Mehtod Validation - LOQ

[skyllberg]

Dear all,

I have been looking through the forum for a while but not been able to find an answer to my question, and would grateful if you could help me.

I am currently doing a project on profiling of fragrances using GC and determining the concentration of some compounds. I have made up solutions in the expected concentration range, and for method validation purposes all solutions have been made up in triplica and injected three times each.

However, as many of my concentrations are very low, I would like to make sure that they are above the LOQ, though I am very confused as how to go about and measure this. Would it be enough to show that my signal/noise ratio is >10, and if so, what time window should I use for my noise determination?

I've also read it's possible to determine the LOQ using statistics of the calibration curve, however I have not been able to find a suitable way of doing this.

Thanks a lot!

E

[krickos]

Hi

In the pharmaceutical buissness there is a guideline (ICH Q2 R1) that gives some information around this topic:

6. QUANTITATION LIMIT
The quantitation limit of an individual analytical procedure is the lowest amount of analyte in a sample which can be quantitatively determined with suitable precision and accuracy. The quantitation limit is a parameter of quantitative assays for low levels of compounds in sample matrices, and is used particularly for the determination of impurities and/or degradation products.

7. QUANTITATION LIMIT
Several approaches for determining the quantitation limit are possible, depending on whether the procedure is a non-instrumental or instrumental. Approaches other than those listed below may be acceptable.
7.1. Based on Visual Evaluation
Visual evaluation may be used for non-instrumental methods but may also be used with instrumental methods.
The quantitation limit is generally determined by the analysis of samples with known concentrations of analyte and by establishing the minimum level at which the analyte can be quantified with acceptable accuracy and precision.
7.2. Based on Signal-to-Noise Approach
This approach can only be applied to analytical procedures that exhibit baseline noise.
Determination of the signal-to-noise ratio is performed by comparing measured signals from samples with known low concentrations of analyte with those of blank samples and by establishing the minimum concentration at which the analyte can be reliably quantified. A typical signal-to-noise ratio is 10:1.

7.3. Based on the Standard Deviation of the Response and the Slope
The quantitation limit (QL) may be expressed as:
QL =
10 *σ/S
where σ = the standard deviation of the response
S = the slope of the calibration curve
The slope S may be estimated from the calibration curve of the analyte. The estimate of σ may be carried out in a variety of ways for example:

7.3.1 Based on Standard Deviation of the Blank
Measurement of the magnitude of analytical background response is performed by analyzing an appropriate number of blank samples and calculating the standard deviation of these responses.

7.3.2 Based on the Calibration Curve
A specific calibration curve should be studied using samples, containing an analyte in the range of QL. The residual standard deviation of a regression line or the standard deviation of y-intercepts of regression lines may be used as the standard deviation.

As for the time window to use: The european pharmacopea used to use a factor of 20 but has from 1st of April reduced it to a factor 5, see below:

Signal-to-noise ratio
The signal-to-noise ratio (S/N) influences the precision of quantification and is calculated from the equation: S/N= 2*H/h

H = height of the peak (Figure 2.2.46.-4) corresponding to the component concerned, in the chromatogram obtained with the prescribed reference solution, measured from the maximum of the peak to the extrapolated baseline of the signal observed over a distance equal to 20 times the width at half-height,
h = range of the background noise in a chromatogram obtained after injection or application of a blank, observed over a distance equal to 20 times the width at half-height of the peak in the chromatogram obtained with the prescribed reference solution and, if possible, situated equally around the place where this peak would be found.

Hope it helped a bit

Cheers Chris

[DR]

There are a few different approaches to determining both LOQ and LOD (limit of detection) - which you choose will be determined by the expectations of your instructor.

To help you search within this forum's archives or Google... check combinations of S/N, LOD, LOQ, RSD and Calibration Curve.

