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

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 fitted to these data to predict whether

or not the patient developed a surgical wound infection

during hospitalization. The abbreviated variable names

and the manner in which the variables were coded in the

model are described as follows:

Variable Abbreviation Coding

Type of hospital HT 1 ¼public, 0¼private

Size of hospital HS 1 ¼large, 0¼small

Degree of

contamination

CT 1 ¼contaminated,

0 ¼clean

Age AGE Continuous

Sex SEX 1 ¼female, 0¼male

In the questions that follow, we assume that type of hospi-

tal (HT) is considered the exposure variable, and the other

four variables are risk factors for surgical wound infection

to be considered for control.

1. In defining anE, V, Wmodel to describe the effect of HT
   on the development of surgical wound infection,
   describe how you would determine theVvariables
   to go into the model. (In answering this question, you
   need to specify the criteria for choosing theVvariables,
   rather than the specific variables themselves.)


2. In defining anE, V, Wmodel to describe the effect of
   HT on the development of surgical wound infection,
   describe how you would determine theWvariables to
   go into the model. (In answering this question, you
   need to specify the criteria for choosing the W
   variables, rather than specifying the actual variables.)


3. State the logit form of a hierarchically well-formulated
   E, V, Wmodel for the above situation in which theVs
   and theWs are theCsthemselves.Whyisthismodel
   hierarchically well formulated?


4. Suppose the product term HTAGESEX is added
   to the model described in Exercise 3. Is this new model
   still hierarchically well formulated? If so, state why; if
   not, state why not.


5. Suppose for the model described in Exercise 4 that a
   Wald test is carried out for the significance of the
   three-factor product term HTAGESEX. Explain

Practice Exercises 197