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

Practice
Exercises

The following questions and computer information con-

sider the Evans Country dataset on 609 white males that

has been previously discussed and illustrated in earlier

chapters of this text. Recall that the outcome variable is

CHD status (1¼case, 0¼noncase), the exposure variable

of interest is CAT status (1¼high CAT, 0¼low CAT), and

the five control variables considered are AGE (continuous),

CHL (continuous), ECG (0,1), SMK (0,1), and HPT (0,1).

The SAS output provided below was obtained for the fol-

lowing logistic model:

Logit PðXÞ¼aþb 1 CATþg 1 AGEþg 2 CHLþg 3 ECG

þg 4 SMKþg 5 HPTþd 1 CCþd 2 CH,

where CC¼CATCHL and CH¼CATHPT

Analysis of Maximum Likelihood Estimates

Standard Wald

Parameter DF Estimate Error Chi-

Square

Pr>

ChiSq

Intercept 1 4.0497 1.2550 10.4125 0.0013

cat 1 12.6894 3.1047 16.7055 <.0001

age 1 0.0350 0.0161 4.6936 0.0303

chl 1 0.00545 0.00418 1.7000 0.1923

ecg 1 0.3671 0.3278 1.2543 0.2627

smk 1 0.7732 0.3273 5.5821 0.0181

hpt 1 1.0466 0.3316 9.9605 0.0016

cc 1 0.0692 0.0144 23.2020 <.0001

ch 1 2.3318 0.7427 9.8579 0.0017

Association of Predicted Probabilities and Observed Responses

Percent Concordant 78.6 Somers' D 0.578

Percent Discordant 20.9 Gamma 0.580

Percent Tied 0.5 Tau-a 0.119

Pairs 38,198 c 0.789

Classification Table

Correct Incorrect Percentages

Prob

Level Event

Non-

event Event

Non-

event Correct

Sensi-

tivity

Speci-

ficity

False

POS

False

NEG

0.000 71 0 538 0 11.7 100.0 0.0 88.3.

0.020 68 35 503 3 16.9 95.8 6.5 88.1 7.9

0.040 67 127 411 4 31.9 94.4 23.6 86.0 3.1

0.060 60 226 312 11 47.0 84.5 42.0 83.9 4.6

0.080 54 326 212 17 62.4 76.1 60.6 79.7 5.0

0.100 50 393 145 21 72.7 70.4 73.0 74.4 5.1

0.120 41 425 113 30 76.5 57.7 79.0 73.4 6.6

0.140 37 445 93 34 79.1 52.1 82.7 71.5 7.1

0.160 34 463 75 37 81.6 47.9 86.1 68.8 7.4

0.180 34 477 61 37 83.9 47.9 88.7 64.2 7.2

0.200 31 495 43 40 86.4 43.7 92.0 58.1 7.5

0.220 29 504 34 42 87.5 40.8 93.7 54.0 7.7

0.240 28 509 29 43 88.2 39.4 94.6 50.9 7.8

0.260 27 514 24 44 88.8 38.0 95.5 47.1 7.9

0.280 25 519 19 46 89.3 35.2 96.5 43.2 8.1

0.300 23 525 13 48 90.0 32.4 97.6 36.1 8.4

Practice Exercises 377