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

The Wald test we have just described tests the

null hypothesis that the coefficient of the CAT

variable is 0 in the model containing CAT and

five covariables. An equivalent way to state this

null hypothesis is that the odds ratio for the

effect of CAT on CHD adjusted for the five

covariables is equal to the null value of 1.

The other chi-square statistics listed in the

table provide Wald tests for other variables in

the model. For example, the chi-square value

for the variable CHL is the squared Wald sta-

tistic that tests whether there is a significant

effect of CHLon CHD controlling for the other

five variables listed, including CAT. However,

the Wald test for CHL, or for any of the other

five covariables, is not of interest in this study

because the only exposure variable is CAT and

because the other five variables are in the

model for control purposes.

A 95% confidence interval for the odds ratio for

the adjusted effect of the CAT variable can be

computed from the set of results for the no

interaction model as follows: We first obtain a

confidence interval forb, the coefficient of the

CAT variable, by using the formulab^plus or

minus 1.96 times the standard error of^b. This

is computed as 0.5978 plus or minus 1.96 times

0.3520. The resulting confidence limits for^b

are0.09 for the lower limit and 1.29 for the

upper limit.

Exponentiating the lower and upper limits

gives the confidence interval for the adjusted

odds ratio, which is 0.91 for the lower limit and

3.63 for the upper limit.

Note that this confidence interval contains the

value 1, which indicates that a two-tailed test is

not significant at the 5% level statistical signif-

icance from the Wald test. This does not con-

tradict the earlier Wald test results, which were

significant at the 5% level because using the CI,

our alternative hypothesis is two-tailed instead

of one-tailed.

EXAMPLE (continued)

H 0 : b¼ 0
equivalent to
H 0 : adjusted OR¼ 1

Variable Coefficient S.E. Chi sq P
Intercept
CAT
AGE
CHL.
..
HPT

0.0088 0.0033 7.18

Not of interest

0.0074

95% CI for adjusted OR:
First, 95% CI forb:

^b 1 : 96 s^b

0.59781.960.3520

CI limits forb:(0.09, 1.29)

exp(CI limits forb)¼ðÞe^0 :^09 ;e^1 :^29

= (0.91, 3.63)

CI contains 1,
so
do not rejectH 0
at
5% level (two-tailed)

Presentation: VIII. Numerical Example 149