- a.
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Sensitivity1.0
1–specificity
b. AUC¼c¼0.840; good discrimination (grade B).
c. 19,950¼ 114 175, where 114 is the number of
true cases and 175 is the number of true noncases.
Thus, 19,950 is the number of distinct case/noncase
pairs in the dataset.
d. AUC¼c¼
wþ 0 : 5 z
np
¼
19 ; 950 ð: 838 Þþ 0 : 5 ð 19 ; 950 Þð: 004 Þ
19 ; 950
¼ 0 : 840
- a. Area within entire rectangle¼ 114 715 ¼19,950,
which is the number of case/noncase pairs in the
dataset used to compute the AUC.
b. The area under the superimposed ROC curve is
16,758, which is the numerator in the AUC formula,
giving essentially the number of case/noncase pairs
in which the predicted risk for the case is at least as
large as the predicted risk for the corresponding
noncase in the pair (where ties are weighed by 0.5).
- a. Yes, the model fits the data because the HL statistic
is highly nonsignificant. Also, the corresponding
observed and expected cases are very close in each
decile, as is the corresponding observed and
expected noncases.
b. The distribution of observed cases indicates that
the higher is the decile, the higher is the number of
observed cases. The distribution of observed
noncases indicates that the lower is the decile, the
higher is the number of observed noncases. This
indicates that the model provides good
discrimination of the cases from the noncases.
c. The table provided for this part indicates that the
model poorly discriminates cases from noncases
and also provides poor GOF. Both the observed
cases and the observed noncases appear to be
Chapter 10 683
