262 PART 5 Looking for Relationships with Correlation and Regression

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 cal-

culated the LD50 using the data in Table  18-1, a

4 83

.

and b

0 0115

.

, so

a b

/

.

/ .

4 83

0 0115, 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 probabil-

ity. 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 stra-

tegically 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 pre-

dicted 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 clas-

sification 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 use-

ful measures of the model’s predicting ability for any specified cut value, includ-

ing the following: