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

C. 100(1a)% CI formula for OR usingE, V, W

model:

exp^lZ 1 a 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

dvar^l



Þ

q

;

whereORd¼e

l^

;^l¼^bþ~

p 2

j¼ 1

^djWj

anddvar^l



Þ¼dvar^b



þ~

p 2

j¼ 1

Wj^2 dvard^j



þ 2 ~

p 2

j¼ 1

Wjcovd ^b;^dj



þ 2 ~

j

~

k

WjWkcovd^dj;^dk



:

D. Model 3 example ofE, V, Wmodel:X 3 ¼E,

X 1 ¼V 1 ,X 2 ¼V 2 , and for interaction terms,

p 2 ¼2,X 1 ¼W 1 ,X 2 ¼W 2.

VIII. Numerical example(pages 146–153)

A. Printout provided for two models (A and B) from

Evans County, Georgia data.

B. Model A: no interaction terms; Model B:

interaction terms.

C. Description of LR and Wald tests for Model A.

D. LR test for no interaction effect in Model B:

compares model B (full model) with Model A

(reduced model). Result: significant interaction.

E. 95% CI for OR from Model B; requires use of CI

formula for interaction, wherep 2 ¼2,

W 1 ¼CHL, andW 2 ¼HPT.

Practice
Exercises

A prevalence study of predictors of surgical wound infec-

tion in 265 hospitals throughout Australia collected data

on 12,742 surgical patients (McLaws et al., 1988). For each

patient, the following independent variables were deter-

mined: type of hospital (public or private), size of hospital

(large or small), degree of contamination of surgical site

(clean or contaminated), and age and sex of the patient. A

logistic model was fit to this data to predict whether or not

the patient developed a surgical wound infection during

hospitalization. The largest model fit included all of the

above variables and all possible two-way interaction terms.

The abbreviated variable names and the manner in which

the variables were coded in the model are described as

follows:

156 5. Statistical Inferences Using Maximum Likelihood Techniques