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 Pros and cons of normalizing the data

The dose-response model has four parameters: the bottom plateau, the top plateau, the EC50, and the slope factor (which is often constrained to a standard value).

The main goal of fitting the dose-response curve in many situations is to determine the best-fit value of the EC50, which is the concentration that provokes a response halfway between the top and bottom plateaus. If those plateaus are not well defined, the EC50 will be very uncertain. Think of it this way: If you have not defined "100" and "0" very precisely, you also have not defined "50" precisely, and therefore cannot determine the EC50 precisely. If your data doesn't really define the plateaus and you don't have any control data that assesses the top and bottom plateau, then there is no way to determine the EC50 precisely.

Many experiments include controls to measure the maximum and minimum possible response. There are two ways to include these controls in your analysis:

Constrain the Top and Bottom to values determined from your controls. Then only fit the EC50 and slope.

Normalize your data so responses run from 0 to 100, using your controls to define 0 and 100 using Prism's Normalize analysis. Then use nonlinear regression to fit  a "normalized response" model. These models don't fit the bottom and top plateaus, but rather force the bottom plateau to equal 0 and the top plateau to equal 100.

Include all the data in the fit. For the control defined by the absence of drug, enter a very low concentration as X, perhaps two orders of magnitude less than the smallest concentration you actual use. For the nonspecific control defined by another drug, enter a large concentration, perhaps two orders of magnitude larger than your largest concentration. Now all the data are in one table, with sensible X values.  Use nonlinear regression to fit all four parameters (Bottom, Top, EC50 and slope). The blank and nonspecific data help define the curve, but don't overwhelm the calculations as they do with the first two methods listed above. Weimer and colleagues suggest using this method (1).

Notes:

It is not necessary to normalize before fitting dose-response data. In many cases, it is better to show the actual data.

You can only plot several different dose-response curves on one graph using one axis when they are comparable. If the different experiments measured different variables, normalizing puts them into comparable units. This can be useful.

Whether or not you choose to normalize your data, you still need to choose how to fit the data. Do you want Prism to find best-fit values for the Top and Bottom plateaus? Or do you want those plateaus to be determined by control data? This is an important decision.

If you normalize your data, you can choose one of the normalized dose-response equations. These constrain the the curve to run from 0% to 100%. This kind of constraint only makes sense, when 0% and 100% are defined by good control data. If the definitions of 0% and 100% are ambiguous, then so is the definition of "50%", and thus the EC50 is also ambiguous.

Just because you chose to normalize your data doesn't mean you must constrain the curve to run from 0 to 100%. It can still make sense for Prism fit those two plateaus, so all the data (and not just the controls used to normalize) are used to fit the plateaus. Weimer and colleagues show that this is a good way to analyze data (1).

If you don't normalize your data, you can use the Constrain tab to fix Top and Bottom to values determined from control experiments. So the decision to constrain Top and Bottom is quite distinct from the decision to normalize your data before fitting.

It is possible to fix one of those parameters (Top or Bottom) to a constant value but not the other.

If you normalize, don't also choose to differentially weight the data. Once you subtract off the baseline (nonspecific) values, the variance among Y replicates is unlikely to be proportional to Y.

## Reference

1.Weimer, M., Jiang, X., Ponta, O., Stanzel, S., Freyberger, A., and Kopp-Schneider, A. (2012). The impact of data transformations on concentrationâ€“response modeling. Toxicology Letters 213: 292â€“298.