3.4. Validation protocol for a calibration line

To use the logit regression correctly, the test must be validated for the measurement range LLOQ (lowest dose) - ULOQ (highest dose) where the logit regression is applied.

The LLOD is determined by measuring multiple blanks.

It is important that the calibration line is homoscedastic (homogeneity of variance) throughout the measurement range. This avoids test result from having a different reproducibility per dose c.q. dilution.

If the measuring range is too large, the variation at the ends thereof will be unacceptably greater than results obtained from the middle of the measuring range.

Homoscedasticity determines the measuring area and not the steepness or how flat the line is plotted in a graph at the ends of the chosen measuring area. Hence, it is essential to first verify the reproducibility at the center and edges of the measurement area prior to commencing the actual validation process.

Once the LLOQ and ULOQ have been established, the actual validation can begin.

The logit - log transformed measurement area is a straight line. This is plotted in the top graph in the Logit worksheet.

The linearity of the logit - log measurement area of the calibration line is monitored by the correlation.

The results obtained from the chosen measuring range must behave linearly with respect to the dose.

In essence, the outcome, once adjusted for dilution, should remain consistent across all responses, from the lowest to the highest, throughout the entire range of measurement. This principle also extends to any pre-dilutions conducted. Such consistency is ascertained during the recovery tests.

Validation protocol of the calibration line. Before a test can be validated, it must first be determined whether the measuring range of the calibration line used in this test is appropriate. Before any validation starts, first determine the reproducibility of the measurement range. Establish a requirement from the beforehand. For an ELISA, an inter-assay coefficient of variation of <10% or <15% for the reproducibility of the calculated results measured at the lowest, halfway and at the highest response of the calibration line is achievable.

Reproducibility The reproducibility of the measuring range must be equal to or better than a predefined requirement. Calculate the reproducibility (interassay variation coefficient) of the test by measuring samples with a low, medium and high concentration in at least 5 independently performed tests.

LLOD The LLOD is the lowest concentration that can still be reported with some reliability as being non-zero. The reliability of this result is determined by measuring several blanks at different times.

Measure ten or more blanks together with a calibration line and a control sample. Calculate the average blank response + n * the standard deviation of the blank response. (n is explained further on in the text)

To do this, enter the calibration curve and this response with dilution 1 in the logit regression.

Enable “blank - highest dose extrapolation” in the logit calculation sheet.

Calculate the concentration of the value average + n * standard deviation. This is the first LLOQ value. Repeat the test four more times and calculate the average LLOQ with the standard deviation over these five values. The value for n depends on the probability that a sample without analyte can give a value above the LLOD. With n = 2 the chance is 5%, with n = 3 this chance of a false positive result drops to 1% and with n = 6 the chance of this is less than 1 in a million.

The choice of n depends on the purpose of the test and how it is performed.

If the test is stressed to measure as low as possible, it must be prevented that at a high dilution a sample with a low concentration nevertheless gives a response that falls in the calibration line. If this result is then multiplied by the dilution of, say, 10,000, the result is a normal concentration. If many low concentrations have to be measured with the test, the factor n is set to 3 or even to 2, with the risk that a false positive result will be reported from time to time.

The average + 3 * standard deviation is a common limit.

LLOQ The lowest concentration of the calibration line must be higher than the LLOD. This is the lowest concentration of the test that is reported if undiluted measurement is allowed. If the minimum dilution of the test is 1:10, the LLOD becomes 10 times the dose or concentration of the lowest point of the calibration line.

Linearity of the test results Linearity of the results of a calibration line can be validated in various ways.

A simple method is to calculate the average result per doses may over 5 to 7l independent tests and demand that the averaged deviation from the nominal value is smaller than, say, 5%. This value is chosen arbitrarily but 5% is a fair value to use as a starting point.

Example: Deviation of the calculated value from the nominal value of a calibration point per dilution (duplicate measurement per dilution) of 7 independently performed tests.

An alternative method is described in NCCLS document EP6-A.

In this document the difference is calculated of a linear regression through the calculated results and the nominal concentration of that dose and the most suitable 2nd-degree and 3rd-degree polynomial regression through these points. The idea is that if a quadratic or cubic polynomial fits better that a linear regression the results of the logit regression line are not linear.

A simplified implementation of this is described below and can be performed with Microsoft Excel.

For the method described in EP6-A, the software must calculate a standard error (SE) of the calculated coefficients in order to determine the reliability of the polynomial parameters. In our example we use the correlation for this. It is advisable to consult the EP6-a document before applying this simple Excel method. This example is only made to get more insight in the performance of the calibration line.

Dilute a series of concentrations separated at a fixed distance from each other (for example (100%, 90%, 80%, 70% 60% etc.) and measure this independently at least five times.

Type in Excel the expected nominal activities underneath each other and in the column next to these the measured results. Now series in two columns is created with the five experiments below each other Make an XY (scatter) chart with the expected activity on the X-axis and the measured activity on the Y-axis

Calculate the linear, second and third degree polynomial parameters and the correlation in Excel using a trend line.

The linear regression is a straight line. This is the calculation for the most appropriate straight line whether the method is linear or not. The second order regression describes a curved line and the third order regression an S-shaped, sigmoid, curve.

Calculate the theoretical activity based on the calculated parameters for the linear regression and the polynomial regression with the lowest correlation per activity. Y = (aX3 +)optional bX2 + cX + d. The parameters, a to d, are written in the formulas in the graph. X is the expected concentration. The expected concentration Y after regression then follows from the calculation. Calculate the concentration based on these parameters for linear regression and polynomial regression, with the highest correlation per activity. Calculate the percentage difference between the theoretical and expected activity. With a "difference plot" the differences can be made more transparent.

The results dilute parabolic

A sigmoid curve often due a too long calibration line and therefor a poor logit fit.

Accuracy A test result is worthless if the accuracy is not correct.

• Measure a primal standard of the test as sample to prove that measurements accurate.
• Measure the primal standard of the test as a sample in 6 separate measurements and calculate the mean and variation coefficient of the result.
• Reject the test if the value deviates more than 4% from the nominal value of the standard or if the coefficient of variation of the average is greater than 8%.
• Repeat this accuracy test once the requirements are not met.

This is the minimum protocol to validate logit regression in an ELISA. In addition, matrices in which measurements are made, disturbing elements in the samples, robustness, normal values, carry-over and sample stability are important elements in the validation.

Recovery The recovery of the calculated value in relation to the nominal value of the dose is ideally 100%. Mix several known amounts of the standard with samples that are normally measured to obtain a proper matrix. Combine this test with the accuracy test. State a requirement in advance and check whether it is being met.