I have calculated IC50 using Hill equation and non-linear regression. the dose response is fluorescence measurement for 20 minutes. Kindly guide me in this regard.
These attachments should be able to handle your needs. Best wishes David Booth
In my experience, the standard error of a parameter calculated by nonlinear regression is reported by the nonlinear regression computer program. The documentation for how this calculation is performed may be available from the company that made the program. Here are 2 very technical articles on this subject:
Article Analysis Of Nonlinear Regression Models: A Cautionary Note
https://stat.ethz.ch/~stahel/courses/cheming/nlreg10E.pdf
The standard error of a parameter calculated by nonlinear regression should not be confused with the standard error of the mean (SEM). In order to calculate the SEM of the IC50, you will have to measure the IC50 multiple independent times and calculate the mean of the measurements. The SEM is the standard deviation of the mean divided by the square root of the sample size (the number of IC50 measurements used to calculate the mean.)
Dear Adam B Shapiro , regarding your last paragraph about the SEM: If the different concentrations are given to independent samples, I thought the standard error of the estimate (EC50) represents what you call the SEM (that, accroding to you, would need a set of several fitted curves). I would accept your statement for cases where the series of concentrations is tested non-independently, e.g. using a single cell cuture (n-well plate).
What do you say? Do you have any references for the statement? Thank you!
Supporting what Adam B Shapiro said, this link may help with a very simple explanation (I think that statistical treatment for IC50, is quite similar to LD50, LC50 or EC50):
https://www.graphpad.com/guides/prism/latest/curve-fitting/reg_why_prism_fits_the_logec50_rat.htm
Best regards
Considering an IC50 to be a calculation made with a series of inhibitor concentrations and corresponding responses, each of the multiple IC50 measurements used to calculate the SEM of the mean IC50 requires an independent measurement, preferably with a separate set of inhibitor concentrations to capture variation in the preparation of the dilutions. (There are various levels of experimental variation that could be captured if one wished, including the variation in weighing out the solid used to make the inhibitor stock solution, variations between synthetic batches of the inhibitor, and variation between operators.) In contrast, the standard error of a single IC50 measurement is a measurement of the scatter in the data from a single set of inhibitor concentrations.
Sure, the measurements capture technical variation, but for concluding the effect one also needs the information about biological variation. If the technical variation is large compared to the biological variation, varying the preparations of the inhibitor is very relevant, as you say. I am used to think of biological variation being way larger than technical variation, but you are correct: there can be a large variance between preparations, and biological variation could be small if the target system is a stable cell line, for instance.
So please let me rephrase my question:
If you measure the dose-response curve using, say, 10 different animals, and each animal gets a different dose of an independently prepared inhibitor solution, so that each data point of this curve is independen from all others by animal and by inhibitor preparation: would then the SEM of the IC50 determined from this one curve be a (more or less) correct measure of the SEM?
No. It would be the standard error of a single IC50, not the standard error of the mean of the IC50, because it is a single IC50 measurement from a single dose-response curve. To have a mean (average), you require multiple measurements of the same parameter.
Interesting question of Jochen Wilhelm. I think that If the experiment is repeated twice or more times with independent preparations of the concentrations of inihibitor solutions each time and different animals for each solution, you will be capable to measure the aleatory effects in X and Y respectively. Then the SEM will represent the variation for the average IC50 due by the effect of the two variables in different experiments. But that it could be possible only if the true concentration of each inhibitor solution can be determined. If the concentration of the inhibitor solutions can not be measured exactly, you must asume that all different preparations of the same concentration will be free of experimental or technical errors, then you will have a model with no aleatory effect in X and only a single measure of the IC50, without an average IC50 and consecuently no SEM can be calculated.
Best regards.
I think you are correct, but I will need some time to pin this down in my head. The non-negligible uncertainty in the effective concentration of the inhibitor seems to be the key. I would check this in some simulations to get a better understanding, but I don't have the time for this atm. Thank you for your help!
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