Accuracy is a critical parameter in method validation as it confirms the suitability of the method and ensures accurate quantification of the analytes in the sample.
True positive and true negative is the observation that is correctly predicted and therefore shown in green. We want to minimize false positive and false negative, so they are shown in red. Confused already! Let’s deconstruct each term.
Figure 1
For any fellow chemist the Christmas happens when green dominates the red. Partly, this means less investigations are required. Although, these trues are good, however, they can be misleading when evaluated in isolation. So, let’s heed on the words of Socrates and start by understanding what each term means, how they’re generated.
Figure 2
True positive – these are correctly estimated positive values which means that the theoretical and the found concentration are within the acceptance criteria of less than or equal to 2.0%.
Example: if the theoretical spike input is 649.2 mcg/mL and the found concentration came out to be 649.7 mcg/mL
% Recovery = (649.7/649.2) * 100% = 100.07%
True Negative – these are correctly predicted negative values. The sample contains in correct amount of the analyte.
False Positives – due interference that enhances the signal or lack of selectivity.
False Negatives – due to interference that hinders the signal.
When we think of a one performance metric for evaluating the capability of the method, often we optimize for the true positive as a measuring while we’re assaying a compound.
Accuracy as per ICH, is the ratio of the found value to the theoretical value. But how close the measured value to the true value be in reality?
As per ICH guidelines on the validation of analytical procedures accuracy and trueness can be used synonymously. In fact, trueness is the closeness of the agreement between the average value obtained from a large cluster of test results and the accepted value.
Accuracy = Reference value – Experimental value
In contrast, accuracy is the least amount of error rendered in an individual result. Therefore, accuracy is the summation of the following equation:
Accuracy = Trueness + Precision + Linearity + Selectivity
Consequently, when performing method validation, the accuracy is determined for each individual test result. However, the overall reporting as a mean, this value reflects the trueness of the method.In the confrontation between accuracy and precision the table below demonstrates the differences.
Figure 3
In the first row, the pattern of numbers is disproportionally spaced out and away from the mean. The precision is low which is reflected in a high %CV as numbers exhibits are variation and the trueness is low because the numbers are not close to the target mean.
In the second row, the pattern is relatively in proximity but away from the target mean. The precision is high and reflected with low %CV.
In the third row, the pattern of numbers is distant from each other but revolving around the target mean. The trueness is improved as the numbers are clustered around the target mean.
In the fourth row, the pattern of numbers is proportionally close to each other and clustered around the target mean. The precision is high as the numbers are clustered proximally and represented by a low %CV and the trueness is high as the numbers are around the target mean.
As we start performing accuracy study for a specific product the estimated result may be within the range but then it may fluctuate as the chosen concentration of the sample changes. The impact of concentration of the sample on the closeness of the results to the true value is due to bias.
Trueness of the method is quantitatively expressed as bias, in which bias is defined as the estimate of the systematic error. The bias function:
B (X,Y,Z) = (aka bias is a function of X,Y, and Z)
X = bias due to matrix effect (i.e. ionization suppression / enhancement)
Y = bias due to purity of the standard, calibration of the volumetric glassware
Z = bias due to analyte loss during sample preparation, or stability of the analyte in the sample solution
Figure 4
As evident from the above picture the maximum possible accuracy can be achieved by minimizing the bias.
Figure 5
A) Comparison to standard
The most straightforward practice when assessing accuracy of the method is to use a certified reference material (CRM) or (SRM) that is as close as
possible to the matrix of interest if available and prepare the certified material in triplicates at the vicinity of low, middle, and high concentrations
of the linearity.
Figure 6
The following example shows you how to use standard reference material to determine accuracy.
Figure 7
This approach is commonly preferred for pure drug substance (DS), where the analyte is largely assayed a certified standard such as NIST or CRM can be sourced. However, this approach is not necessarily instrumental with complex sample matrices such as botanicals, multivitamin products, new drug candidates, biological fluids, etc.
Conversely, if the standard is not widely available a special lot of the material can be used as a reference standard. But how can one qualify the lot?
It is paramount to ensure a highly purified and characterized material to assure authenticity as a standard.
Figure 8
B) Analyte Recovery
Another way of assessing the method’s accuracy of is to check the capability of the method to separate and quantify the analyte agnostically i.e., without any impact from the sample matrix as that could lead to false positive or false negative results. This can be done through measuring the analyte recovery.
This approach is highly instrumental when the subjected material is in complex from such as multivitamin finished product that contain many other ingredients.
To study the effect of the sample matrix on the compound of interest you spike a placebo/blank matrix with a pure standard of known concentration at the beginning of the sample preparation at 50 – 150% of the level expected for the analyte in triplicates. The determination of the concentration of the spiked amount has an acceptance recovery between 98.0 – 102.0%.
To better understand the & recovery lets use the following example of assaying of sodium (Na) by ICP-OES.
Figure 8
After running the test solutions at each level in triplicate. We can then use the following formula to calculate the accuracy as the % recovery.
C) Standard Addition Method
The third way of determining the accuracy of the method is by comparing the results to the standard addition method.
What is the standard addition method?
Every study sample is divided into aliquots of equal volumes, and the aliquots are spiked with known and varying amounts of the analyte to build the calibration curve.
How the sample calculation is calculated?
It is the negative x-intercept of the calibration line.
What are the advantages of method of standard addition?
This method is very accurate because it allows direct quantitation of endogenous analytes without manual subtraction of background peak areas.
What are the disadvantages?
It requires a large amount of sample and it could be time consuming and labor intensive.
The following example shows you how to use standard addition to determine accuracy.
Figure 9
Accuracy is a critical parameter in method validation as it confirms the suitability of the method and ensures accurate quantification of the analytes in the sample.
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