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

H 0 :d 11 ¼0,H 0 :d 21 ¼0, andH 0 :d 33 ¼0 arenon-

significantin the reduced model (withoutE 1 C 1 C 2

andE 2 C 1 C 2 ). Then, as the next step in interaction

assessment, the model should be further reduced

to

logit PðXÞ¼aþb 1 E 1 þb 2 E 2 þb 3 E 3 þg 1 C 1 þg 2 C 2

þg 3 C 3 þg 12 C 1 C 2 þd 12 E 1 C 2

þd 22 E 2 C 2 þde 13 E 1 E 3 þde 23 E 2 E 3 :

prior to the assessment of confounding.

2. Suppose that after interaction assessment involving
   bothEViandEiEjterms in the initial model stated in
   question 1 , the following reduced model is obtained:

logit PðXÞ¼aþb 1 E 1 þb 2 E 2 þb 3 E 3 þg 1 C 1 þg 2 C 2

þg 3 C 3 þg 12 C 1 C 2 þd 11 E 1 C 1 þd 22 E 2 C 2

Suppose further that the assessment of confounding

willonlyconsider changes in the odds ratio that com-

pares a person for whomE 1 ¼E 2 ¼E 3 ¼1 to a per-

son for whomE 1 ¼E 2 ¼E 3 ¼0.

Based on the recommended guidelines for the assess-

ment of confounding described in this chapter:

a. What is the formula for theestimatedodds ratio in the

gold standard model that should be used to assess

confounding?

2 b. Assuming that you will need to consider tables of odds

ratios that consider different subsets of potential con-

founders,describe what a table of odds ratios would

look like for the gold standard modelusing the rectangle

shown below for the (outside) borders of the table. In

your answer, make sure tostate the formulae for the

odds ratiosthat will go into the different boxes in the

table.Hint.You will need to draw horizontal and ver-

tical lines to subdivide the rectangle and label the

different row and column categories of the table,

recognizing that the odds ratios being represented

reflect the interaction effects that are present in the

gold standard model.

290 8. Additional Modeling Strategy Issues