LOQ is smaller than lowest calibration point

[hyou0710]

Hello,

I have a question about LOQ determination.

Per ICH, I used 5 points to make a calibration curve (serial dilution). The analyte concentrations are 1, 2 ,4, 8, 16 ug/mL. Then, in order to determine the LOQ, I used 10 times of the residual standard deviation of this calibration curve (σ) to divide the slope: LOQ=10σ/slope. The result is around 1.4 ug/mL.

My question is: now I know my LOQ has exceeded my lowest point, can I still use my old calibration curve to calculate the sample's concentration? My concern is that the curve was made from some information that is not valid anymore (the peak area of my lowest calibration point, 1 ug/mL).

Do I have to re-run the calibration curve for my routine analysis?

Thank you so much!

[HPLC chemist]

Did you determine the results in triplicate, calculate the standard deviation, and the statistical LOQ?

[Himar]

I would say it depends on what type of standards your lab enforces. What was the typical concentration of your samples? If it was closer to the higher end of the curve, then it might be a non issue. Also, most data systems can recalculate a curve for you, allowing you to reprocess data in a relatively painless process.

[Peter Apps]

Hello,

I have a question about LOQ determination.

I used 5 points to make a calibration curve (serial dilution). The analyte concentrations are 1, 2 ,4, 8, 16 ug/mL. Then, in order to determine the LOQ, I used 10 times of the standard deviation of this calibration curve (σ) to divide the slope: LOQ=10σ/slope. The result is around 1.4 ug/mL.

My question is: now I know my LOQ has exceeded my lowest point, can I still use my old calibration curve to calculate the sample's concentration? My concern is that the curve was made from some information that is not valid anymore (the peak area of my lowest calibration point, 1 ug/mL).

Do I have to re-run the calibration curve for my routine analysis?

Thank you so much!

Welcome to the forum.

Serial dilution is not the best way to make a calibration series - it concentrates the points in the lower left corner of the plot, and makes the line look more linear than it rally is (serial dilution with 10 times dilution at each step is a favourite trick to inflate linearity - it effectively gives a three point line, no matter how many very dilute standards are crowded into the bottom corner.

Ten times the sd of the curve is very conservative - is it official guidance ?

That aside, you can still use the lowest point in your series because you did not measure its concentration by analysis, you know it in advance from the composition of the standard, and the variability in the peak area has already contributed to the uncertainty of the curve.

Peter

[lmh]

Yes, the method the original poster used is a standard method; it's described (far too briefly) in ICH Q2(R1)
http://www.ich.org/fileadmin/Public_Web ... deline.pdf

Caveat: I don't work in a regulated environment, so don't trust me. Yes, I think you can use the lowest point in your calibration curve during quantification. The reasons I believe it are:
(1) unless the absolute standard deviation of the lowest point (not relative standard deviation) is vastly greater than that of the nearby points, or it's mean (were you to measure it multiple times) is way off the linear trend of the line, then the lowest point only introduces error into the calibration curve in exactly the way the LOQ calculation expects. It contributes to the sigma value just like all the other points, so the statistical validity of the calibration curve is already based on this point, and your LOQ has already taken it into consideration.
(2) If the lowest point, were you to measure it multiple times, had a drastically different s.d. to the other points, or its mean were drastically away from the calibration curve, it would indicate that the basic assumptions behind the LOQ calculation are false. This is one of several good reasons for running this calibration point routinely. It's a control. What I mean is this: if the basic assumptions behind the LOQ are true, then it shouldn't make any statistically significant difference to the calibration curve or your data whether you include the lowest point or not.
additionally:
(3) You can't quantify below your LOQ, and it's bad practice to extrapolate off the ends of your calibration curve, so you can't quantify below the lowest point that you include. For this reason, if you insist on excluding any point below the LOQ, you've got the dilemma that you can't then measure at the LOQ (which by definition should be possible) unless you re-run all your standards and samples with a new standard exactly at the LOQ. But since the LOQ varies from day to day, the new standard might turn out to be just fractionally below the new LOQ, in which case you're back to square one.
(4) the SD of the curve may be different if measured a long way from the low end, and it's the SD at the low end that dictates the LOQ, so it's important you measure the SD close to the LOQ. The only sensible approach is therefore to include a range of calibration points above and just below the expected LOQ.

[Peter Apps]

I would say that the second paragraph of this from the link that lmh posted is the important part;

7.4 Recommended Data
The quantitation limit and the method used for determining the quantitation limit should be presented.

