Forcing calibration curves through zero

[sdegrace]

This topic came up before... I maintained that it can sometimes be acceptable to force a calibration curve through zero (force b =0, not just including (0,0) as a point) and that in some circumstances, such as when you expect to report values close to the LOQ, that it may be desirable if the calibration curve can be forced through zero to avoid situations such as physically interpreting negative results arising from the intercept. I note that many commerical chromatographic software packages such as Empower include fitting forced through zero, indicating that some consensus must exist somewhere that doing so is not automatically mathematically and analytically fraudulent. However, I didn't have any good criterion to present to decide when to force b=0.

Recently I found this article:

http://chromatographyonline.findanalyti ... ail/588090

This article provides rational bases for the decision of how to create the calibration curve, including the decision whether to force b=0. I found it beneficial and I thought I would share it. I'm looking forward to the rest of the articles in the series.

Stephen

[sassman]

He he. Talk about corny titles. Stir the pot. Prepare for the firestorm. BTW, I totally agree with you:)

[lmh]

OK, my take on the firestorm:

It was an interesting article, but I thought a bit of a no-brainer. The conclusion seemed to be that if the y-axis intercept was statistically indistinguishable from zero, it was OK to force it to zero.

sdegrace, you're right that the only real application of forcing to zero is to avoid handling negative values from measurements very close to zero. But actually this doesn't add up. Since the LOD is usually defined in terms of a few standard deviations divided by slope, the only way you can have a measurement at or above the calculated LOD, but below zero, is if the LOD has been estimated from a set of calibration points far too high above the LOD, and we've used the s.d. of the curve rather than the s.d. of the y-axis intercept. The second "if" is allowed, but the first "if" isn't.

So the conclusion is that if you need to force through zero to avoid problems (and I'm guilty: been there and done that), you're almost certainly measuring below the limit of detection, and the answers are a best guess at rubbish, anyway... In fact, worse, if you force small measurements to be above zero, then a normally-distributed population of measurements of zero, which would generally have an average of zero, will suddenly have an average above zero.

The real test of any calibration curve is how well it returns the right answer for a suitable standard (spiked blank sample) within the range over which the assay is to be used.

[sdegrace]

Practically speaking, I tend to use it for equipment cleaning verifications for cleaning validation studies. In this case I think it's important to have meaningful values at low response levels, and while the value found could be over a fairly wide (low) range, the exact value is more crucial the lower it is. I always have a coupon spike level close to the LOQ anyway. I figured the treatment is valid as long as there is no response in the blank diluent and the r2 conforms. This also comes up with residual solvents sometimes. This is a decently common situation for me, unfortunately... if I'm doing an assay where I don't need the range of the method to be close to the LOQ, I don't worry about how close the intercept is to the origin.

I do happen to think that close to the LOQ, for a calibration which really should go through the origin, the results quantifying from the calibration curve actually will be more accurate if the curve is forced through the origin.

[Peter Apps]

Are then any benefits to zero forcing besides;

1) removing one term from the simple arthmatic of the calibration equation

2) post hoc manipulation of results to make them closer to expectation

Peter

[sdegrace]

*Any* type of fitting is essentially a type of post hoc manipulation and a judgement call which granted needs to be made on sound statistical criteria, IMO. No particular type of fitting I think has an inherently greater claim to Truth handed down by God except if it can be shown to be statistically superior for a particular data set.

We love plain vanilla least squares, though. I have a BCA total protein assay kit where the manufacturer's documentation specifically calls for least squares fitting of the calibration curve and boasts of their formulations' superior linearity... it's good, but I find that a second order polynomial fit consistently provides a statistically superior fit of the calibration data. I still use least squares with it anyway, though, because it's easier and the r2 is good enough to justify it .

[HW Mueller]

Well, I think enough has been said about this before, though a comment on the above link seems in order. I go with Imh´s first paragraph on this: The article gives the ok only if it is really irrelevant, it is a very diplomatic way to say why do this nonesense?
One can argue about the merits of statistics, but it is not conjecture (arbitraryness) like forcing through zero.

