At the recent BEBPA meeting, in response to the question: ‘If you have a zero dose control on your plate do you include it in your 4PL model?’
78% responded either “no” or “don’t know” or “did not know I could”.
Well you can!
Just add them into the datapoints for the reference and /or the test samples and you have an extra point that will help fix the low dose asymptote.
In this example (deliberately constructed for illustration) there were only 4 data points, so the model had to be linear (left panel). But it is clearly not a good fit, and the curvature can be seen. Parallelism failures might be expected with samples that did not have RP values close to one.
Adding the zero dose control that was already on the plate to the model enabled a 4PL fit (right panel).
Note: this is an extreme example for illustration, normally we would recommend at least six doses for a 4PL.
Note that the zero concentration value is actually at negative infinity, but shown, disconnected, by the y axis to indicate that it is used.
In this extreme example, the extra point enables a 4PL fit to be used making parallelism failures less likely.
In general, even if there are enough doses without it, adding the zero dose results in a better estimate of the lower asymptote and tighter confidence limits on the RP calculations.
Is this just a 3pl?
No, this is not the same as using a 3pl model. A 3pl ties the asymptote to a fixed absolute value. The problem with this is that it undermines a fundamental principle of the relative potency approach, that is, the reference and test items should be able to “float” together. Thus if the assay changes a little such that the whole dose response moves up the vertical axis, this has no impact on the RP. But if you’ve fixed an absolute value for an asymptote by using a 3pl the entire dose response curve will be distorted, and the RP will be invalid. If you use a zero dose well it will have moved with the rest so all is well.
Note about software:
Not all software can handle this. The problem is that the dose is logged for the calculations and log zero is undefined but tends toward negative infinity. Some software just falls over, others just ignore the data. Try it and see. If the curve parameters are unchanged between the fit with and without the zero dose, then the software is just ignoring the information.
QuBAS software (by Quantics) handles this correctly and will accept zero dose as a valid data point and use it in curve fitting.
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