Inferring trueness from linearity – 2. Approach: Recovery

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).