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

Parameter DF Estimate

Standard

Error

Wald

Chi-Square Pr>ChiSq

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

Association of Predicted Probabilities and

Observed Responses

Percent Concordant 71.8 Somers' D 0.489

Percent Discordant 22.9 Gamma 0.517

Percent Tied 5.3 Tau-a 0.111

Pairs 13635 c 0.745

Classification Table
Correct Incorrect Percentages
Prob
Level Event

Non-

Event Event

Non-

Event Correct Sensitivity Specificity

False

POS

False

NEG

0.000 45 0 303 0 12.9 100.0 0.0 87.1.
0.050 39 93 210 6 37.9 86.7 30.7 84.3 6.1
0.100 36 184 119 9 63.2 80.0 60.7 76.8 4.7
0.150 31 200 103 14 66.4 68.9 66.0 76.9 6.5
0.200 22 235 68 23 73.9 48.9 77.6 75.6 8.9
0.250 16 266 37 29 81.0 35.6 87.8 69.8 9.8
0.300 6 271 32 39 79.6 13.3 89.4 84.2 12.6
0.350 3 297 6 42 86.2 6.7 98.0 66.7 12.4
0.400 3 301 2 42 87.4 6.7 99.3 40.0 12.2
0.450 2 301 2 43 87.1 4.4 99.3 50.0 12.5
0.500 0 303 0 45 87.1 0.0 100.0. 12.9

The table in the output titled “Association of Predicted Probabilities and Observed
Responses” is now described. There are 45 cases and 303 noncases of knee fracture
yielding 45
303 ¼13,635 pair combinations (4th row, 1st column of output). For
these pairs, 71.8% had the case with the higher predicted probability (percent con-
cordant in the output), 22.9% had the noncase with the higher predicted probability
(percent discordant in the output), and 5.3% had the same predicted probability for
the case and noncase (percent tied in the output). If the percent tied is weighted as
half a concordant pair then the probability of having a concordant pair rather than a
discordant pair is estimated as 0.718þ0.5(0.053)¼0.745. This is the value of the c
statistic (4th row, 2nd column of output) and is the estimate of the area under the
ROC plot.

The classification table 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 requested in the model statement. For example
in the third row, the cut point is 0.100. A cut point of 0.100 indicates that any patient
whose predicted probability is greater than 0.100 will receive an X-ray. In other

SAS 615