S/N calculation per EP and USP

[jdolan]

Maybe I'm the only one that missed this, but someone just brought it to my attention that the EP defines the signal-to-noise ratio as twice the peak height divided by the width of the baseline noise band. In checking with USP, there is a proposal in Pharm Forum to harmonize with this definition. I've always seen S/N as just that, the height of the peak divided by the width of the baseline.

Certainly this will affect about a gizillion methods that have S/N as part of system suitability.

Can anyone illuminate me on why one should use 2xheight? Thanks -- John

[LC_reader]

Actually, it is "the width of the baseline noise band" devided by 2 instead of "2 x Height". In EP, there is a graphic explanation about the calculation of S/N, which looks like very reasonable. By the way, about one or two years ago, USP company was contacted by us regarding no clearly defining S/N calculation, and replied that they will elaborate S/N in the coming USP/NF books.

[danko]

I think it was a year ago, or something like that, we discussed this very topic, but I don’t remember how it ended.
My humble opinion at that time was exactly as it is now; namely a senseless perception of the issue. The rationale, as I’ve been told, is as follows: The signal (the actual peak) is (supposed to be) measured from the mean of the baseline noise (i.e. the noise amplitude divided by two, so that the imaginary zero signal is in the middle of the amplitude) to the very apex of it. But as we all know the noise value is calculated by subtracting the lowest point from the highest ditto of the noise amplitude, so that the whole amplitude is regarded as noise (i.e. the negative plus the positive part of the amplitude). According to the proponents of this “innovativeâ€

[HW Mueller]

As I remeber that "older" discussion the last sentence of Dancho´s statement was what many of us concluded: A totally superfluous exercise.

[jdolan]

According to Dancho, a better value of the signal is to measure from the top edge of the baseline noise band to the top of the peak. This is logical, but not the customary method. But, as he says, doubling the peak size does nothing to correct for noise on top of the peak. In fact, it makes the error worse for small peaks, where s/n may be critical.

[Uwe Neue]

John, so what is what you call "the customery method"?

To measure the signal height from the top of the baseline noise to the top of the peak is logical and correct.

It is also not too difficult to decide that the baseline noise is the width of the baseline, free of peaks.

Whether I divide this value by 2 or not, is the real question. It actually is logical to do that and to use such a value as a criterium, but the value of this is then not signal to noise, but signal to half-the-noise. With other words, the value of signal to half-the-noise is the best way to judge, if you can see a small peak or not. However, I think that these things are semantics, and of little real value.

[jdolan]

Uwe, whether you measure the signal from the middle or top of the noise band, signal-to-noise has always meant to me the height of the peak (signal) divided by the noise band (peak to peak). I poked around on the web today (don't have any books with me) and could find nothing that defined noise as 2xsignal/noise.

One might logically use 4x signal/noise = signal /(noise/4), since in most error discussions in chromatography we use 1-sigma values, and noise/4 ~ 1 sigma. But half the noise signal (or 2x height) doesn't seem logical at all. So my puzzlement is how this got into the EP regulations in the first place -- there must be a logical reason.

Finally, in terms of measuring signal, the more I think about it the more I'm convinced that the middle of the noise band to the top of the peak is correct. There is error in picking the top of the peak, but the error of being low (signal - noise error) vs being high (signal + noise error) should be equal, shouldn't it? If that's the case, measuring signal from the top of the noise band to the top of the peak would, on the average, undercalculate the peak height.

[HW Mueller]

As I understand this, all integration software measures peak hights from an average baseline value (the "middle" of the baseline). Any other type of peak hight measurement would then introduce a new definition of peak hight which seems unnecessary. In the old days I used to report what we called sensitivity as x grams or mole per volume at a S/N of 4, or near there. Thus to me it appears a bit ridiculous to tell people I decided to call it quits at 2S/N of 2 instead of S/N of 4.

