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

Tests based on CIs aretwo-tailed
In EPID, most tests of E–D
relationship areone-tailed

One-tailed tests:
Use large sample

Z¼

estimate

standard error

Furthermore, tests of significance can be car-

ried out using the confidence intervals. To do

this, one must determine whether or not the

null value of the odds ratio, namely, 1, is

contained within the confidence limits. If so,

we do not reject, for a given CHL, HPT combi-

nation, the null hypothesis of no effect of CAT

on CHD. If the value 1 lies outside the confi-

dence limits, we would reject the null hypothe-

sis of no effect.

For example, when CHL equals 200 and HPT

equals 0, the value of 1 is contained within the

limits 0.89 and 11.03 of the 95% confidence

interval. However, when CHL equals 220 and

HPT equals 0, the value of 1 is not contained

within the limits 3.65 and 42.94.

Thus, when CHL equals 200 and HPT equals 0,

there is no significant CAT, CHD effect,

whereas when CHL equals 220 and HPT equals

0, the CAT, CHD effect is significant at the 5%

level.

Note that tests based on confidence intervals

are two-tailed tests. One-tailed tests are more

common in epidemiology for testing the effect

of an exposure on disease.

When there is interaction, one-tailed tests can

be obtained by using the point estimates and

their standard errors that go into the computa-

tion of the confidence interval. The point esti-

mate divided by its standard error gives a large

sampleZstatistic, which can be used to carry

out a one-tailed test.

EXAMPLE (continued)

Tests of significance:

Is

null value

(OR = 1) contained

within CI?

Do not

reject H 0 :

no CAT,

CHD

effect

Reject H 0 : no effect of

CAT on CHD

Ye s

No

95% CI:

CHL = 200, HPT = 0:

CHL = 220, HPT = 0:

(0.89 11.03)

(3.65 42.94)

0

1

1

Test results at 5% level:

CHL¼ 200 ;HPT¼ 0 :no significant

CAT;CHD effect

CHL¼ 220 ;HPT¼ 0 :significant

CAT;CHD effect

230 7. Modeling Strategy for Assessing Interaction and Confounding