Example: Global nonlinear regression (dose-response curves)
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Example: Global nonlinear regression (dose-response curves) |
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1. Create the data table From the Welcome or New Table dialog, choose to create an XY data table, and select the sample data "EC50 shift by global fitting". Choose to plot the mean with error bars defined by the range.
2. Inspect the data The sample data may be partly covered by a floating note explaining how to fit the data (for people who are not reading this help page). You can move the floating note out of the way, or minimize it.
The X values are the logarithm of the concentration of agonist. The Y values are responses, in duplicate, in two conditions. 3. View the graph
4. Choose nonlinear regression Click Alternatively, click the shortcut button for nonlinear regression.
5. Choose a model On the Fit tab of the nonlinear regression dialog, open the panel of inhibitory dose-response models and choose: log(inhibitor) vs. response -- variable slope. For now, leave all the other settings to their default values. Click OK to see the curves superimposed on the graph.
6. Inspect the results
The control results are labeled ambiguous. This means that Prism is unable to find a unique curve through the data. Lots of other sets of parameter values would lead to curves that fit just as well. You can see which parameters are ambiguous by looking at the 95% confidence intervals. Instead of reporting an interval, Prism reports 'very wide' for the Bottom and logEC50. The data do not define a bottom plateau for the control (circles) data set, so its best-fit value is ambiguous. The EC50 is the concentration that gives a response half way between the bottom and top plateaus of the curve. If the bottom is ambiguous, so is the EC50. The treated curve is not labeled 'ambiguous', but the confidence intervals are wider than you'd like. 7. Go back to the dialog, and share three parameters You can get much better results from this data set if you are willing to assume that that the top and bottom plateaus, and the slope, are the same under control and treated conditions. In other words, you assume that the treatment shifts the EC50 but doesn't change the basal response, the maximum response, or the Hill slope. Return to the nonlinear regression dialog by clicking the button in the upper left of the results table.
Go to the constraints tab and choose to share the value of Bottom, Top, and HillSlope. When you share these parameters, Prism fits the data sets globally to find one best-fit value for Bottom, Top and HillSlope (for both data sets) and separate best-fit values for the logEC50.
8. View the revised graph and results
The fit is no longer labeled 'ambiguous' and the confidence intervals are much tighter. 9. View the revised graph and results From the results in step 8, you can compute what you want to know -- the ratio of the two EC50 values. But Prism can calculate this value directly. Go back to the analysis parameters dialog, and on the Fit tab, change the equation to "EC50 shift" (also in the specialized dose response section). Accept all defaults and click OK. The graph will look identical, as the model is equivalent. But now, rather than fitting two logEC50 values, Prism fits one and also fits the ratio.
This equation was designed to do exactly what is needed for this example. Read about how this equation was set up, so you can construct your own equations when necessary. |
