© John Wiley & Sons, Inc.

FIGURE 18-5: The logistic curve that fits the data from Table 18-1.

Calculating effective doses on a logistic curve

One point of special significance on a logistic curve with a numerical predictor is a median effective

dose. This is a dose (X) that produces a 50 percent response, meaning where

, and is

designated ED50. Similarly, the X value that makes

is called the 80 percent effective dose and

is designated ED80, and so on. You can calculate these dose levels from the a and b parameters of the

fitted logistic model in the preceding section.

Using your high-school algebra, you can solve the logistic formula

for X as a

function of Y. If you don’t remember how to do that, don’t worry, here’s the answer:

where log stands for natural logarithm. If you substitute 0.5 for Y in the preceding equation because

you want to calculate the ED50, the answer is

. Similarly, substituting 0.8 for Y gives the

.