Chromatography Forum

Hi,

Looking for a little help if possible.

I have a 6 point calibration that has lower accuracy at the low end (about 105-110% of true value). Verified by 6 independent calibration series' made on different days. Accuracy at my lowest point is always the same.

I have done an F-test with 6 independently prepared standards at the top, mid and bottom range of the calibration and shown the data is heteroscedastic and the sum relative error is the lowest with 1/amount2 weighting.

Out of interest I also decided to try a Quadratic fit with no weighting and it also gives much increased accuracy; even better than the linear weighting above for all curves and brings the low calibration point accuracy down to around 102%. It has also improved LLOQ accuracy from 115% to 101%.

Is there a standard way to choose which route I go with; quadratic fit or linear weighting? Detector is a D.A.D which I thought were always linear? Samples are derivatised...could this be a source of non-linearity?

Thanks for any help.

Usually depends on the regulatory body you report to and/or the lab director. If there's no guidance from either, then *shrug*

So many try to stay away from quadratic fit, but often times it is the best fit, especially when you can see the points form a nice smooth curve instead of a straight line.

Using quadratic to "fix" a calibration that has scatter of points above and below the line over the calibration range is always bad. But often we see a nice bow in the points and that is where quadratic works best. The downside to quadratic is when any point falls outside of the range of the calibration. I have seen some curves that bow so much that once you get a little above the response of the upper point, your calculated results begin to decrease and if the response is high enough above the upper calibration point the result will even go negative. If an analyst is not paying attention to the overall size of the response and only the final value it can lead to a false report of not detected when is reality it is a very large result.

As for a DAD always being linear, as with all detectors they are linear over a certain range, but not for all ranges. If there is anything present that either enhances or reduces the response a tiny amount, then it will cause a deviation at low concentrations, and once saturation is reached, there are deviations at the high end of the range.

You also have to take into account everything happening to the analyte as it goes through the system. With my GCMS run that has over 150 analytes in it, I will have one analyte that gives less than 1% RSD on an average response factor calibration or near 1.0 r2 while another analyte will give 50% RSD and a 0.8r2 while the quadratic fit is 0.997. Same run and same conditions but each analyte responds to the complete system differently, and same can happen for LC and UV detectors. Beer's Law works in a perfect world, but just as in Physics lab, not all real life situation are in a vacuum on a frictionless surface.

So many try to stay away from quadratic fit, but often times it is the best fit, especially when you can see the points form a nice smooth curve instead of a straight line.

Using quadratic to "fix" a calibration that has scatter of points above and below the line over the calibration range is always bad. But often we see a nice bow in the points and that is where quadratic works best. The downside to quadratic is when any point falls outside of the range of the calibration. I have seen some curves that bow so much that once you get a little above the response of the upper point, your calculated results begin to decrease and if the response is high enough above the upper calibration point the result will even go negative. If an analyst is not paying attention to the overall size of the response and only the final value it can lead to a false report of not detected when is reality it is a very large result.

As for a DAD always being linear, as with all detectors they are linear over a certain range, but not for all ranges. If there is anything present that either enhances or reduces the response a tiny amount, then it will cause a deviation at low concentrations, and once saturation is reached, there are deviations at the high end of the range.

You also have to take into account everything happening to the analyte as it goes through the system. With my GCMS run that has over 150 analytes in it, I will have one analyte that gives less than 1% RSD on an average response factor calibration or near 1.0 r2 while another analyte will give 50% RSD and a 0.8r2 while the quadratic fit is 0.997. Same run and same conditions but each analyte responds to the complete system differently, and same can happen for LC and UV detectors. Beer's Law works in a perfect world, but just as in Physics lab, not all real life situation are in a vacuum on a frictionless surface.

Thanks so much for the reply James.

My calibration range 0.1 - 6ppm...so hardly huge so I thought I'd be fine. But 6 entirely independent calibration sets all show extremely high accuracy when set to quadratic. Approximately 101% accuracy at my two lowest calibration points, whereas linear is 110%~ at the same two points.

I wondered if this was due to the range, so I made 6 independent 6 point calibration sets from 0.1 - 2.5ppm. Accuracy is increased at the low end compared to the 6ppm calibration runs, but again, setting it to quadratic tightens up that low end accuracy so much more than linear.

The linear calibration example below (0.1-6ppm) doesn't scream quadratic as say an IC suppressed anion calibration curve does, but the data doesn't lie.

Curve as linear


Same curve as quadratic


But 0.1-6ppm isn't exactly a range I'd expect a UV detector to deliver a non-linear data set?

Maybe not. But it isn't always the UV detector that causes the non linearity.