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2008102128

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[求助] 四参数方程 IC20，IC80，IC10的计算问题

The four-parameter logistic equation used for the standard curve fitting is correct:
Y = %(B/B0) = A2 + (A1-A2/((1+(X/X0)expP).

However, the following assumptions and operations should have been taken into account and applied in a proper calculation procedure, but they were not:

* As known, the X0 value provided by the curve fitting IS DIRECTLY the IC50 value, without any modification. Therefore, the true is IC50 = X0 = 0.46609.

* As usual for a real ELISA standard curve, in the depicted salbutamol standard curve "A1" is not actually the theoretically ideal "100" and "A2" is not actually the ideal "0". Therefore, in order to accurately calculate the relevant inhibition percentages on the experimental curve, the reference value could not be as simple as "100", as authors wrongly applied. Instead, the difference between the maximum and the minimum asymptotes (A1 - A2) should be considered as the reference (100%) and the background signal ("A2" value) should always be added. From simple arithmetic operations it is deduced that the correct "Y" values at 50%, 90%, 80% and 20% inhibition should be calculated as follows:
o For IC50 value: Y(50%) = 0.5*A1 + 0.5*A2
o For IC10 value (LOD): Y(90%) = 0.9*A1 + 0.1*A2
o For IC20 value (range): Y(80%) = 0.8*A1 + 0.2*A2
o For IC80 value (range): Y(20%) = 0.2*A1 + 0.8*A2
From these equations, using the A1 and A2 values provided by the authors:
o For IC50 value: Y(50%) = 48.583
o For IC10 value (LOD): Y(90%) = 84.812
o For IC20 value (range): Y(80%) = 75.756
o For IC80 value (range): Y(20%) = 21.407

* To find out the relevant standard curve parameters it is necessary to interpolate the correct "Y" values in the X=f(Y) equation. This equation was correct as used by the authors, but the "Y" values introduced were incorrect. When the appropriate "Y" values (see above) are used, the following results are obtained:
o IC50 value = 0,466 µg/L (exactly the same as "X0", as it should be)
o IC10 value (LOD) = 0.021 µg/L
o IC20 value (range, minimum) = 0.065 µg/L
o IC80 value (range, maximum) = 3.337 µg/L

不理解的是From simple arithmetic operations it is deduced that the correct "Y" values at 50%, 90%, 80% and 20% inhibition should be calculated as follows:
o For IC50 value: Y(50%) = 0.5*A1 + 0.5*A2
o For IC10 value (LOD): Y(90%) = 0.9*A1 + 0.1*A2
o For IC20 value (range): Y(80%) = 0.8*A1 + 0.2*A2
o For IC80 value (range): Y(20%) = 0.2*A1 + 0.8*A2
这个是什么意思

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