The combined area under the rescaled ROC
curve is then 7,095, which represents a propor-
tion of 0.7095 of the total rectangular area of
10,000.A logistic regression model was used in the
analysis of a dataset containing information
from 348 patients who entered an emergency
room (ER) complaining of blunt knee trauma,
and who subsequently were X-rayed for possi-
ble knee fracture (Tigges et al., 1999).The purpose of the analysis was to assess
whether a patient’s pattern of covariates could
be used as a screening test before performing
the X-ray.Since 1.3 million people visit North American
ER departments annually complaining of
blunt knee trauma, the total cost associated
with even a relatively inexpensive test such as
a knee X-ray (about $200 for each X-ray) may
be substantial.The variables considered in this analysis are
listed at the left. The outcome variable is called
FRACTURE, which represents a binary vari-
able for knee fracture status.The five predictor variables are FLEX,
WEIGHT, AGECAT, HEAD, and PATELLAR,
and are defined at the left.EXAMPLE (continued)
Combined area under rescaled ROC
¼ 5 þ 240 þ 250 þ 500 þ 600 þ
þ 500
¼7,095
Proportion of total area under
rescaled ROC
¼7,095=10,000¼ 0 : 7095 ð¼AUCÞV. Example from Study
on Screening for Knee
Fracture
EXAMPLE
Logistic model
n¼348 ER patients
Complaint: blunt knee trauma
X-rayed for knee fracture Study purpose: use covariates to
screen for decision to perform
X-ray 1.3 million people per year visit
ER with blunt knee trauma
Substantial total cost for X-raysOutcome variable:
FRACTURE¼knee fracture status
(1¼yes, 0¼no)
Predictor variables:
FLEX¼ability to flex knee
(0¼yes, 1¼no)
WEIGHT¼ability to put weight
on knee (0¼yes,
1 ¼no)
AGECAT¼patient’s age
(0¼age<55,
1 ¼age55)
HEAD¼injury to knee head
(0¼no, 1¼yes)
PATELLAR¼injury to patella
(0¼no, 1¼yes)Presentation: V. Example from Study on Screening for Knee Fracture 365