# What is the formula to establish ec50 reproducibility with respect to dose response curves for some drug?

The EC50 is determined by fitting a standard curve to the experimentally obtained control values for each dose response curve using some software that does trial and comparison until satisfactory(nonlinear regression).

In the literature, it is mentioned that experimentally obtained control values for the dose response curves, are EC50 reproducible. To my current understanding meaning that EC50's obtained for different for several dose response curves are actually 'close enough'(in some formal statistical sense) together. Is there some procedure or formula for formally establishing EC50 reproducibility?

Thank you :)

• Welcome to Biology SE. What do you mean by "trial and error"? EC50 analysis is usually done by nonlinear regression, typically with some sigmoid function. There are many methods for estimating variances / confidence intervals for parameters in nonlinear regression, so if you can give a bit more details about your specific model and data, that might help. Also, the Statistics SE might be appropriate for your question. – Roland Jul 14 '16 at 7:03
• Hi Roland, thanks for your reply! Actually from your reply I can phrase better what I meant to ask. Basically a sigmoid is fitted to experimental data using nonlinear regression as you said for each experiment. Now the aim is to conclude reproducibility of these sigmoids for added experiments(dose response curves). So basically comparing the fit parameters(EC50, slope) and establishing that they follow a concentrated pattern. Some researchers refer in articles to this as 'EC50 reproducibility'. I was wondering whether there are widely used methods of establishing this reproducibility. – jfs Jul 14 '16 at 8:52
• And the data itself is confidential btw. But the model used is basically a sigmoid as you mentioned. Thank you for your reply. – jfs Jul 14 '16 at 8:53
• If you have multiple EC50 estimates from separate independent measurement series, then it should be easy to see if they are in agreement? You could do mean +/- std dev of the EC59 values (assuming a normal distribution), but personally I prefer just tabulating/plotting the data. If the data is tight, is usually obvious. The situation is more tricky when there is only one measurement series and some variances estimate must be derived from the regression analysis. – Roland Jul 14 '16 at 21:31
• The DRC package, in the paper from my answer, includes functions to directly compare parameters such as the slope, from nonlinear regressions. – Michael_A Jul 14 '16 at 23:10

The different models that can be used to fit the curves do differ. The linked paper and this website outline the differences; the discussion revolves around an R package called DRC but much of the information is generally applicable. Modelling can also be used to estimate ED50.
(VALUE - topdrugmean)/(nodrugmean-topdrugmean)