Using log-log regression with quantitative LC-MS/MS

[bbkf]

I have developed a method to measure compound X (If you really need the name of the compound, i could give it but we are about to publish the method.)

I had problems with linearity where the calibration curves generated were "quadratic". Calibration range was 50ng/mL to 5000ng/mL. This method also included five hydroxy metabolites with calibration range from 1ng/mL to 500ng/mL. Even the hydroxy metabolites generated "quadratic" like calibration curves. Is this common with LC-MS/MS (we are using a heated ESI source)? I know for a fact that this is a MS related issue because we have a PDA detector in line and the calibration curves for the major compound (the one that is calibrated from 50ng/mL to 5000ng/mL is linear...we need the MS for the metabolites).

Second part of my question:

my chromatography software has a curve fit option for "linear log-log" and "quadratic log-log". When using these log-log functions, 1) the R-squared value for my curve increases AND 2) the backcalculated values for my lowest calibrators actually fall within an acceptable %bias less than 10% (where without the log-log function the lowest calibrators are 100+% off). I have not seen much on using log-log regression analysis for methods like the one i developed. Are these ok to use if it makes your data work better?

[lmh]

I'm no expert, but I'll read this with interest as I certainly see, very commonly, much curvier calibration curves from MS than from UV. I usually use a quadratic fit. Incidentally, if you can use an internal standard method, the problem usually disappears (along with all worries about cosuppression, varying ionisation efficiency etc.).

The more parameters your curve-fit function has, the more likely it is that it will be able to fit itself to the calibration data, whether they are right or wrong. The R-squared will almost certainly improve as you move to more complicated curves.

My attitude is that a calibration fit should not be more complicated than it needs to be, but it's completely wrong to choose a function that doesn't follow the points. So putting a straight line calibration curve through a curving set of points is plain daft.

[Uwe Neue]

There is an interesting aspect of the log-log versus lin-lin curvefit. On a log-log fit the relative error is assumed to be constant, while on a lin-lin fit the absolute error is assumed to remain constant. With the experimental protocols that most of us are using, the relative error is commonly constant, not the absolute error.

[Christian Eckhoff]

Read this paper:

Singtoroj et al., J Pharmac Biomed Analys 41 (2006) 219-227

You will see that a linear fit of log-log transformed data with no weighting factor provided the best overall results. What data system do you have? I am interested because it seems to allow you to transform your data before regression analysis.

For regulated work you should probably stick with a linear fit model and no data transformation. You can use a weighting factor if the bottom end of the calibration needs some help. If the non linear peak response is severe you can shorten the calibration range and validate dilution factors for samples with concentrations higher than the ULOQ.

[Alp]

You might also wish to see if the same type of regresssion consistantly gives better fit over several calibration curves. Sometimes you will find that on one run a more linear fit is found and on another run it is a bit quadratic.

Alp

[bbkf]

Read this paper:

Singtoroj et al., J Pharmac Biomed Analys 41 (2006) 219-227

You will see that a linear fit of log-log transformed data with no weighting factor provided the best overall results. What data system do you have? I am interested because it seems to allow you to transform your data before regression analysis.

For regulated work you should probably stick with a linear fit model and no data transformation. You can use a weighting factor if the bottom end of the calibration needs some help. If the non linear peak response is severe you can shorten the calibration range and validate dilution factors for samples with concentrations higher than the ULOQ.

Thank you for that literature reference!

AND

THANK ALL of you for you help!

[tima]

I used to process data sets of LC/MS/MS data on clinical trial drugs. We submitted our data to the FDA and even went through an FDA audit during one of our studies. OK ....we used quadratic fit throughout and because we had SOP's that defined our acceptance criteria for each batch, using a quadratic curve was accepted. Our QC's passed, our calibration met our acceptance criteria (+- 15% on each calibration pt, 20% at the LOD and R2 of at least 0.998)

More importantly, LC/MS/MS ESI mode will have a quadratic response at higher concentration due to the nature of the ionization process. As the droplet size decreases as desolvation is occurring there is a competitiveness between ionized species and the sample. So response or ion formation will decrease in a quadratic manner It part of the LC/MS/MS and is expected at higher concentration of analyte. Some one correct me if I'm wrong. Timothy

[Alp]

Your explanation sounds good tima, but I always thought that it was the electron multiplier (detector) that did not show linear response over larger ranges.

This droplet idea may be worth looking into. Maybe it is a little of both effects?



Alp

[bbkf]

I've calibrated my method with many ranges during pre-validation to check out why I was seeing a quadratic response.

The method was quadratic with the range of 25ng/ml to 1000ng/mL and also quadratic from 1ng/mL to 100ng/mL (both sets of data had 9 points in the curve).

i still don't know why the response is quadratic....it just is. I have lots of data showing that the quadratic log-log regression is best for this particular method, so I guess that's the way to roll...

[tima]

I wish I could provide a reference but this is fundamental. As the electro spray droplet is nebulized (desolvation) there are limits to the proton transfer as the droplet becomes smaller and smaller. So the response becomes a quadratic. Timothy