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

C. Examples of no interaction and interaction on a

multiplicative scale.

D. A logistic model that allows for the assessment of

multiplicative interaction:

logit P(X)¼aþb 1 Aþb 2 Bþb 3 AB

E. The relationship ofb 3 to the odds ratios in the no

interaction formula above:

b 3 ¼ln

OR 11

OR 10 OR 01



F. The null hypothesis of no interaction in the above

two factor model: H 0 :b 3 ¼0.

IV. TheE,V,Wmodel – A general model containing a

(0, 1) exposure and potential confounders and

effect modifiers(pages 55–64)

A. Specification of variables in the model: start with

E, C 1 ,C 2 ,...,Cp; then specify potential

confoundersV 1 ,V 2 ,...,Vp 1 , which are functions

of theCs, and potential interaction variables (i.e.,

effect modifiers)W 1 ,W 2 ,...,Wp 2 , which are also

functions of theCs and go into the model as

product terms withE, i.e.,EWj.

B. TheE, V, Wmodel:

logit PðÞ¼X aþbEþ~

p 1

i¼ 1

giViþE~

p 2

j¼ 1

djWj

C. Odds ratio formula for theE, V, Wmodel, whereE

is a (0, 1) variable:

RORE¼ 1 vs:E¼ 0 ¼exp bþ~

p 2

j¼ 1

djWj

!

D. Odds ratio formula forE, V, Wmodel if no

interaction: ROR¼exp(b).

E. Examples of theE, V, Wmodel: with interaction

and without interaction

66 2. Important Special Cases of the Logistic Model