Limits of detection

[hungryfriend]

i'm abit confused over lod

so in a journal article, how do they determined lod?...most usually use s/n=3
reason being sometimes im quite skeptical abt some journal with such low lod

so is lod refering to how low my instruments can "see"?
example: i inject a 0.5ppb std and its peak height is 3 times higher than my noise, my lod is 0.5ppb

or it refers to how low my sample prep can extract such that my instrument can "see"?
example: the lowest my instrument can detect is 0.5ppb but my sample prep give me 100 fold enrichment so my lod will be 0.005ppb instead of 0.5ppb

so which is correct?
or is there any other ways?

[Peter Apps]

3 times baseline noise on one run invariably gives absurdly optimistic values for a method's limit of detection. I cannot understand why journals still accept such values.

Google IUPAC limit of detection for a more rigorous and rubust approach.

Peter

[lmh]

do some searching on this forum, there have been some good postings over the years.

I'm also dubious about levels based on S/N. If nothing else, there are plenty of instruments where the noise can potentially be nothing - for example, many ion-traps used in MRM mode (quantifying MS2 chromatograms). Especially if the original software suppresses signals below a certain value, these very often give chromatograms with zero intensity everywhere except the peak -so no matter how excruciatingly tiny, misshapen and noisy the pathetic little peak has, it still has infinite S/N ratio - and will do as you decrease the concentration, right up to the point where it vanishes altogether.

Personally I prefer to estimate the LOD and LOQ based on the measured standard-deviation of the calibration curve as it crosses the axis of the calibration curve. This makes sense to me, because it means limits of detection are directly related to probabilities, and limits of quantification are directly related to percentage errors on the measurements. I think the IUPAC rules Peter mentioned do refer to estimates based on the standard deviation of the calibration curve - if not, post again, and I'll see if I can find a reference.

[rb6banjo]

I don't like using the y-intercept because if you do the statistics for the calculations used estimate that value, you will see that the majority of the error in the fitting process goes into that value. Most analytical methods should show no response at zero concentration. Most will show no response for the analyte when it is present at less than the detection limit. That's why, the LOD should be based on some measured signal-to-noise ratio. In fact, the intercept from a least-squares fit of the data can be calculated as (model is y = m*x + b):

b = ybar - m*xbar

ybar = average value of the y's and the xbar = average value of the x's. Which means that the "best fit" line must go through the average values of x and y and thus the intercept is dictated - at least somewhat - by our choice of standards. That does not seem to me to be a good way to estimate your LOD.

I have had GCMS methods where S/N = 2 for the analyte gives me a mass spectrum of sufficiently good quality where the library search showed reasonable confidence that it was indeed my analyte. Whether S/N = 3 is the magic number or not is up to debate, but LOD should be based on the signal for the analyte above the noise of the detector. If your noise is small, you'll be able to see your analyte at much lower concentrations. It's a good place to be.

[Peter Apps]

The problem with the LOD = 3 x baseline noise approach is that it completely ignores sampling and sample prep as sources of variability in the signal for a given quantity of analyte. It estimates the LOD only for the instrumental step, and if the LOD is taken from a single chromatogram it ignores even the variability in the injection step.

Peter

[tom jupille]

The other problem with S/N is "how and where do you measure the noise?". Just before the peak? Just after the peak? How long a stretch do you need? What do you do if there are other peaks present?

And then there's the whole discussion of the strange way USP and EP define S/N:
viewtopic.php?f=1&t=20977

S/N >= 10 should not *define* LOQ; it is an *estimate*. The actual definition is:
the lowest amount that can be measured [b]with acceptable precision and accuracy[/b].

Check out these articles from the Coleman & Vanatta series in American Laboratory:
http://www.americanlaboratory.com/913-T ... roduction/
http://www.americanlaboratory.com/914-A ... on-Limits/
http://www.americanlaboratory.com/914-A ... continued/
http://www.americanlaboratory.com/914-A ... concluded/
http://www.americanlaboratory.com/914-A ... a-3-Sigma/
http://www.americanlaboratory.com/914-A ... Concluded/
http://www.americanlaboratory.com/914-A ... t-Summary/

[lmh]

rb6banjo, sorry, I didn't explain clearly. I don't believe in trying to estimate the error from genuine blank runs. I meant that I like to use a LOD/LOQ based on the error at zero as estimated from a series of calibration points approaching the lower limit of the method. The idea is that you run a calibration curve at very low concentration, ideally with replicates of each concentration, so that in all cases there is a real peak to integrate. Obviously as the peak becomes very small, there will be significant errors in the quantification. You then estimate the vertical error of the calibration curve. This seems to be referred to by different bits of software by different names, even when numerically identical: (Excel: standard error of the y-estimate; Chemstation: standard deviation of the residuals).

The point about this vertical error is that it is a very real estimate of error, taken from real measurements, close to the point where you want to know the error. If you can tolerate a 5% error in quantification, and you find that the measured error is actually 0.5 pmoles, then your LOQ is 10pmoles.

For reference to this and other methods, including S/N, my favourites so far are still: Épshtein, Pharmaceutical Chemistry Journal 38: 212-225, and also LC-GC Europe Feb 2009, 22:82-85. The ICH site is http://www.ich.org, and the most relevant section is Q2(R1)

[richiekichi]

They are confusing. And nobody ever agrees.

I prefer to determine my limits from spiked samples first. If I can repeatedly see 0.5ppb in my sample with a S/N of 3 then that's my LOD for a specified method.

Of course if I have a concentration factor of one hundred then I would also have to see less than a 0.005ppb standard with a reasonable S/N ratio in order to quantify my analyte (although to quantify you'd really want a better S/N).

As to how you calculate S/N..............and fight!

[Peter Apps]

They are confusing. And nobody ever agrees.

I prefer to determine my limits from spiked samples first. If I can repeatedly see 0.5ppb in my sample with a S/N of 3 then that's my LOD for a specified method.By definition; at a S:N of 3:1 you will fail to distinguish the peak form noise in one out of three runs. I prefer to look at this as the known concentration (by spiking blank matrix or whatever) for which the rsd of the results is less than 33% for LOD and less than 10% for LOQ

Of course if I have a concentration factor of one hundred then I would also have to see less than a 0.005ppb standard with a reasonable S/N ratio in order to quantify my analyte (although to quantify you'd really want a better S/N).You have this backwards - if you have a concentration step then the concentration in the original sample, and so the LOD/LOQ in the original sample are lower than in the extract that you analyse

As to how you calculate S/N..............and fight! If you go with the rsd of the results you do not need to determine S:N on the chromatogram

Peter

[richiekichi]

Yes, I have written that incorrectly. Glad someone is paying attention.