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

E, V, WModel

k¼p 1 þp 2 þ 1 ¼no. of variables
in model
p 1 ¼no. of potential confounders
p 2 ¼no. of potential interactions
1 ¼exposure variable

 V 1 ,...,Vp 1 are potential
confounders

 Vs are functions ofCs

e.g.,V 1 ¼C 1 ,V 2 ¼(C 2 )^2 ,V 3 ¼C 1 C 3

 W 1 ,...,Wp 2 are potential effect
modifiers

 Ws are functions ofCs

e.g.,W 1 ¼C 1 ,W 2 ¼C 1 C 3

The generalE, V, Wmodel containsp 1 plusp 2

plus 1 variables, wherep 1 is the number of

potential confounders in the model,p 2 is the

number of potential interaction terms in the

model, and 1 denotes the exposure variable.

In the CHD study example above, there arep 1

equals to five potential confounders, namely,

the five control variables, and there are p 2

equal to two interaction variables, the first of

which is CATCHL and the second is CAT

HPT. The total number of variables in the

example is, therefore,p 1 plusp 2 plus 1 equals

5 plus 2 plus 1, which equals 8. This corre-

sponds to the model presented earlier, which

contained eight variables.

In addition to the exposure variableE,the gen-

eral model containsp 1 variables denoted asV 1 ,

V 2 throughVp 1. The set ofVs are functions of

theCs that are thought to account for con-

founding in the data. We call the set of these

Vspotential confounders.

For instance, we may haveV 1 equal toC 1 ,V 2

equal to (C 2 )^2 , andV 3 equal toC 1 C 3.

The CHD example above has fiveVs that are

the same as theCs.

Following theVs, we definep 2 variables that

are product terms of the formEtimesW 1 ,E

timesW 2 , and so on up throughEtimesWp 2 ,

whereW 1 ,W 2 , throughWp 2 , denote a set of

functions of the Cs that are potential effect

modifierswithE.

For instance, we may haveW 1 equal toC 1 and

W 2 equal toC 1 timesC 3.

The CHD example above has twoWs, namely,

CHL and HPT, that go into the model as prod-

uct terms of the form CATCHL and CAT

HPT.

CHD EXAMPLE

p 1 ¼5: AGE, CHL, SMK, ECG, HPT

p 2 ¼2: CATCHL, CATHPT

p 1 þp 2 þ 1 ¼ 5 þ 2 þ 1 ¼ 8

CHD EXAMPLE

V 1 ¼AGE,V 2 ¼CHL,V 3 ¼SMK,

V 4 ¼ECG,V 5 ¼HPT

CHD EXAMPLE

W 1 ¼CHL,W 2 ¼HPT

Presentation: IV. TheE,V,WModel 57