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

(Note. In answering all of the above questions, make sure to

state your answers in terms of the coefficients and vari-

ables that you specified in your answers to Exercises 1

and 2).

Consider the following printout results that summarize the

computer output for two models based on follow-up study

data on 609 white males from Evans County, Georgia:

Model I OUTPUT:

2lnL^¼400.39

Variable Coefficient S.E. Chi sq P

Intercept 6.7747 1.1402 35.30 0.0000

CAT 0.5978 0.3520 2.88 0.0894

AGE 0.0322 0.0152 4.51 0.0337

CHL 0.0088 0.0033 7.19 0.0073

ECG 0.3695 0.2936 1.58 0.2082

SMK 0.8348 0.3052 7.48 0.0062

HPT 0.4392 0.2908 2.28 0.1310

Model II OUTPUT:

2lnL^¼357.05

Variable Coefficient S.E. Chi sq P

Intercept 3.9346 1.2503 9.90 0.0016

CAT 14.0809 3.1227 20.33 0.0000

AGE 0.0323 0.0162 3.96 0.0466

CHL 0.0045 0.00413 1.16 0.2821

ECG 0.3577 0.3263 1.20 0.2729

SMK 0.8069 0.3265 6.11 0.0134

HPT 0.6069 0.3025 4.03 0.0448

CC¼CATCHL 0.0683 0.0143 22.75 0.0000

In the above models, the variables are coded as follows:

CAT(1¼high, 0¼low), AGE(continuous), CHL(continu-

ous), ECG(1¼abnormal, 0¼normal), SMK(1¼ever,

0 ¼never), HPT(1¼hypertensive, 0¼normal). The out-

come variable is CHD status(1¼CHD, 0¼no CHD).

8. For Model I, test the hypothesis for the effect of CAT
   on the development of CHD. State the null hypothesis
   in terms of an odds ratio parameter, give the formula
   for the test statistic, state the distribution of the test
   statistic under the null hypothesis, and, finally, carry
   out the test for a one-sided alternative hypothesis using
   the above printout for Model I. Is the test significant?

158 5. Statistical Inferences Using Maximum Likelihood Techniques