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

Test computation:Z= 0 : 0683 = 0 : 0143 ¼ 4 : 77 ; alterna-

tively,Z^2 ¼22.75; the two-tailedP-value is 0.0000,

which is very significant.

The LR statistic is 43.4, which is almost twice as large

as the square of the Wald statistic; however, both

statistics are very significant, resulting in the same

conclusion of rejecting the null hypothesis.

Model II is more appropriate than Model I because the

test for interaction is significant.

12. The formula for the estimated odds ratio is given by

ORdadj¼exp ^bCATþ^dCCCHL



¼expðÞ 14 : 089 þ 0 : 0683 CHL;

where the coefficients come from Model II and the

confounding effects of AGE, CHL, ECG, SMK, and

HPT are adjusted.

13. Using the adjusted odds ratio formula given in Exer-
    cise 12, the estimated odds ratio values for CHL equal
    to 220 and 240 are:
    CHL¼220: exp[14.0809þ0.0683(220)]
    ¼exp(0.9451)¼2.57
    CHL¼240: exp[14.0809þ0.0683(240)]
    ¼exp(2.3111)¼10.09


14. Formula for the 95% confidence interval for the
    adjusted odds ratio when CHL¼220:

exp^l 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffi

dvarð^lÞ

q

;where^l¼^bCATþ^dCCð 220 Þ

and vardð^lÞ¼vardð^bCATÞþð 220 Þ^2 dvarð^dCCÞ

þ 2 ð 220 Þcovdð^bCAT;^dCCÞ;

wheredvarðb^CATÞ;dvarð^dCCÞ;andcovdðb^CAT;^dCCÞare ob-

tained from the printout of the variance– covariance

matrix.

164 5. Statistical Inferences Using Maximum Likelihood Techniques