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Dear Group,
I have two sets of concentrationresponse data each for one drug. I use the Emax model in Winnonlin to estimate the EC50 and Emax. The output has the parameter estimate and S.E. for both parameters.
Which statistical test shall I use to show the two EC50 are statistically different or not? How can I calculate the 95% CI for EC50?
Thanks,
Norman

Norman Zhou NSEC fellow, The Ohio State University College of Pharmacy
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Norman,
The most robust test of whether the parameters can be considered the same or different is to fit both sets of data simultaneously. If you have the log likelihood of two models with one model estimating separate EC50s and one model estimating the same EC50 you can see if 2*logL difference is > 3.84 for a Type 1 Error of 0.05 (approx). I don't know if WNL reports log likelihood but if not you can compare the AIC to decide if one model is better than the other but this is not a hypothesis testing method so no P values.
Using WNL's asymptotic standard errors to compute confidence intervals for nonlinear models is not a good idea. The CIs are often asymmetrical for parameters like Emax and EC50 and SE based CIs require the naive assumption that the uncertainty is symmetrical (and usually assumed to be normal).
I would recommend using bootstrap estimates of CIs if you really are interested in the CI and not on deciding if the Emax and/or EC50 is the same for both drugs.
Nick
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Hi Nick,
I appreciate your suggestions. WinNonlin does report AIC, I will be able to use the method you suggested to identify difference of IC50 of the two drugs. One more question pop up is how I can compare IC50 of several drugs.
As discussed several times in this list, bootstrap is a more reliable way to obtain CI, which does not require assuming symmetrical and normal distribution. Yet, I am not aware of how WinNonlin can do bootstrap. I know this can by done by NM and PsN. Can anybody in the list provide any comments on doing bootstrap with WinNonlin?
Thanks,
Norman

Norman Zhou NSEC fellow, The Ohio State University College of Pharmacy
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Hi Nick,
I appreciate your suggestions. WinNonlin does report AIC, I will be able to use the method you suggested to identify difference of IC50 of the two drugs. One more question pop up is how I can compare IC50 of several drugs.
As discussed several times in this list, bootstrap is a more reliable way to obtain CI, which does not require assuming symmetrical and normal distribution. Yet, I am not aware of how WinNonlin can do bootstrap. I know this can by done by NM and PsN. Can anybody in the list provide any comments on doing bootstrap with WinNonlin?
Thanks,
Norman

Norman Zhou NSEC fellow, The Ohio State University College of Pharmacy
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