Two methods of calculating the lower limit of quantification (LLOQ) disagree. Which, if either, is correct?
Recently, a reader e-mailed me with a problem he was having determining the lower limit of quantification (LLOQ) for his method,
which had a target LLOQ of 0.01 μg/mL for his analyte. He compared the LLOQ calculated using the International Committee on
Harmonization guidelines (ICH) (1) with replicate injections of a reference standard and found that the two differed by more
than an order of magnitude. He came to me to help him figure out what was wrong. The method was proprietary, and the reader
needed to stay anonymous, so I've disguised things a bit, but this case study helps us to better understand how to evaluate
a calibration curve.
The ICH (1) presents a formula to calculate what they call the quantitation limit (QL), but what most users call the limit
of quantification (LOQ) or LLOQ:
where σ is the standard deviation of the response (the standard error [SE]) and S is the slope of the calibration curve. This is calculated easily from the regression statistics generated in Excel or your
data system software. Let's see how this works.
Table I: Input data and error calculations
Table I includes the initial data from the calibration curve. The user injected eight concentrations of his analyte, ranging
from 0.01 to 1.0 μg/mL, generating the peak areas shown in the "Response" column of Table I. I used Excel's regression tool
to generate the regression statistics, part of which I've included in Table II. These include the coefficient of variation
2), the standard error of the curve (SE-curve), the y-intercept (intercept-coefficient), the standard error of the y-values (intercept-SE-y), and the slope of the curve (X variable). Calculated values for these variables are shown in the second two columns of Table II, headed "With 1.0 μg/mL."
Table II: Summary of Excel regression statistics
The reader used equation 1 with the standard error of the curve (SE-curve) and slope, and found that the LLOQ was predicted
to be ~0.15 μg/mL (summarized as the first entry of Table III). (Here I'll pause to remind you that I've rounded and truncated
numbers in the tables for ease of viewing; if you try to repeat my calculations, your results may differ slightly.) Yet, when
he injected n = 10 replicates of a 0.01 μg/mL solution, he found the percent relative standard deviation (%RSD) was 1.1% (last entry, Table
III), which he felt indicated the LLOQ was considerably lower than the 0.15-μg/mL prediction using the ICH technique. At this
point he contacted me.
Table III: Summary of LLOQ calculations