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Fitting a dose-response curve to find the absolute IC50

The concept of an absolute IC50 is not standard, and many find it not to be useful. But if you do, it is not hard to fit a curve to determine it. This EPA document gives the needed equation (which I have generalized a bit, so does not require that the data already be normalized).


Y= Bottom + (Top-Bottom)/(1+10^((LogIC50-X)*HillSlope + log((Top-Bottom)/(Fifty-Bottom)-1))) 

Note the distinction between the parameter Bottom and Baseline. Bottom is the Y value of the bottom plateau of the curve itself. Baseline is the Y value that defines 0% -- maximal inhibition by a standard drug. You'll definitely want to constrain Baseline to be a constant value based on controls. You may also want to constrain Top.

Download the Prism file that fits that equation to make the graph shown above. When fitting data to that equation, don't forget to constrain Baseline and Top to appropriate values determined by controls.  Additionally, this file contains another graph where the data are already normalized to run from 0 to 100%. These data are fit to a simpler equation where Baseline is set to equal zero, and Top is set to equal 100. These are hard wired into the equation, so you don't have to remember to constrain those two parameters to constant values.  

An alternative approach for normalized data

Here is an alternative approach you can use if your data are normalized.

1.Make sure that your data are normalized to some controls. That means the response at the left end (low concentrations) is near 100%, and the response at higher concentrations is above 0%. If the response plateaus at 0%, then an absolute and relative IC50 are the same, and  you can just fit the usual dose-response curve to find the IC50.

2.At the bottom of the data table, add a new row of data. Enter 50 into each Y column. Leave X blank for this row.

3.Use nonlinear regression to fit the data to the log(inhibitor) vs. response (variable slope) curve.

4.On the first (fit) tab of the nonlinear regression dialog, check the option: " Interpolate unknowns from standard curve." Of course, these data are not a standard curve, and there are unknowns. But this option asks Prism to interpolate the X value of the curve when Y=50.

5.On the Constrain tab, consider constraining Top to have a constant value of 100. If you have used good controls to normalize your data, then you know the top plateau of the curve has to be Y=100, so should tell Prism to use that constraint.

6.The IC50 reported as part of the main results table will be the relative IC50.

7.Look on the additional results page of interpolated results to see the value of X when Y=50. This is the absolute IC50.

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