Biostatistics For Dummies, 2nd Edition (Monika Wahi, John Pezzullo)

CHAPTER 18 A Yes-or-No Proposition: Logistic Regression 263

» ^{Overall accuracy:}^{This refers to the proportion of accurate predictions, as}

shown in the concordant cells, which are the upper-left and lower-right. Of the

30 individuals in the data set from Table 18-1, the logistic model predicted

correctly 13

= 0.87, or about 87 percent of the time. This means with

the cut value where you placed it, the model would make a wrong prediction

only about 13 percent of the time.»

» ^Sensitivity:^{This refers to the proportion of}^yes^{outcomes predicted accu}^-

rately. As seen in the upper-left cell in Figure 18-6, with the cut value where it

was placed, the logistic model predicted 13 of the 15 observed deaths (yes

outcomes). So the sensitivity is 13 15

= 0.87, or about 87 percent. This means

the model would have a false-negative rate of 13 percent.»

» ^Specificity:^{This refers to the proportion of no outcomes predicted accurately.}

In the lower-right cell of Figure 18-6, the model predicted survival in 13 of the

15 observed survivors. So, the specificity is 13 15

= 0.87, or about 87 percent.

This means the model would have a false-positive rate of 13 percent.

Sensitivity and specificity are especially relevant to screening tests for diseases.

An ideal test would have 100 percent sensitivity and 100 percent specificity, and

therefore, 100 percent overall accuracy. In reality, no test could meet these stan-

dards, and there is a tradeoff between sensitivity and specificity.

By judiciously choosing the cut value for converting a predicted probability into a

yes or no decision, you can often achieve high sensitivity or high specificity, but

it’s hard to maximize both simultaneously. Screening tests are meant to detect

disease, so how you select the cut value depends upon what happens if it produces

a false-positive or false-negative result. This helps you decide whether to priori-

tize sensitivity or specificity.

The sensitivity and specificity of a logistic model depends upon the cut value you

set for the predicted probability. The trick is to select a cut value that gives the

optimal combination of sensitivity and specificity, striking the best balance

between false-positive and false-negative predictions, in light of the different

FIGURE 18-6:

The classification

table for the

radiation

example.