USP / EP formula to calculate S/N ratio

[Kwet80]

Can someone explain me why USP and EP formula to calculate S/N ratio is 2*H/h while nearly all other chromatographists in the world are using H/h?



Is it to enhance the S/N ratio by a factor 2 to look better or is there another explaination?

[danko]

EP got it wrong in the first place. Then USP and EP harmonized it and chose the wrong one. Probably because - as you suggested - the "new" value/result looked more attractive
There has been at leat one huge discussion of the matter on this very board some years ago if memory servs me.

Best Regards

[Coffo]

Hmmm, I thought it was H/(h/2) ... hence 2*H/h ?
I could be wrong though!

[lmh]

I'd go with Coffo's answer, the problem being that height of peak is being measured from the middle of the baseline, while noise is measured on both sides of the baseline. But there is no "right" or "wrong", it's just a number, and provided everyone who looks at it knows how it was defined, the exact definition doesn't matter.

If it is any consolation, the signal:noise ratios quoted by the Genesis and ICIS integrators in Xcalibur (Thermo) come up with wildly different values (10-fold different is quite common) for the same peak.

Yes, this is a regular here, but I can't remember the last thread...

[danko]

There are at least two important matters to keep in mind here:

1. The noise is per definition (and mostly in practice) constant throughout the trace (the absorbance trace that is) i.e. both the baseline (the plain region of the chromatogram) and the peaks are plotted with that noisy line. So, even the peak’s very apex could be and often is the highest noise fluctuation.

2. Anyone who has worked with any CDS has most probably zoomed in (at least once) and observed the integration line (start and stop). It never starts or ends in the middle of the noise/waves! Does it?

So, what happens is - unless a person draws all these lines manually with a pencil – the beginning of the peak (and it’s end for that matter) is taken from the lowest point of the trace – i.e. the lowest noise valley. The peak apex on the other hand is taken at the highest point of the absorbance/trace/noise.

So, taking the above in consideration – where exactly is the peak/signal “cheated”/ underestimated in comparison with the baseline noise?

Best Regards

[Peter Apps]

Hi Danko

Using Genesis, peak starts and stops are quite commonly not at the top or bottom of the baseline noise because there is a settable smoothing function that looks for sustained departures from baseline in order to detect peak onset and end. I got my Genesis crossgraded to Compass yesterday, so I do not yet know if Compass will do the same.

Since signal:noise on a chromatogram usually gives hopelessly optimistic estimates of LOD and LOQ for a whole method, whether it is calculated from H or 2H is not of much real significance.

Peter

[danko]

Hi Peter,

I’m aware of all that but it does not – in any way – support the validity of the “2 factor” for the signal/peak. I’m not familiar with Genesis, so there might be other rationales and factors to be considered in that context, but the scope of my post/thoughts was more general/universal if you like

Best Regards

[Kwet80]

Hello,

I can admit that is just a definition and so it can be correct. I understand the 1/2 h used in term on half of the baseline noise but I don't think it's correct if we still used the reference S/N value for LOD, LOQ. With this formule, we have to multiply by 2 the "usual" value of S/N = 3 for LOD, S/N = 10 for LOQ --> USP S/N for LOD = 6, USP S/N for LOQ = 20. And I'm pretty sure it's rarely the case in practices in laboratories!

Eventhought, I agree that these values are indicatives and not formal definition or demonstration of LOD or LOQ.

I found an internet site were we can simulate a chromatogram entring a S/N value calculated as the USP S/N definition:

http://www.shimadzu.com/an/definition_sn_ratio.html

http://www.shimadzu.com/an/simulation_sn_ratio.html

Here is the result with commonly used key values of S/N: 3, 5, 10 & 20:

[dblux_]

Hmmm, I thought it was H/(h/2) ... hence 2*H/h ?
I could be wrong though!

Even if you are, this is the best explanation

[lmh]

The fact that an integrator might (but not all do) choose the lowest point in the noise for its baseline and the highest point for the top of its peak is a different issue to where the factor of 2 comes in.

If the integrator does this, it is overestimating H, the height of the peak, but it doesn't affect its estimate of h, the lowest-to-highest height of the noise. What it's calculating is (H+h)/h, or 2*(H+h)/h according to definition.

I'm in agreement with Peter, that S/N is a poor way to estimate LOD or LOQ, so it's really best used as an in-house measure of whether a system is working as expected. It doesn't matter how you define it, provided everyone in-house using that instrument/procedure is defining it the same way.

By the way, my usual argument for why S/N is a terrible estimate of LOQ is to look at the examples of either an oldish ion-trap with low capacity, or (nowadays!) super-duper instrument where actually only a handful of ions can give a measurable signal. In either case, you can have a baseline that actually contains no noise whatsoever, and a peak (signal) that is full of huge random error, and yet the S/N ratio is infinite (or very nearly so). Or, another totally trivial example: imagine a detector that is far too slow for the chromatography. The measured peak might consist of a single detected point, taken at a random time-point from an actual Gaussian peak. As a result it has very large variability depending on where in the Gauss-curve it happens to fall. You'll see this variability if you make a series of injections at high dilution (a good way to assess LOQ), but every injection will have a very good S/N ratio.

The bottom line anyway is that you cannot claim a LOD of X, or a LOQ of Y, without going back and making a series of runs injecting X or Y and demonstrating that you can, in fact, detect X, and quantify Y with the appropriate relative standard deviation. Calculated LODs and LOQs are provisional things that must be reality-checked.

[danko]

The fact that an integrator might (but not all do) choose the lowest point in the noise for its baseline and the highest point for the top of its peak is a different issue to where the factor of 2 comes in.

To my knowledge all CDS do that. If there is a single CDS that does not – we need to clarify what that particular one does. If you look at the Kwet80 post above you’ll se how a typical peak is plotted and then you can imagine how the integration application will proceed. Have you seen other options?

If the integrator does this, it is overestimating H, the height of the peak, but it doesn't affect its estimate of h, the lowest-to-highest height of the noise. What it's calculating is (H+h)/h, or 2*(H+h)/h according to definition.

The integrator (The CDS) will not calculate anything like this. The software will calculate peak height and the nose. You’ll have to edit a formula/equation and then you can choose to include the factor of 2.

I'm in agreement with Peter, that S/N is a poor way to estimate LOD or LOQ

Yeah - not least because they are hugely overestimated. So, you’d like to make things twice as worse by multiplying the signal (peak height) by 2.

Best Regards

[mk_3249]

Can someone explain me why USP and EP formula to calculate S/N ratio is 2*H/h while nearly all other chromatographists in the world are using H/h?



Is it to enhance the S/N ratio by a factor 2 to look better or is there another explaination?

Here I am quite confuse. What is H and h? I am new to this and am also stucked in this situtation.

[danko]

You are not serious - are you?

[mk_3249]

You are not serious - are you?

Ya M serious. Coz m new to this. I've performed AMV for one of our product. As I am doing right the first time, m confuse which value should be considered for H and h.

Pls. help me.

Thanks.

[lmh]

h is from the bottom of the noise to the top of the noise (i.e. define a region that you consider to be background, draw a line that just touches the bottoms of the noise spikes, and another that just touches the tops, and measure the distance between them). H is the height of the peak, theoretically measured from the middle of the base-line to the middle of the noise at the top of the peak, but as danko has pointed out, because of software constraints, it's usually measured somewhere else. Frankly it doesn't matter, because S/N is just not a good way to determine LOD/LOQ. It's better used as an ongoing measure of performance, in which case it doesn't matter how you define it, provided you always calculate it the same way.