Weighting with 1/x^WE, 1/y^WE or 1/s^WE

[dresdentl]

Sometimes, weights (g) are calculated from the y or x-values. They often recommend to use 1/y^WE, because these are more closely related to the standard deviations (s) of y. If you use this procedure, you assume that relative standard deviations are the same for all concentrations, which is not realistic.

On the other hand, you can calculate g from the true standard deviations, which you know from larger validation data. According to my experience, you can get a good calibration curve if you use the real s-values.

I'm skeptic about the use of 1/x^WE, 1/y^WE.

Has someone a different opinion?

[dresdentl]

According to my knowledge, the Chromatography software which I use, doesn't offer the possibilty of 1/s^WE-weighting. There only 1/x^WE or 1/y^WE is possible. WE can be 1 or 2.

I calculated via Excel 1/y^WE and 1/s^WE. 1/s^WE leads to better results for accuracy.

[MSCHemist]

We usually just use equal weight (simple dad peak areas). However, recently I began using weight is linear inversely proportional to amount for one of my methods. There is an option in Chemstation for that.

[MaryCarson]

I calculated via Excel 1/y^WE and 1/s^WE.

OK. Idiotic question here: Can you do a 1/x^2 weighted regression analysis using Excel?

Really, I just want to get some standard errors of the intercepts (so I can do the LOD and LLOQ calculations mentioned in another thread), but I use weighted regression for the calibration curves, and the chromatography software I'm using only spits out slope, intercept, and Rsquared.

[lmh]

MaryCarson, with Excel, only with extreme difficulty. Two suggestions: (1) name your chromatography software. Someone here might know whether it does indeed calculate the s.d. of the regression line in some way, and if so, what it calls it, and where it hides it. (2) Is it possible to do your LOD and LOQ with shortened calibration curves containing only a few levels around the LOD and LOQ? Weighting will be less relevant to these than a full calibration curve up to the upper limit, so you may be able to use a non-weighted regression. I think this is still valid for your method, but do check with someone who knows. The reason I think it's valid (but I'm not sure, and would value being corrected by a statistician) is that what you really want to know for a LOD is the s.d. of the measurement at the LOD, so that you know that it is statistically unmistakeable with zero (there is definitely something there). This should depend on the scatter of points at a low concentration. If you weight a calibration curve differently, it may pass through the points differently, but the scatter of a set of points at one concentration should be unchanged. Accuracy is different, precision the same? In any case, if the curve is seriously and repeatably displaced it suggests systematic errors that mean the fit is wrong, in which case LOQ is irrelevant anyway.

[MaryCarson]

Weighting is definitely needed--it's a mass spec method and calibrants go over 4 orders of magnitude. Yes, for my QAU audit I said they could estimate low end (where all the action is, of course) calibration by just using the bottom 4 calibrants without weighting. They did that, and their results were close enough to mine that they were satisfied. However, they didn't look for SE-intercepts.

I caved, got a copy of SAS last week, and an SAS calibration program someone else wrote, and am in the process of learning to use it. On the plus side, the SAS calibration curves do seem to replicate EXACTLY (5+ digits) the intercepts and slopes generated by chromatography data system (a program not likely to be used by very many other folks on this forum). Gives a warm, fuzzy feeling for the part of me that thinks software validation (or is it qualification?) is important...

[lmh]

(1) Fully agreed, never for a moment would I suggest not using weighting over your full calibration curve; I only suggested missing out the weighting when looking at low concentration points for LOD.
(2) Thanks for reporting back that your QA audit were OK about this; locally here the QA people are less aware of specific chromatography issues, so I appreciate feedback from those in the know.
(3) Yes, I remember the warm, fuzzy feeling I got when I realised the standard error of the curve as calculated by Chemstation agreed to 5+ digits with Excel's linest function. It's nice when you get the feeling software calculates things consistently.