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

Note that because we cannot drop either of the

variables AGE, SMK, or ECG as nonconfoun-

ders, we do not need to consider possible gain

in precision from deleting nonconfounders. If

precision were considered, we would compare

tables of confidence intervals for different

models. As with confounding assessment,

such comparisons are largely subjective.

This example illustrates why we will find it

difficult to assess confounding and precision

if our model contains interaction terms. In

such a case, any decision to delete possible

nonconfounders is largely subjective. There-

fore, we urge caution when deleting variables

from our model in order to avoid sacrificing

validity in exchange for what is typically only

a minor gain in precision.

To conclude this example, we point out that,

using the final model, a summary of the results

of the analysis can be made in terms of the

table of odds ratios and the corresponding

table of confidence intervals.

Both tables are shown here. The investigator

must use this information to draw meaningful

conclusions about the relationship under

study. In particular, the nature of the interac-

tion can be described in terms of the point

estimates and confidence intervals.

For example, as CHL increases, the odds ratio

for the effect of CAT on CHD increases. Also,

for fixed CHL, this odds ratio is higher when

HPT is 0 than when HPT equals 1. Unfortu-

nately, all confidence intervals are quite wide,

indicating that the point estimates obtained

are quite unstable.

EXAMPLE (continued)

No need to consider precision in this
example:
Compare tables of CIs – subjective

Confounding and precision difficult if
interaction (subjective)

Caution. Do not sacrifice validity for
minor gain in precision

Summary result for final model:

Table of OR

Table of 95% CIs

HPT=0HPT=1

HPT=0 HPT=1

CHL
200 3.16 0.31

(0.89, 11.03)

(3.65, 42.94)

(11.79, 212.23)

(0.10, 0.91)

(0.48, 3.10)

(1.62, 14.52)

12.61 1.22

50.33 4.89

220

240

CHL
200
220
240

Use to draw meaningful conclusions

CHL

CHL fixed: ORCAT, CHD > ORCAT, CHD

⇒ ORCAT, CHD

HPT= 0 HPT= 1

All CIs are wide

Presentation: V. The Evans County Example Continued 229