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

Under this reduced model, the estimated odds

ratio adjusted for the effects of theVvariables

is given by the familiar expression e to the^b,

whereb^is the coefficient of the exposure vari-

able SMK.

The results from fitting this model and reduced

versions of this model which delete either or

both of the potential confounders SBP and

ECG are shown here. These results give both

conditional (C) and unconditional (U) odds

ratio estimates and 95% confidence intervals

(CI) for the conditional estimates only. (See

Computer Appendix.)

From inspection of this table of results, we see

that the unconditional estimation procedure

leads to overestimation of the odds ratio and,

therefore, should not be used.

The results also indicate a minimal amount of

confounding due to SBP and ECG. This can be

seen by noting that the gold standard esti-

mated odds ratio of 2.07, which controls for

both SBP and ECG, is essentially the same as

the other conditionally estimated odds ratios

that control for either SBP or ECG or neither.

Nevertheless, because the estimated odds ratio

of 2.32, which ignores both SBP and ECG in

the model, is moderately different from 2.07,

we recommend that at least one or possibly

both of these variables be controlled.

If at least one of SBP and ECG is controlled,

and confidence intervals are compared, the

narrowest confidence interval is obtained

when only ECG is controlled.

Thus, the most precise estimate of the effect is

obtained when ECG is controlled, along, of

course, with the matching variables.

Nevertheless, because all confidence intervals

are quite wide and include the null value of 1, it

does not really matter which variables are con-

trolled. The overall conclusion from this analysis

is that the adjusted estimate of the odds ratio for

the effect of smoking on the development of MI

is about 2, but it is quite nonsignificant.

EXAMPLE (continued)

RORd ¼e^b

Vs in model OR¼eb 95% CI

SBP and ECG C 2.07 (0.69, 6.23)

U3.38
SBP only C2.08 (0.72, 6.00)
U3.39
ECG only C2.05 (0.77, 5.49)
U3.05
Neither C2.32 (0.93, 5.79)
U3.71

C¼conditional estimate

U¼unconditional estimate

Minimal confounding:
Gold standarddOR¼ 2 : 07 ,
essentially
same as otherdOR

But 2.07 moderately different from
2.32, so we control forat leastone of
SBP and ECG

Narrowest CI: Control for ECG only

Most precise estimate:
Control for ECG only

All CI are wide and include 1

Overall conclusion:
AdjustedORd 2 , but is
nonsignificant

Presentation: V. An Application 403