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The Linearity Story

Validation Manager offers a wide set of tools for validations. In November, we released a study for evaluating the linear range of a quantitative method.

Why is this so cool?

Typically, when you use a quantitative method to obtain knowledge about some analyte concentration in a sample, the signal of the detection instrument is converted to concentration values with a linear function, but the detector response is not perfectly linear compared to true concentration levels. There is a certain concentration interval in which the response is very near to linear, but outside this interval the values do not give reliable information about concentration levels.

A graph visualizing detector signal and linear rangeLinear range of a method means the concentration interval in which the quantitative values provided by the method are reliable. Values outside this interval may give information on whether the concentration is above or below the linear range, but the exact values do not give relevant information about analyte concentration in the sample.

This is why it’s important to make sure that the method is linear within the used measurement range.

How are we doing it?

Validation Manager uses CLSI EP06-A approach (originally proposed by Kroll et al.) for assessing linearity. A nonlinear polynomial is fitted to the data to examine if it describes the results better than a linear function. Statistical significance of each nonlinear coefficient is estimated to find if the nonlinearity of the data is within the goals. Since poor precision hinders evaluating linearity, replicate measurements are used to check for poor repeatability.

How to conduct the study?

To conduct a linearity study, your laboratory should set goals for repeatability and nonlinearity of the methods to be validated. This is done separately for each studied analyte. A statistical minimum for the study requires using five concentration levels with two replicates of each concentration, and this is also the minimum setup for verifying the linear range of a method. To establish the linear range of a new method more concentrations are needed, and it may be beneficial to have more replicates as well. Even if you decide to be really precise in establishing linearity, the amount of measurements needed is quite moderate, as CLSI suggests up to eleven concentrations with at most four replicates.

The concentration levels should be designed to include claimed minimum and maximum concentration and medical decision limits. It is recommended that the sample concentrations are equally distant from each other, but this is not required. If the concentrations are unknown, linearity can be studied by making dilutions of a sample to obtain a dilution series where sample concentrations are known relative to each other. Validation Manager offers a simple design tool for creating the dilution scheme.

Ideally, all results should be collected during one day.

When analyzing results in Validation Manager, first evaluate replicates visually. If one replicate is a clear statistical outlier, it can be excluded. If there seems to be more outliers, there is reason to doubt the testing systems performance.

After checking the replicates, evaluate the result vs concentration plot visually to find obvious nonlinearity and to decide if the range should be narrowed or expanded. If this is not enough to make the results linear, there is a problem with the method or the measurement setup that should be corrected and then the measurements should be repeated.

The method is found linear if both nonlinearity and repeatability are within the set goals. If nonlinearity exceeds the goal, you should investigate the reason to remove the problem and then rerun the experiment. If nonlinearity only exceeds the goal at either end of the measuring range, linear range can be reduced by excluding that concentration. Calculating linearity requires at least five concentrations to be used in analysis, so if the number of concentrations falls below, the study should be redesigned and measurements conducted again.