaluate that your instrumentation’s performance is up to clinical standards. Using samples that reflect the lab’s testing population will offer the best insights into the evaluation
✅
Do: Prepare your Cualia MV before taking measurements: Having a blueprint of work provides a smooth experience.
✅
Do: Enter Results Directly into Cualia: Taking down results to enter them into a spreadsheet just to copy them into Cualia will increase sources of error. When a result is returned, enter it directly into Cualia. You will be able to immediately have feedback into the success state of the experiment, identifying any missing variables that will hinder your MV.
✅
Do: Ask for clarification. Talk to regulators, auditor, consultants and don’t hesitate to reach out to support@cualia.io with questions.

Data Table

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Data Table Columns

Level | Read Only - The specific concentration point within the group of levels.

Reference | Number only - The true value as measured from the reference method.

Replicate(R) 1 to X | Number only - The measured value of the replicate. A color may indicate whether the result is within agreeable parameters.

Calculations

Slope

Slope: The slope equation using the Passing Bablok assesses the relationship between measured and reference values, providing a robust estimate of how measured values change relative to reference values.

y=mx+by = mx + bm=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}b=∑y−m∑xnb = \frac{\sum y - m \sum x}{n}

m: The slope of the line, which indicates how much y changes for a unit change in x.

b: The y-intercept of the line, which is the value of y when x=0.

n: The number of data points or observations in the dataset.

x: The independent variable values in the dataset.

y: The dependent variable values in the dataset.

R-squared Coefficient of Determination (R²)

R-squared Coefficient of Determination (R²): R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, with higher values indicating a better fit. Usually >0.95 is considered statistical correlation.

R2=1−∑i=1n(yi−y^i)2∑i=1n(yi−yˉ)2R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}i)^2}{\sum{i=1}^{n} (y_i - \bar{y})^2}

R2R^2 = Coefficient of determination yiy_i = Observed value y^i\hat{y}_i= Predicted value yˉ\bar{y} = Mean of observed values nn = Sample size

Spearman Rank Correlation Coefficient (p)

Spearman Rank Correlation Coefficient (p): Measures the strength and direction of a monotonic relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation.

p=1−6∑di2n(n2−1)p = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}

did_i= Difference between ranks of X and Y nn = Number of pairs

Passing Bablok Correlation Coefficient (r)

Passing Bablok Correlation Coefficient (r): Measures the strength and direction of the linear relationship between two measurement methods using Passing Bablok regression. A minimum absolute value of 0.95 is standard for strong correlation.

r=Cov(X,Y)Var(X)+Var(Y)r = \frac{Cov(X, Y)}{Var(X) + Var(Y)}

Cov(X,Y)Cov(X, Y) = Covariance of X and Y

Var(X)Var(X) = Variance of X

Var(Y)Var(Y) = Variance of Y

Spearman Rank Correlation Coefficient (p)

Spearman Rank Correlation Coefficient (p): Measures the strength and direction of a monotonic relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation.

p=1−6∑di2n(n2−1)p = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}

did_i= Difference between ranks of X and Y nn = Number of pairs

Deming Variance Ratio (vr)

Deming Variance Ratio (vr): Quantifies the agreement between two measurement methods, considering measurement errors. A maximum allowable difference from 1 is standard.

VR=Var(X)+Var(Y)Var(X−Y)VR = \frac{Var(X) + Var(Y)}{Var(X - Y)}

Var(X)Var(X) = Variance of X Var(Y)Var(Y) = Variance of Y

Sample Correlation Coefficient (R)

Sample Correlation Coefficient (R): The sample correlation coefficient (R) quantifies the strength and direction of the linear relationship between two variables based on sample data. A min value of 0.95 is standard.

