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

a. What is the area within the entire rectangle and

what does it have in common with the formula for

the area under the ROC curve?

b. Using the AUC calculation formula, what is the

area under the ROC curve superimposed on the

above graph? How do you interpret this area?

5. Below is additional output providing goodness of fit
   information and the Hosmer-Lemeshow test for the
   model fitted to the MRSA dataset. The column labeled
   as “Group” lists the deciles of risk, ordered from smal-
   lest to largest, e.g., decile 10 contains 23 patients who
   had had the highest 10% of predicted probabilities.
   mrsa¼1 mrsa¼ 0
   Group Total Observed Expected Observed Expected
   1 29 1 0.99 28 28.01
   2 31 5 1.95 26 29.05
   3 29 2 2.85 27 26.15
   4 29 5 5.73 24 23.27
   5 30 10 9.98 20 20.02
   6 31 12 14.93 19 16.07
   7 29 16 17.23 13 11.77
   8 29 20 19.42 9 9.58
   9 29 22 21.57 7 7.43
   10 23 21 19.36 2 3.64
   Hosmer and Lemeshow Goodness-of-
   Fit Test
   Chi-Square DF Pr>ChiSq
   7.7793 8 0.4553

a. Based on the above output, does the model fit the

data? Explain briefly.

b. What does the distribution of the number of

observed cases and observed noncases over the 10

deciles indicate about how well the model discri-

minates cases from noncases? Does your answer

384 10. Assessing Discriminatory Performance of a Binary Logistic Model