[Question] Non-linear standard (calibrator) curves

[Anna01]

Merry Christmas!

I have a problem that perhaps some of you might help me with

I am setting up a LC-MS/MS analysis of various hormones, but somehow the standard curves (12 points) are not quite linear. Here are the key points:
- I try to quantify over a pretty large range (1 - 2000 nmol/L).
- The highest concentration seem to fall a little (15-30%) too low.
- I have tried preparing the standards in H2O, MeOH, MeOH:H2O, bovine serum albumin and stripped serum - but the non-linearity seems consistent.
- My internal standards are deutered isotopes of the analytes and coelute exactly with my substances.
- ISs are in a rather low concentration (10-50nmol/L), as for most of my samples this will give approx 1:1 ratio between the substances and IS. This is a compromise as this method is not all about measuring "normal" human beings, but rather also quantify very high pathological values.
- I am doing fully automated cleanup online coupled with an analytical column (SunFire).

So...why have I ran into this kind of trouble? And how do I solve this??? Eh...

Perhaps I was to optimistic to expect perfect linearity over such a large range? Maybe it has something to do with the IS has way lower concentration than the hormones? I think (but have not fully tested this) that the situation improves by injecting lower sample volumes when running "high samples". Or maybe this should make me really reconsider my method, perhaps something is completely wrong?

Anyway...here is my suggestions of different workarounds. Which is the most appropriate?

- Rerun every sample beyond a certain concentration, but with lower sample volume.
- Rerun every sample beyond a certain concentration, but first dilute.
- Rerun every sample beyond a certain concentration, but add more IS to the sample and standard curve.
- Add more IS to every sample
- Apply a "quadratic regression" - this way it all seems to fit nicely. But I don't know the mathematics. Is this ok?

If would be nice if anyone here can point me in the right direction? Or better - have a definite answer!

Yours,
Anna

[tom jupille]

It's a common problem, due to the fact that standard linear least squares is not really suitable for wide-range chromatographic data. The work-arounds are to do a log-log fit or a weighted least squares.

There is some background material in this excerpt from our Bioanalytical LC-MS/MS course:
http://www.lcresources.com/resources/ex ... ghting.pdf

[Anna01]

Good answer, Tom! This really clear things up...

From your post I presume you don't think that there are any thing seriously wrong with the method, but this non-linearity is something I have to expect.
I also understand that I shouldn't need to dilute/reduce sample volume.

I have of course played around using weighting 1/x and 1/x2, which improves the standard curve a lot, at the expense of the high standard being seemingly ignored. As I mentioned I get an even better fit doing quadratic regression. The software states that the quadratic calculation equation is:

y = a2X² + a1X + a0,

where y = ratio analyte:IS and x=concentration of substance

More info about calculation of the polynomial co-efficients (a1, a2 and a3) are also given.

Is it ok to utilize quadratic calculation? Or should I stay with 1/x or 1/x2?

Anna

[tom jupille]

Is it ok to utilize quadratic calculation? Or should I stay with 1/x or 1/x2?

My personal opinion is that so long as you have a well characterized relationship (e.g., quadratic) with a sufficient number of calibration points, there is no problem.

Unfortunately, the idea of "linearity" has been so belabored that many people (including reviewers and auditors) are uncomfortable with anything else. Hence the use of "weighted" least squares. This allows a linear fit and gets around the heteroscedasticity problem, but it doesn't address the fact that your linear range may simply not be wide enough for your purpose. There is a more complete discussion of the pros and cons of weighted least squares on the NIST web site:
http://www.itl.nist.gov/div898/handbook ... pmd143.htm

The "bottom line" is that you would probably have an easier time "selling" an auditor on weighted least squares than on a quadratic regression.

[Anna01]

Brilliant and to-the-point answer! Thank you!

Anna

[Uwe Neue]

There is no fundamental reason that says that any detector has to be linear from 0 to infinity. As a matter of fact, mass spectrometric response is often not linear at all over the range that you are looking at. There is nothing worng with a properly designed non-linear curvefit.

[ods-at-pacific]

You do not say what instrument you are using. This can make a difference in linearity over a large range.

What is your instrument?

[Anna01]

I use two instruments, API 3000 and API 4000 from AppliedBioSystems, both equipped with TurboIonSpray.

From what I have read I agree that the standard curve doesn't need to be linear over a large range to be valid. The problem now is that I need other colleges to agree too Perhaps a spike-in recovery study might convince them?

Anna

[DWR]

This is a bit obvious but, have you considered that at the high concentrations you are trying to measure, there may be significant contributions form natural isotopes towards the internal standard signal. This would be particularly marked if the deuterated standards differ by less than 3 daltons from your native compounds.
Using response ratios to construct your standard curve would result in non linearity at the top end of your curve.

Best Wishes
DWR

[Stryder08]

Yes, sometimes Quadratic curves are the only way to go.