[Uwe Neue]

John,
The noise on top of the peak is the same as noise in the baseline. Therefore, if I want to subtract this noise from my measurement of the signal, I measure the signal as the difference between the top of the peak and the top of the noise. I have no clue if standard software does this, and my book on such things is at work, but I woudl do it this way manually.

[danko]

A CDS will easily and unequivocally find the top of the peak by finding the highest absorbance value in the region between peak start and peak end. So, the noise on the top of the peak will be included in the peak’s height – unless some set up errors cause a missing data point on the top (e.g. too low sampling rate).

As for the peak base, the things get more complicated. Here is the virtual baseline (the one drawn by the software or assigned by the user) that serves as the lowest point. This line does not include any noise (naturally) because it is artificial, thus not build up from actual data/measurements. The question here is where is that line placed? In automatic integration mode it will be placed according to certain integration parameters, such as threshold and peak width. In a manual integration mode the user will just place it where he thinks it’s reasonable to do so. In both cases I’m almost certain that this line won’t represent an extension of the baseline from the middle of its noise. And anyone who cares to zoom in an integrated peak (in an appropriate degree of magnification) will be convinced that the line (the virtual peak base) is almost impossible to be located in the middle of the noise amplitude.
So, all these reflections on the peak start and worst of all doubling the peak height value are petty considerations, with no practical application – certainly no significant qualitative effect on the actual chromatographic results.

My private conclusion is: The S/N calculation is (or should be) “What you see is what you getâ€

[jdolan]

So we all seem to agree that S/N is the signal divided by the noise, not twice the signal. This is consistent with everything I've read and been taught. We also agree that the top of the peak is the appropriate place to measure the signal. We have some disagreement about where to place the baseline, but this is all within the noise band, so is likely of little consequence as long as the procedure is used consistently for a give method.

So where does the EP 2s/n come from? And why is USP on track to publish a definition to agree with this? I have a probe into my contacts at USP. Does anyone know someone within the EP who could give us the reasons for 2s/n?

[Peter Apps]

A pedant might argue that if peak area is used to quantify response, that peak area is the signal. Then the variance of the area at the same retention time in the blank is the noise. Since integration parameters are usually set so as not to integrate baseline noise an infinite signal:noise ratio is easily achieved, and a more practical measure of signal:noise is the repeatability of the peak area, which includes terms for the injector repeatability, and any drift. It seems to me that determining signal:noise by measuring peak height and baseline on one chromatogram is unproductively reductionist - whatever uncertainty is contributed is also inevitably included in peak area repeatability from replicate injections, and that is included in the repeatability of the whole method. If the repeatability of the whole method is suitable for purpose, than all the subsidiary contributors to that repeatbaility must also be suitable for purpose.

If there was a smiley for pot stirring I would insert it here

Peter

[jdolan]

I have no arguent that the best way to measure LOD or LLOQ, repeatability, etc is statistically from a standard curve, repeated measurements, etc, so you are quite right. However... S/N has been one of the classical ways to determine LOD and LLOQ, both in practice and guidance, so there should be an unequivocal way to measure it, don't you think?

Potstirrers ..... harumphhhh!

[grzesiek]

"so there should be an unequivocal way to measure it, don't you think? " - john I really don't think there is such need, as I see it s/n is useful as a SST parameter and how it should be measured can be (and should) specified in the method

for me it is a matter of defining it in the method description/laboratory SOP etc.

[Peter Apps]

Hi John

You hit it on the head with "classical" - the peak height vs baseline noise goes all the way back to isothermal only, packed columns and counting squares on strip chart (I'm thinking GC here). With modern hardware the instrument S:N noise (which is all that you are measuring with height/baseline) is (or certainly should be if the hardware is set up properly) only a small part of the total variation in the method, and for trace analysis involving, say, extraction, SPE cleanup and an evaporation step it is a really minor contributor, so minor that it can be ignored as long as the whole method is working right.

Peak height vs baseline might have some utility for trouble shooting - but, imho, as a method QC parameter it has been superseded by repeatability.

Peter