[Peter Apps]

What I had in mind as post hoc manipulation is something like this:

You run a calibration series and it looks pretty linear so you fit the best straight line and get the calibration equation.

You then run a sample and calculate the result using the calibration equation.

Shock horror the result is out of spec, not what you/the customer/the regulators want.

THEN you go back and look at the calibration line, and it looks a bit curved so you fit a second order polywhatsitsname and have another shot at the calculation, if that doesn't work you fit a higher order or try a log - log etc. Maybe leaving the line linear but moving it a bit will do the trick, lets try forcing zero. Sighs of relief all round the plant can market the batch, you can publish the paper, the product can be imported/ exported.

What makes this post hoc manipulation (of the result) is that none of it would have happened if the result had been in spec.

This is just as poor as running dozens of different statistical tests on a given set of data until you find one that just happens to come up significant, which was a remarkably common practise in the soft sciences when big number crunching computer programmes first became widely available.

Peter Apps

[sdegrace]

Well, I would never condone that sort of behaviour. I always pick a type of fitting when I'm developing the method and then afterwards I refuse to budge from it when reporting results... the only way I would ever consent to change is if there were a body of data showing that I had made a mistake back in the development phase that somehow managed to slip through the qualification or validation, which should not happen. I've never changed the way I quantify a result for an established method in order to get the "right" result and I would never consent to having my name associated with results that were massaged to fit like that.

Stephen

[marina1111]

I do not have any knowledge about fitting statistics. But you can not really report negative results – it is also not truth of course. So when wide range is expected – such as in cleaning verification - I prepare 2 calibrating curves – one for higher range – around the specification, and one just above the limit of quantitation. Is that acceptable and is it what is commonly done? Personally, just as common sense, I would think that forcing through zero is acceptable for routine analysis – It provides answer which is good enough (usually the answer does not need to be as precise as for assay) and it is surely more precise and correct then negative. Also, and this is important for routine analysis, it is simple and efficient (you does not need to prepare lots of standards).

[rick1112]

hi

i just found an article in LCGC....hope u find this useful

http://chromatographyonline.findanalyti ... ryId=42487

[Don_Hilton]

One thought crosses my mind as I read this: My limit of detection usually falls above 0. While I do run a standard below anything that I will report, I've had a devil of a time finding a peak when I shoot a zero concentration analyte. What's worse is that even if I could find the peak, I would have a hard time demonstrating that I could tell the difference between no response and no resonse. Sorry, I just had to toss that in.

[sdegrace]

Marina, I tend to agree. To me, especially to attempt to quantify very low levels, forcing through zero avoids negative numbers with problematic interpretations, and also reflects physical reality. Furthermore, for the type of methods where this type of quantitation is used, it tends to bias towards higher reported results, adding a margin to safety (since low is generally better).

In my own experience, for cleaning verification, in practice the actual specification levels are sometimes very low for us, or we wish to clean to extremely low levels even if not strcitly required, so quantitation tends to be on the close side to the limit of quantitation of the method - if a larger amount is found by some chance it is interesting in the sense that it gives an idea of "how far" the cleaning still has to go, but that's it. And also, cleaning tend to actually be very effective, so often no peak is seen in most swab or rinse samples. So in practise, we find ourselves reporting close to the LOQ, or that the level of residue is less than some limit defined by measuring the LOD by virtue of the fact no peak was detected.

[HW Mueller]

Do you also force through 100%? It is just as unrealistic to get a value of 105% of an analyte as it is to get -5%, as an example. Since you may know that you can weigh quite well you force through all the other points also, since you know they can not be anything different.
Actually, the last method is at least consequent and not really that bad if you are in a range where the values are equivocal anyway. But how is one going to explain this in a publication?

[Peter Apps]

Hans, that is a VERY good point.

Steve and Marina, obviously you cannot have less than nothing of anything, but because every measurement process is variable it is entirely possible to get a negative measured quantity result when the "true" quantity is positive. If you want a truly conservative measurement of the effectiveness of e.g. cleaning then you need to take the measurement result plus its expanded uncertainty as the criterion. If this is ever negative then there is something wrong with the method and its validation.

Peter