Chromatography Forum

I need to calculate lod/loq by regression. It has been a few years since i have done this. I've found equations, e.g., lod = 3.3SD/Slope

SD has been defined for blank, residual sd of line, or sd of y intercepts. STats have been more than a few years ago. So, I need to be steered in the right direction.

Thanks!
Wanda

In this context, you want the SD of the y-intercept. The general idea of limits of detection is what you can confidently distinguish from zero. An amount of zero is at the y-intercept; the SD that you can measure is for the peak response, so dividing by the slope gives the SD of the amount. The factor of 3.3 is for the confidence you want in your LOD.

Two cautions. One, make sure you have enough data points to generate a meaningful SD: at least 3 reps at 3 levels. Two, check that the linear fit is satisfactory; the least-squares method of line-fitting treats noise and nonlinearity the same, but you should not.

Not to say that the other measures are less useful, only that they are used for different approaches to the same subject.

Thanks, Mark. Your explanation made the math make more sense for the derivation of the equations. However, I'm still confused about the sd at the intercept. I have never done this, and am not sure how to approach this calculation. the next is what to use other than least squares. I've not heard of using anything other; I guess we assume that at a narrow range with multiple injections things would be linear. How do you account for noise, and is it that necessary?

We actually did LOD/LOQ by the 3(or10)*S/N, but the boss didn't like the #, so I said I'd calculate them.

The SD of the Y-intercept will be calculated for you in Excel by the LINEST function (see Excel help for more); Excel calls this the standard error of the constant or s.e.b.

Least-squares can be used to fit polynomials to the data. The whole discussion of nonlinearity is complex and frustrating because the math tools are clumsy, while your eye and brain can spot it immediately. Your intuition is right, restrict the range and stay close to the detection limit.

By noise, I meant random statistical error; that was a poor choice of words. I meant to say that least-squares does not distinguish between normal random error and a systematic misfit of the line to non-linear data.

Personally, I like the DL = 3*S/N approach too.

thanks again! SigmaPlot does it almost automatically, so once I knew what i was looking for, bingo! It worked!

Wanda