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

EXAMPLE (continued)

Option C(continued)

Model III* Output

Analysis of maximum likelihood estimates

Param DF Estimate

Std

Err ChiSq Pr>ChiSq

Intercept 1 2.6264 0.4209 38.9414 <.0001

PREVHOSP 1 1.2851 0.5107 6.3313 0.0119

PAMU 1 0.8002 0.7317 1.1960 0.2741

GENDER 1 0.4633 0.3066 2.2835 0.1308

PRHPAM 1 0.9374 0.8432 1.2358

Model C:

Logit PðXÞ¼aþðb 1 E 1 þb 2 E 2 Þþg 2 V 2

Can we dropE 1 orE 2 from Model C?

Model C Output

Cannot drop either E 1 or E 2

Option C conclusion:

Model C is best model

X*¼ðE 1 *¼ 1 ;E 2 *¼ 1 Þvs:

X¼ðE 1 ¼ 0 ;E 2 ¼ 0 Þ

ORModel C¼exp½b 1 þb 2 Š

ORModel C = exp[b 1 +b 2 ]

= exp[1.6627+1.4973]

95% CI: (10.7737, 51.5684)

= 23.5708

For the next step, we would test whether the

E 1 E 2 product term is significant. Using the

output for Model III* (shown at the left), we

find that the Wald test for the PRHPAM term

(i.e.,E 1 E 2 ) is not significant (P¼0.2663). The

corresponding LR test is also not significant.

We can now reduce our model further by

dropping the E 1 E 2 term, which yields the

reduced Model C, shown at the left.

The only other variables that we might con-

sider dropping at this point are E 1 or E 2 ,

provided one of these is not significant,

controlling for the other.

However, on inspection of the output for

this model, shown at the left, we find that the

Wald statistic for E 1 is highly significant

(P<0.0001), as is the Wald statistic for E 2

(P<0.0001). Thus, based on these Wald statis-

tics, we cannot drop eitherEvariable from the

model (and similar conclusions from LR tests).

Consequently, if we decide to useOptionC, and

we allow Models I* and Models III* to be can-

didate models that control for confounding,

then ourbest modelis given by ModelC.To

make this choice, we considered precision as

well as significance of the E in the model.

For this model, then, the OR that compares a

subjectX*who is positive (i.e., yes) for bothEs

with a subjectXwho is negative (i.e., no) for

bothEs simplifies to the exp formula shown at

the left.

Below this formula, we show the estimated OR

and a 95% confidence interval around this

odds ratio, which indicates a very strong and

significant (but highly variable) effect.

258 8. Additional Modeling Strategy Issues