# Inferring accuracy from linearity – 2. Approach: Recovery

Written by Dr. Janet Thode on . Posted in Method validation

In our last blog post we had a look on the first approach to infer accuracy from linearity in method validations by applying normalization. This can be used to determine accuracy in case no alternative methods or impurities for spiking are available. Apart from normalization, another possibility to solve this problem exists, which will be highlighted today.

We stick to our example of the last time: a SE-HPLC method is used for purity determination. The impurities are given as the sum of minor peaks, while the main peak is our desired product. The approach to infer accuracy from linearity is allowed by the ICH Q2(1) validation guideline, when specificity (we suppose this again) and precision is given.

So we take the already known data set (5 concentrations for linearity, each with three independent replicates):

 Absolute peak area [µAU*s] Examination level (%) Sum of minor peaks Main peak 120 99104 15949990 96153 15988085 97723 15879248 110 89383 14567078 87474 14592610 88355 14558575 100 77587 13275901 76162 13264078 78209 13285496 90 65802 11513839 67811 11937356 68012 12037029 80 54208 10489899 55611 10594228 56819 10683872

and prepare graphs for linearity (for simplification we used the examination level in % instead of the actual product / impurity concentrations in mg/mL):

These figures will help us in determining the theoretical absolute peak areas using the respective regression line (y = m * x + n). Of course, in Excel we can also use the formulas INTERCEPT(known_y's; known_x's) for the y-intercept (n) and SLOPE(known_y's; known_x's) for the slope (m). Thus, our two regression lines consist of the following parameters:

 slope m y-intercept n Regression lineSum of minor peaks 1054.2 -28196 Regression lineMain peak 134429 -201743

By applying the examination levels as x-values to the regression line (for example, 1054.2 * 120 + (-28196) = 98312), we obtain the following data:

 Absolute peak area [µAU*s] Examination level (%) Sum of minor peaks Main peak 120 98312 15929731 110 87770 14585442 100 77227 13241152 90 66685 11896863 80 56143 10552573

We remember to compare measured values with theoretical values for accuracy’s determination. In doing that, we can check the "quality" of our measurements calculating recovery (= measured value / theoretical value * 100%). Recovery is telling us how close our measured values stick to the theoretical ones.

 Sum of minor peaks Main peak Examination level (%) Measured value Theoretical value Recovery [%] Measured value Theoretical value Recovery [%] 120 99104 98312 101 15949990 15929731 100 96153 98 15988085 100 97723 99 15879248 100 110 89383 87770 102 14567078 14585442 100 87474 100 14592610 100 88355 101 14558575 100 100 77587 77227 100 13275901 13241152 100 76162 99 13264078 100 78209 101 13285496 100 90 65802 66685 99 11513839 11896863 97 67811 102 11937356 100 68012 102 12037029 101 80 54208 56143 97 10489899 10552573 99 55611 99 10594228 100 56819 101 10683872 101

Looking at the recovery rates, we can see that all measured values correspond to almost 100% of the respective theoretical value. Excellent!

With appropriate scientific justification, it can be sufficient for accuracy in method validations to solely determine the recovery of the main peak (using absolute peaks areas). Additionally, for both parameters (sum of minor peaks and main peak) precision should be evaluated using relative peak areas (as shown last time).

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