by
lmh » Wed May 08, 2019 10:48 am
There's a risk of restarting the entire debate here, but perhaps that's no bad thing; more than a decade has passed, and opinions change.
There is some confusion about the role of multiple points on a calibration curve. You have two sources of error.
(1) Random variation
(2) A systematic difference between the true curve of response versus concentration, and your calibration curve (which is an approximation to the true curve of response versus concentration). (I assume concentration but the situation is just the same if you're measuring amount).
You need to get a result that is sufficiently close to the correct value. If you are suffering from random variation, then multi-point calibration is not going to rescue you, since the overall error results both from inaccuracies in the calibration curve, and inaccuracies in the measurement of the sample. In this instance you need to replicate calibration and also sample measurements, until the standard error on the mean of the multiple measurements is small enough compared to your required precision. In this particular situation, the calibration curve's contribution to the overall error depends on its standard deviation at the concentration of the sample. Merely adding more points might not improve the situation. For example, if you're currently using 1 point calibration at 100nM, and you add a couple more calibration points at 10 and 20uM, the resulting curve will be almost unchanged around 100uM, so any random error in the 100uM point will have just the same effect as before; the standard deviation of the curve at 100uM is unchanged, but you have no way to know this. You'd need more replicates of the 100uM point.
Multiple points in the calibration curve are the thing that solves problem (2). It's quite simple: over the region in which you intend to measure samples, the deviation between the true curve and the calibration curve must be smaller than the acceptable precision (allowing also for additional errors from random variation). Single point calibration is, as Peter Apps said, actually 2-point calibration using the origin as a spare point, so if all your measurements are within a few percent of the calibrant value, and you've proven that the curve is approximately linear at the calibrant value, and points towards the origin, then your single-point calibration is safe. If the calibration curve is proven to be approximately linear at the calibrant value but it's not pointing towards the origin, then you will need at least two points, to find the slope and intercept.
The main point is you don't have to worry what the curve does outside the region in which you intend to use it, but you do have to worry about what it does at all points between your lowest and highest samples. This means that you need enough calibration points to define the curve. You cannot, unfortunately, set a global rule of what this is, or at least not without knowing about the curvature and characteristics of the detector. I suppose it might be possible to assume that all detectors follow smooth curves, not strange S-bends (though this is a bit dangerous; MS can happily do an S-shape), and state some sort of rule of starting with 3 calibration points, A, B and the average of A and B, and determining the number of required calibration points based on the deviation of the mean of A and B from the standard containing the mean concentration (does that make sense?). I.e. how far does the curve that we measure deviate from a straight line that we can easily fit? But it's all a bit guessworkish. Good statistical packages can actually show the confidence intervals on a regression, which is really what you want to know. If I think my curve is sufficiently well defined by 5 points, how far off could it be?
In practice, use multiple replicates of points at single concentrations if your assay is to be used over a narrow range, but you are fighting against random errors for precision. Use multiple points over an appropriate range if you're measuring samples over a wider range, and fighting a curvy calibration curve. I don't know how you put that in concrete terms in a document intended for less-informed readers!