The limit should be subsequently validated by the analysis of a suitable number of samples known to be near or prepared at the quantitation limit.

My bold and underline.

Peter

[James_Ball]

I would say that the second paragraph of this from the link that lmh posted is the important part;

7.4 Recommended Data
The quantitation limit and the method used for determining the quantitation limit should be presented.

The limit should be subsequently validated by the analysis of a suitable number of samples known to be near or prepared at the quantitation limit.

My bold and underline.

Peter

This sounds similar to what the EPA is doing with new drinking water methods. You determine the Minimum Reporting Limit (similar to LOQ) then you make a calibration and the requirement is that one point must be at or below the MRL. The test to show that the lowest point is valid is that it must quantitate at +/- 50% of the true value when calculated against the calibration curve it is a part of. The MRL also has be be proven using seven replicate analysis at the MRL level then passed through statistical processing that gives a high and low variance limit that must fall in the 50-150% ranges. (the exact formula can be found in new methods such at EPA 525.3)

What the EPA is putting forth is that the lowest calibration point can be lower than the Quantitation Limit but must be close enough that it does not suffer from too much uncertainty, given by the 50% window for accuracy. This is being done to prevent laboratories from reporting unrealistically low Quantitation Limits.

[Steve Reimer]

From SW-846 method 8000D

The LLOQ is the lowest concentration at which the laboratory has demonstrated target
analytes can be reliably measured and reported with a certain degree of confidence, which must
be ≥ the lowest point in the calibration curve. The laboratory shall establish the LLOQ at
concentrations where both quantitative and qualitative requirements can consistently be met (see
Sections 9.7.3 and 11.6). The laboratory shall verify the LLOQ at least annually, and whenever
significant changes are made to the preparation and/or analytical procedure, to demonstrate
quantitation capability at lower analyte concentration levels. The verification is performed by the
extraction and/or analysis of an LCS (or matrix spike) at 0.5-2 times the established LLOQ.
Additional LLOQ verifications may be useful on a project-specific basis if a matrix is expected to
contain significant interferences at the LLOQ. The verification may be accomplished with either
clean control material (e.g., reagent water, solvent blank, Ottawa sand, diatomaceous earth) or a
representative sample matrix, free of target compounds. Optimally, the LLOQ should be less
than the desired decision level or regulatory action level based on the stated DQOs.

[hyou0710]

Sorry I was not clear enough, I have made the changes on my original post. I used residual standard deviation of the curve. I didn't run replicate injections for my lowest point.

Did you determine the results in triplicate, calculate the standard deviation, and the statistical LOQ?

[hyou0710]

Hello, I work in the dietary supplement industry. AOAC, USP, and FDA is the normal standard that we go for. We can dilute our sample to the concentration that we like. Yes, deleting the lowest point is an option. Thanks for the reminding!

I would say it depends on what type of standards your lab enforces. What was the typical concentration of your samples? If it was closer to the higher end of the curve, then it might be a non issue. Also, most data systems can recalculate a curve for you, allowing you to reprocess data in a relatively painless process.

[hyou0710]

Thank you, Peter. This is an awesome forum. I love it!

Thank you for pointing out the serial dilution issue. Most organization didn't specify how they want the calibration curve to be designed. In your opinion, does equal space design work better (e.g. 1, 4, 7, 10, 13, 16 ug/mL, come from the same stock solution)?

Yes. I used ICH guideline in this case.

Welcome to the forum.

Serial dilution is not the best way to make a calibration series - it concentrates the points in the lower left corner of the plot, and makes the line look more linear than it rally is (serial dilution with 10 times dilution at each step is a favourite trick to inflate linearity - it effectively gives a three point line, no matter how many very dilute standards are crowded into the bottom corner.

Ten times the sd of the curve is very conservative - is it official guidance ?

That aside, you can still use the lowest point in your series because you did not measure its concentration by analysis, you know it in advance from the composition of the standard, and the variability in the peak area has already contributed to the uncertainty of the curve.

Peter

[hyou0710]

Thanks a lot for the detailed reply. In your opinion, is it a good practice for me to use 3 points from my original curve (1,2,4 ug/mL) to calculate LOQ (still use residual standard deviation and slope), and then use my full 5 point curve to do the regular analysis?

