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

Classification Table (continued)

Correct Incorrect Percentages

Prob

Level Event

Non-

event Event

Non-

event Correct

Sensi-

tivity

Speci-

ficity

False

POS

False

NEG

0.320 23 526 12 48 90.1 32.4 97.8 34.3 8.4

0.340 22 528 10 49 90.3 31.0 98.1 31.3 8.5

0.360 21 529 9 50 90.3 29.6 98.3 30.0 8.6

0.380 21 529 9 50 90.3 29.6 98.3 30.0 8.6

0.400 18 529 9 53 89.8 25.4 98.3 33.3 9.1

0.420 18 531 7 53 90.1 25.4 98.7 28.0 9.1

0.440 18 531 7 53 90.1 25.4 98.7 28.0 9.1

0.460 18 531 7 53 90.1 25.4 98.7 28.0 9.1

0.480 18 531 7 53 90.1 25.4 98.7 28.0 9.1

0.500 18 532 6 53 90.3 25.4 98.9 25.0 9.1

0.520 18 532 6 53 90.3 25.4 98.9 25.0 9.1

0.540 16 532 6 55 90.0 22.5 98.9 27.3 9.4

0.560 16 532 6 55 90.0 22.5 98.9 27.3 9.4

0.580 15 532 6 56 89.8 21.1 98.9 28.6 9.5

0.600 13 533 5 58 89.7 18.3 99.1 27.8 9.8

0.620 11 534 4 60 89.5 15.5 99.3 26.7 10.1

0.640 10 535 3 61 89.5 14.1 99.4 23.1 10.2

0.660 10 535 3 61 89.5 14.1 99.4 23.1 10.2

0.680 10 535 3 61 89.5 14.1 99.4 23.1 10.2

0.700 10 536 2 61 89.7 14.1 99.6 16.7 10.2

0.720 9 536 2 62 89.5 12.7 99.6 18.2 10.4

0.740 8 536 2 63 89.3 11.3 99.6 20.0 10.5

0.760 8 536 2 63 89.3 11.3 99.6 20.0 10.5

0.780 8 536 2 63 89.3 11.3 99.6 20.0 10.5

0.800 8 536 2 63 89.3 11.3 99.6 20.0 10.5

0.820 6 536 2 65 89.0 8.5 99.6 25.0 10.8

0.840 6 537 1 65 89.2 8.5 99.8 14.3 10.8

0.860 5 537 1 66 89.0 7.0 99.8 16.7 10.9

0.880 5 537 1 66 89.0 7.0 99.8 16.7 10.9

0.900 5 537 1 66 89.0 7.0 99.8 16.7 10.9

0.920 5 537 1 66 89.0 7.0 99.8 16.7 10.9

0.940 4 538 0 67 89.0 5.6 100.0 0.0 11.1

0.960 3 538 0 68 88.8 4.2 100.0 0.0 11.2

0.980 3 538 0 68 88.8 4.2 100.0 0.0 11.2

1.000 0 538 0 71 88.3 0.0 100.0 · 11.7

1. Using the above output:
   a. Give a formula for calculating the estimated proba-
   bility ^PðXÞof being a case (i.e., CHD¼1) for
   asubject(X) with the following covariate values:
   CAT¼1, AGE¼50, CHL¼200, ECG¼0, SMK¼0,
   HPT¼0?
   [Hint: ^PðXÞ¼ 1 =f 1 þexp½logitP^ðXފg where
   logitP^ðXÞ is calculated using the estimated
   regression coefficients for the fitted model.]
   b. Compute the value ofP^ðXÞusing your answer to
   question 1a.
   c. If a discrimination cut-point of 0.200 is used to
   classify a subject as either a case or a noncase,
   how would you classify subjectX* based on your
   answer to question 1b.
   d. With a cut-point of 0.000, the sensitivity of the
   screening test is 1.0 (or 100% – see first row). Why
   does the sensitivity of a test have to be 100% if the
   cut point is 0? (assume there is at least one true
   event)

378 10. Assessing Discriminatory Performance of a Binary Logistic Model