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

EXAMPLE (continued)

Best Model Summary: Options A,

B, C

Options A and B (same result):

ModelA: contains PREVHOSP,

PAMU, AGE,

and GENDER

Option C:

ModelC: contains PREVHOSP,

PAMU, and

GENDER

Model A Output (Best: Options A

and B)

Analysis of maximum likelihood estimates

Param DF Estimate Std Err ChiSq Pr>ChiSq

Intercept 1 5.0583 0.7643 43.8059 <.0001

PREVHOSP 1 1.4855 0.4032 13.5745 0.0002

PAMU 1 1.7819 0.3707 23.1113 <.0001

AGE 1 0.0353 0.0092 14.7004 0.0001

GENDER 1 0.9329 0.3418 7.4513 0.0063

Model C Output (Best: Option C)

Analysis of maximum likelihood estimates

Param DF Estimate Std Err ChiSq Pr>ChiSq

Intercept 1 2.7924 0.4123 45.8793 <.0001

PREVHOSP 1 1.6627 0.3908 18.1010 <.0001

PAMU 1 1.4973 0.3462 18.7090 <.0001

GENDER 1 0.4335 0.3030 2.4066 0.1525

ORs

PREVHOSP

Modelexp[b 1 ] exp[b 2 ] exp[b 1 +^ b 2 ]

PAMU COMBINED

A 4.417 5.941 26.242

C 5.274 4.470 23.571

MRSA example:OptionsA,B,andC

+

Similar, slightly different numerical

conclusions

In general: No guarantee for
same conclusions

General form of Initial Model

Logit PðXÞ¼aþ~

q

i¼ 1

biEiþ~

p 1

j¼ 1

gjVj

þ~

q

i¼ 1

~

p 2

k¼ 1

dikEiWkþ~

q

i¼ 1

~

q

i^0 ¼ 1

i 6 ¼i^0

d*ii 0 EiEi 0

Summarizing the results we have obtained

from the above analyses on the MRSA data,

we have foundtwodifferent final choices for

the best model shown at the left depending on

three approaches to our modeling strategy,

OptionsAandB(same result) andOptionC.

The outputs for the two “best” models are

shown here.

Both models are no-interaction models, and

they both contain the main effects of two highly

significantEvariables, PREVHOSP and PAMU.

The estimated coefficients of PREVHOSP and

PAMU differ somewhat for each model. The

estimate for PREVHOSP is 1.4855 for ModelA

whereas it is 1.6627 for ModelC. The estimate

for PAMU is 1.7819 for ModelAcompared with

1.4973 for ModelC.

OR estimates from each model are shown in

the table at the left. Both models show moder-

ately strong effects for eachEvariable and a

very strong effect whencomparingX*¼(E 1 ¼1,

E 2 ¼1) with X¼(E 1 ¼0, E 2 ¼0). How-

ever, the effect of PREVHOSP is 16%lowerin

Model A than in ModelC, whereas the effect of

PAMU 25%higherin ModelAthan in ModelC.

We see, therefore, that for our MRSA example,

modeling strategy OptionsA, B, and Cgive

similar, but slightly different conclusions

involving twoEvariables.

In general, as shown by this example, there is

no guarantee that these three options will

always yield the same conclusions. Therefore,

the researcher may have to decide which

option he/she prefers and/or which conclusion

makes the most (biologic) sense.

In summary, we recommend that the initial model

has the general form shown at the left. This model

involvesEs,Vs,EWs, andEEs, so there are two

types of interaction terms to consider.

Presentation: II. Modeling Strategy for Several Exposure Variables 259