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

D. Logistic Model:

logit PðXÞ¼b 0 þb 1 FLEXþb 2 WEIGHT

þb 3 AGECATþb 4 HEAD

þb 5 PATELLAR

E. Results based on SAS’s LOGISTIC procedure (but

can also use STATA or SPSS).

F. ROC plot

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

0.0 0.1 0.2 0.3 0.4 0.5

1 – specificity

Sensitivity

0.6 0.7 0.8 0.9 1.0

G. AUC¼0.745 )Fair discrimination (Grade C)

H. Reduced Model

i. Why? Some nonsignificant regression

coefficients in the full model

ii. Use backward elimination to obtain following

reduced model:

logit PðXÞ¼b 0 þb 2 WEIGHTþb 5 PATELLAR

iii. AUC (Reduced model)¼0.731AUC (Full

model)¼0.745

iv. In general, for nested models, AUC(smaller

model)AUC (larger model),

v. However, if models not nested, it is possible

that AUC(model with fewer variables)>AUC

(model with more variables).

VI. Summary (page 371)

376 10. Assessing Discriminatory Performance of a Binary Logistic Model