Y-intercept of the std curve

[Biopharmchat]

Is it okay to change the Y-intercept of the std curve in order to pass the %recovery acceptance criteria, as long as the R2 stays in 0.99 range?

[Don_Hilton]

How do you plan to move the Y intercept? The fitted regression line should represent what is really going on. If you change the formula for the line without any change in the data, you have line that represents some other set of data - no?

[DR]

It either gets forced through 0 or it doesn't.

Since there is a noise component to chromatographic analysis (I think that's the reason), we generally do not force through zero (unless doing a single point standard) and this generally yields a slightly higher r².

[danko]

(unless doing a single point standard) and this generally yields a slightly higher r²

Single point calibration (i.e. one point plus zero) should result in r² = 1.00000. At leat that's what I learnt in school some years ago Always streight line between 2 points.

Best Regards

[Don_Hilton]

Reasons for not forcing zero. If the only issue were noise, it might be fair to force a curve through zero, since there should be exactly no signal for no analyte and one might expect proportional response from a detector for any compund at low concentration. However, in the real world there are at least two factors that will shift the entire calibration curve. One is the presence of some signal in the background that gives a response that is added in with the response for the analyte of interest. A very small peak coeluting with the analyte of interst may do this. The calibration curve will cross the Y axis at some positive value. A second factor is activity in the system. If there are active sites in the system they can eat up to some quantity of compund from an injection. So as long as you have a sample concentration that will saturate the active sites, the active sites will eat the same level of analyte from all levels. At lower sample levels, where the active sites are not saturated, a smaller portion of the sample will be eaten. In a calibration curve, the plot shows a line that should cross the Y-axis at a negative value. If you look at the curve at very low concentration levels (below where the active sites are saturated with analyte), you will see the curve bend toward the origin of the plot.

And on the r squared for a single point calibration: If you do multipe injections of the single point calibration, you will have a non-zero residual for that point... (Proving: If it works the first time, don't repeat it - just publish!!)

[carls]

Is it okay to change the Y-intercept of the std curve in order to pass the %recovery acceptance criteria, as long as the R2 stays in 0.99 range?

How large is the concentration range spanned by the calibration? If covering more than an order of magnitude weighted calibration is commonly used to reduce the influence (leverage) of high concentration samples on the slope and intercept. This will solve the problem of high errors (residuals) at low concentration. Most chromtography data systems support weighted calibration. Implementing weighted calibration in routine/QC testing is a bit more involved (training) than standard linear regression although it is commonly used in many routine bioanalytical assays.

If your calibration does not span a large concentration range you should look for a cause for the high error at low concentration.

[lmh]

An addendum on forcing to zero: there was an LC-GC article (Dolan, I think) about a year ago on the subject, which concluded that if the y-axis intercept differs from zero by a statistically insignificant amount, it's OK to force it to zero, otherwise it isn't. Not a particularly helpful conclusion as forcing to zero when it was already zero doesn't change anything...

An addendum on weighting and making lines fit: an awful lot of calibration curves and responses in methods are not actually as linear as their creators would like to believe. It doesn't help that linearity is so often held up as an essential feature in a validated method. If your detector isn't perfect, and your points lie on a slight curve, it's (in my opinion) completely wrong to force a straight line through the curve, willy-nilly, and then fiddle around trying to get one part of the line to be a better fit than another (finally accepting a systematic error, provided it's not too big). It's better to admit that the relationship between amount and signal is non-linear, fit a suitable curve, and have little or no systematic error.