Inferring trueness 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 trueness from linearity in method validations by applying normalization. This can be used to determine trueness 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 trueness 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 trueness’ 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 trueness 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).

Tags: method validation purity linear regression linearity recovery trueness

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