Imagine a logistic regression model based on a study of participants taking a drug at different doses

where the predictor is level of drug dose, and the outcome is that it produces a therapeutic response.

The model has

and

mg/dL. In this case, the ED80 (or 80 percent effective

dose) would be equal to

, which works out to about 207 mg/dL.

Calculating lethal doses on a logistic curve

When death is the outcome event, the corresponding terms are median lethal dose (abbreviated LD50)

and 80 percent lethal dose (abbreviated LD80), and so on. To calculated the LD50 using the data in

Table 18-1,

and

, so

, which works out to 420

REMs. An LD50 of 420 REMs dose of radiation means an individual has a 50 percent chance of dying

shortly after being exposed to this level of radiation.

Making yes or no predictions

If you fit a logistic regression model, then learn of the value of predictor variables for an individual,

you can plug them into the equation and calculate the predicted probability of the individual having the

outcome. But sometimes, you are trying to actually predict the outcome — whether the event will

happen or not, yes or no — to an individual. You can do this by setting a cut value on predicted

probability. Imagine you select 0.5 as the cut value, and you make a rule that if the individual’s

predicted probability is 0.5 or greater, you’ll predict yes; otherwise, you’ll predict no.

In the following sections, we talk about yes or no predictions. We explain how they expose the ability

of the logistic model to make predictions, and how you can strategically select the cut value that gives

you the best tradeoff between wrongly predicting yes and wrongly predicting no.

Measuring accuracy, sensitivity, and specificity with classification tables

Software output for logistic regression provides several goodness-of-fit measures (see the earlier

section “Assessing the adequacy of the model”). One intuitive indicator of goodness-of-fit is the extent

to which your yes or no predictions from the logistic model match the actual outcomes. You can cross-

tabulate the predicted and observed outcomes into a fourfold classification table. To do this, you

would ask the software to generate a classification table for you from the data based on a cut value in

the predicted probability. Most software assumes a cut value of 0.5 unless you tell it to use some other

value. Figure 18-6 shows the classification table of observed versus predicted outcomes from

radiation exposure, using a cut value of 0.5 predicted probability.

From the classification table shown in Figure 18-6, you can calculate several useful measures of the

model’s predicting ability for any specified cut value, including the following: