175

0

702

1

232

0

705

1

266

0

774

1

299

0

853

1

303

1

879

1

326

0

915

1

404

1

977

1

In Table 18-1, dose is the radiation exposure expressed in units called Roentgen Equivalent Man

(REM). Because Table 18-1 is sorted ascending by dose, by looking at the Dose and Outcome

columns, you can get a rough sense of how survival depends on dose. At low levels of radiation,

almost all animals live, and at high doses, almost all animals die.

How can you analyze these data with logistic regression? First, make a scatter plot (see Chapter 16)

with the predictor — the dose — on the X axis, and the outcome of death on the Y axis, as shown in

Figure 18-1a.

© John Wiley & Sons, Inc.

FIGURE 18-1: Dose versus mortality from Table 18-1: each individual’s data (a) and grouped (b).

In Figure 18-1a, because the outcome variable is binary, the points are restricted to two horizontal

lines, making the graph difficult to interpret. You can get a better picture of the dose-lethality

relationship by grouping the doses into intervals. In Figure 18-1b, we grouped the intervals into 200

REM classes (see Chapter 9), and plotted the fraction of individuals in each interval who died.

Clearly, Figure 18-1b shows the chance of dying increases with increasing dose.

Fitting a function with an S shape to your data

Don’t try to fit a straight line if you have a binary outcome variable because the relationship is

almost certainly not a straight line. For one thing, the fraction of individuals who are positive for

the outcome can never be smaller than 0 nor larger than 1. In contrast, a straight line, a parabola,