Some of us who don't like loading up their reports with statistics look at average baseline noise amplitude and deem LOD to be 3x that and LOQ to be 10x that. It is best to prepare a series of standards whose concentrations will cover a range from about 125% of your expected concentration down to close to baseline noise values and see how low you can go while still maintaining a good r². Tom Jupille has written about weighted least squares approaches to evaluating such curves.

[larkl]

This may not be as rigorous as approach as you're looking for, but here goes anyway:

We would print out the peak in question (something with a known amount) and determine the peak height, so now we know the concentration/height ratio. Then we'd print out a drastically blown up baseline near this peak. We'd use the vertical breadth of this noise band to determine the noise. Then you can use the conc/height ratio to do what you need with the noise band. We'd usually just calculate the LOD by multiplying the noise height by three (meaning a peak would have to be 3X the noise to be detected) then by the conc/height ratio.

[skyllberg]

Would it be acceptable to use 10sigma/S where sigma is the standard deviation of the residuals and S is the slope?

Does this give me the LOQ in concentration (x-values) or pAs (y-values)?

Thanks

[tom jupille]

Would it be acceptable to use 10sigma/S where sigma is the standard deviation of the residuals and S is the slope?

To me, yes, and this is arguably a better way because it avoids all of the issues of finding a clear section of baseline, measuring peak-to-peak noise, etc.

Does this give me the LOQ in concentration (x-values) or pAs (y-values)?

I'll be cryptic on this one an only give a hint:

"what are the units associated with sigma and S? And what units are left when you divide sigma by S?"

[skyllberg]

So am I right in thinking residuals are 'dy' and therefore PA Ratio in my case, and S is (PA Ratio)/Concentration - so the LOQ value should be concentration.


I also wondered how I determine whether to use weighted regression or not. Linear regression assumes homoscadicity, so testing for that should be a starting point, or is it enough to look at the residual distribution?

Thanks a lot!

[tom jupille]

So am I right in thinking residuals are 'dy' and therefore PA Ratio in my case, and S is (PA Ratio)/Concentration - so the LOQ value should be concentration.

You got it!

I also wondered how I determine whether to use weighted regression or not. Linear regression assumes homoscadicity, so testing for that should be a starting point, or is it enough to look at the residual distribution?

That is a large, economy size can of worms! If you're working over a relatively narrow range, then you can assume homoscedasticity (so long as the residuals don't look too bad). That's the approach that's taken in pharmaceutical regulatory assays for things like potency or content uniformity, where you are only required to be linear from 70 to 130% of the stated value.
Weighted least squares is a better approach for wide-range analyses (and those are the ones where LOD becomes an issue!), but ideally you know something about the error distribution and apply appropriate weighting.
A third approach which is seldom used in chromatography, is to transform your data into a form that is homoscedastic (e.g., log-log).

For a much more detailed discussion of detection limits, check out these three articles from a long-running series on statistics in American Laboratory (you'lll have to register with them in order to download and read):
http://tinyurl.com/b35zwt
http://tinyurl.com/b7hl73
http://tinyurl.com/ahebwe

[skyllberg]

So how would you define 'a relatively narrow range'.

My concentrations usually range between 0.005%-0.5%, but my residuals look OK, i.e. random.

Thanks a lot for the links!

[tom jupille]

So how would you define 'a relatively narrow range'.
My concentrations usually range between 0.005%-0.5%, but my residuals look OK, i.e. random.

I think you're probably OK, but I'll quote from Section 10 of that same series on Statistics in Analytical Chemistry:
"The residual plot is a more informal and somewhat subjective diagnostic.
The LOF test is a formal statistical procedure that does not require the practice or interpretation needed for residual analysis."

At this point, we are on the very ragged edge of my statistics knowledge, so to avoid any misinterpretation, I'll take the coward's way out and refer you to three more articles (on diagnostics) in that series:
Part 8: http://tinyurl.com/dfkajl
Part 9: http://tinyurl.com/auwn7s
Part 10: http://tinyurl.com/bfzkfj