R=r2R = \sqrt{r^2}

r2r^2 = Coefficient of Determination

Pearson Correlation Coefficient (r)

Pearson Correlation Coefficient (r): Measures the strength and direction of a linear relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation.

r=Cov(X,Y)σXσYr = \frac{Cov(X, Y)}{\sigma_X \sigma_Y}

Cov(X,Y)Cov(X, Y) = Covariance of X and Y σXσ_X = Standard Deviation of X σYσ_Y = Standard Deviation of Y

Cov(X,Y)=1n−1∑i=1n(xi−xˉ)(yi−yˉ)Cov(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})

nn = Number of data points xix_i = Individual data point of variable XyiXy_i = Individual data point of variable Y xˉ\bar{x} = Mean of variable X yˉ\bar{y} = Mean of variable Y

Results

🗣️
**Cualia Support Docs Definitions (Public)**

Name
Definition
Deming Variance Ratio (vr)

Quantifies the agreement between two measurement methods, considering measurement errors. A maximum allowable difference from 1 is standard. VR=Var(X)+Var(Y)Var(X−Y)VR = \frac{Var(X) + Var(Y)}{Var(X - Y)} Var(X)Var(X) = Variance of X Var(Y)Var(Y) = Variance of Y

Level(s)

A reference Level within a range to determine performance around that value.

Passing Bablok Correlation Coefficient (r)

Measures the strength and direction of the linear relationship between two measurement methods using Passing Bablok regression. A minimum absolute value of 0.95 is standard for strong correlation. r=Cov(X,Y)Var(X)+Var(Y)r = \frac{Cov(X, Y)}{Var(X) + Var(Y)} Cov(X,Y)Cov(X, Y) = Covariance of X and Y Var(X)Var(X) = Variance of X Var(Y)Var(Y) = Variance of Y

Pearson Correlation Coefficient (r)

Measures the strength and direction of a linear relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation. r=Cov(X,Y)σXσYr = \frac{Cov(X, Y)}{\sigma_X \sigma_Y} Cov(X,Y)Cov(X, Y) = Covariance of X and Y σXσ_X = Standard Deviation of X σYσ_Y = Standard Deviation of Y Cov(X,Y)=1n−1∑i=1n(xi−xˉ)(yi−yˉ)Cov(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y}) nn = Number of data points xix_i = Individual data point of variable XyiXy_i = Individual data point of variable Y xˉ\bar{x} = Mean of variable X yˉ\bar{y} = Mean of variable Y

R-squared (R²) Coefficient

R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, with higher values indicating a better fit. Usually >0.95 is considered statistical correlation. R2=1−∑i=1n(yi−y^i)2∑i=1n(yi−yˉ)2R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}i)^2}{\sum{i=1}^{n} (y_i - \bar{y})^2} R2R^2 = Coefficient of determination yiy_i = Observed value y^i\hat{y}_i= Predicted value yˉ\bar{y} = Mean of observed values nn = Sample size

Range Verified

Range of values from lowest to highest that was measured within a group of samples.

Sample Correlation Coefficient (R)

The sample correlation coefficient (R) quantifies the strength and direction of the linear relationship between two variables based on sample data. A min value of 0.95 is standard. R=r2R = \sqrt{r^2} r2r^2 = Coefficient of Determination

Slope

A statistically calculated line in the notation of Y = mx + b that represents the linear relationship between two datasets. y=mx+by = mx + b m=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} b=∑y−m∑xnb = \frac{\sum y - m \sum x}{n} m: The slope of the line, which indicates how much y changes for a unit change in x. b: The y-intercept of the line, which is the value of y when x=0. n: The number of data points or observations in the dataset. x: The independent variable values in the dataset. y: The dependent variable values in the dataset.

Spearman Rank Correlation Coefficient (p)

Measures the strength and direction of a monotonic relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation. p=1−6∑di2n(n2−1)p = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} did_i= Difference between ranks of X and Y nn = Number of pairs

Test/Analytical Measurement Range (AMR)

Range between the lowest and highest concentrations of an analyte that a test can accurately measure without dilution or concentration.

Line Chart

The line chart plots the results in a line chart. The min and max ranges on the X and Y axis are from the Range Low and Range High (AMR) set within the Test Settings.

X-axis: Reference results

Y-axis: Actual results

Solid Black Line: Line of best fit

Blue Dots: Individual results

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Experiment Pass / Fail

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When the R-squared (R²) Coefficient value is greater than the Min. Coefficient R² value set in the acceptance criteria, the experiment will pass.

Slope

Slope - Slope equation calculated by Passing Bablok.

Sample Coefficient

Sample Coefficient - This value show the regression type set in the experiment settings. The value will be red or green depending on if the results satisfy the requirements.

Options: Deming Variance Ratio (vr), Passing Bablok Correlation Coefficient (r), Spearman Rank Correlation Coefficient (p), Sample , Correlation Coefficient (R), Pearson Correlation Coefficient (r) or R-squared (R²) Coefficient