Yes, the method the original poster used is a standard method; it's described (far too briefly) in ICH Q2(R1)
http://www.ich.org/fileadmin/Public_Web ... deline.pdf

Caveat: I don't work in a regulated environment, so don't trust me. Yes, I think you can use the lowest point in your calibration curve during quantification. The reasons I believe it are:
(1) unless the absolute standard deviation of the lowest point (not relative standard deviation) is vastly greater than that of the nearby points, or it's mean (were you to measure it multiple times) is way off the linear trend of the line, then the lowest point only introduces error into the calibration curve in exactly the way the LOQ calculation expects. It contributes to the sigma value just like all the other points, so the statistical validity of the calibration curve is already based on this point, and your LOQ has already taken it into consideration.
(2) If the lowest point, were you to measure it multiple times, had a drastically different s.d. to the other points, or its mean were drastically away from the calibration curve, it would indicate that the basic assumptions behind the LOQ calculation are false. This is one of several good reasons for running this calibration point routinely. It's a control. What I mean is this: if the basic assumptions behind the LOQ are true, then it shouldn't make any statistically significant difference to the calibration curve or your data whether you include the lowest point or not.
additionally:
(3) You can't quantify below your LOQ, and it's bad practice to extrapolate off the ends of your calibration curve, so you can't quantify below the lowest point that you include. For this reason, if you insist on excluding any point below the LOQ, you've got the dilemma that you can't then measure at the LOQ (which by definition should be possible) unless you re-run all your standards and samples with a new standard exactly at the LOQ. But since the LOQ varies from day to day, the new standard might turn out to be just fractionally below the new LOQ, in which case you're back to square one.
(4) the SD of the curve may be different if measured a long way from the low end, and it's the SD at the low end that dictates the LOQ, so it's important you measure the SD close to the LOQ. The only sensible approach is therefore to include a range of calibration points above and just below the expected LOQ.

[hyou0710]

Thanks for pointing it out. ICH didn't say replicate injection of the same level solution. Do you believe it is a good practice to just use 3 points of my original curve (say 1, 2, 4 ug/mL) to both make the LOQ and validate the LOQ? Can these point be considered as "known to be near or prepared at the quantitation limit."

If that works, it seems we don't need to do extra work.

I would say that the second paragraph of this from the link that lmh posted is the important part;

7.4 Recommended Data
The quantitation limit and the method used for determining the quantitation limit should be presented.

The limit should be subsequently validated by the analysis of a suitable number of samples known to be near or prepared at the quantitation limit.

My bold and underline.

Peter

[hyou0710]

Thanks for the information! It seems to be fine to include that lowest point in the calibration curve for routine analysis.

I would say that the second paragraph of this from the link that lmh posted is the important part;

7.4 Recommended Data
The quantitation limit and the method used for determining the quantitation limit should be presented.

The limit should be subsequently validated by the analysis of a suitable number of samples known to be near or prepared at the quantitation limit.

My bold and underline.

Peter

This sounds similar to what the EPA is doing with new drinking water methods. You determine the Minimum Reporting Limit (similar to LOQ) then you make a calibration and the requirement is that one point must be at or below the MRL. The test to show that the lowest point is valid is that it must quantitate at +/- 50% of the true value when calculated against the calibration curve it is a part of. The MRL also has be be proven using seven replicate analysis at the MRL level then passed through statistical processing that gives a high and low variance limit that must fall in the 50-150% ranges. (the exact formula can be found in new methods such at EPA 525.3)

What the EPA is putting forth is that the lowest calibration point can be lower than the Quantitation Limit but must be close enough that it does not suffer from too much uncertainty, given by the 50% window for accuracy. This is being done to prevent laboratories from reporting unrealistically low Quantitation Limits.

[hyou0710]

Thank you! This is a very clear standard instruction that I can cite.

From SW-846 method 8000D

The LLOQ is the lowest concentration at which the laboratory has demonstrated target
analytes can be reliably measured and reported with a certain degree of confidence, which must
be ≥ the lowest point in the calibration curve. The laboratory shall establish the LLOQ at
concentrations where both quantitative and qualitative requirements can consistently be met (see
Sections 9.7.3 and 11.6). The laboratory shall verify the LLOQ at least annually, and whenever
significant changes are made to the preparation and/or analytical procedure, to demonstrate
quantitation capability at lower analyte concentration levels. The verification is performed by the
extraction and/or analysis of an LCS (or matrix spike) at 0.5-2 times the established LLOQ.
Additional LLOQ verifications may be useful on a project-specific basis if a matrix is expected to
contain significant interferences at the LLOQ. The verification may be accomplished with either
clean control material (e.g., reagent water, solvent blank, Ottawa sand, diatomaceous earth) or a
representative sample matrix, free of target compounds. Optimally, the LLOQ should be less
than the desired decision level or regulatory action level based on the stated DQOs.