Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

The logistic model used in the analysis is

shown at the left, and includes all five predictor

variables. Although some of these predictors

could have been evaluated for significance, we

report here only on the ability of the 5-variable

model to discriminate cases (fracture¼1)

from noncases (fracture¼0).

We summarize the results of this analysis

based on using SAS’s LOGISTIC procedure,

although the analysis could alternatively have

been carried out using either STATA or SPSS

(see Computer Appendix for computer code

and output).

The output showing the fitted model is now

shown at the left.

Notice that three of the variables (FLEX, AGE-

CAT, and HEAD) in the model have nonsignifi-

cant Wald tests, indicating backward elimination

would result in removal of one or more of these

variables, e.g., HEAD would be eliminated first,

sinceithasthehighestWaldP-value (0.5617).

Nevertheless, we will focus on the full model for

now, assuming that we wish to use all five pre-

dictors to carry out the screening.

We now show the classification table that uses

the patients’ predicted outcome probabilities

obtained from the fitted logistic model to

screen each patient. The probability levels

(first column) are prespecified cut points (in

increments of 0.05) requested in the model

statement.

For example, in the third row, the cut-point is

0.100. If this cut-point is used for screening,

then any patient whose predicted probability

is greater than 0.100 will test positive for knee

fracture on the screening test and therefore

will receive an X-ray.

EXAMPLE (continued)

Logistic Model:

logit PðXÞ¼b 0 þb 1 FLEX

þb 2 WEIGHT

þb 3 AGECAT

þb 4 HEAD

þb 5 PATELLAR

Results shown below based on

SAS’s

LOGISTIC procedure

(but can also use STATA or

SPSS)

Fitted Logistic Regression Model:

Parameter DF Estimate

Std

Err

Wald

ChiSq

Pr>

ChiSq

Intercept 1 3.4657 0.4118 70.8372 <.0001

FLEX 1 0.5277 0.3743 1.9877 0.1586

WEIGHT 1 1.5056 0.4093 13.5320 0.0002

AGECAT 1 0.5560 0.3994 1.9376 0.1639

HEAD 1 0.2183 0.3761 0.3367 0.5617

PATELLAR 1 0.6268 0.3518 3.1746 0.0748

 FLEX, WEIGHT, and HEAD have

nonsignif Wald statistics.

 BW elimination would simplify

model

 Focus for now on full model

Classification Table

Prob

Level

Correct

Non-

Event Event

Incorrect

Non-

Event Event

Percentages

CorrectSe Sp1 – Sp †

0.000 45 0 303 0 12.9100.0 0.0100.0

0.050 39 93 210 6 37.9 86.7 30.7 69.3

0.100 36 184 119 9 63.2 80.0 60.7 39.3

0.150 31 200 103 14 66.4 68.9 66.0 34.0

0.200 32 235 68 23 73.9 48.9 77.6 22.4

0.250 16 266 37 29 81.0 35.6 87.8 12.2

0.300 6 271 32 39 79.6 13.3 89.4 10.6

0.350 3 297 6 42 86.2 6.7 98.0 2.0

0.400 3 301 2 42 87.4 6.7 99.3 0.7

0.450 2 301 2 43 87.1

87.1

87.1

87.1

87.1

87.1

87.1

87.1

87.1

87.1

87.1

87.1

4.4 99.3 0.7

0.500 0 303 0

0 0 0 0 0 0 0 0 0 0

45 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

100.0

100.0

100.0

100.0

100.0

100.0

100.0

100.0

100.0

100.0

100.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.550 0 303 45

45

45

45

45

45

45

45

45

45

0.600 0 303

0.650 0 303

303

030

030

303

303

303

303

0.700 0

0.750 0

0

0

0

0

0

0.800

0.850

0.900

0.950

1.000

† (^) 1 – Sp is not automatically output in SAS; s LOGISTIC
366 10. Assessing Discriminatory Performance of a Binary Logistic Model