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

Presentation

I. Overview

FOCUS

Computing OR for

E, D relationship

adjusting for

control variables

 DichotomousE– arbitrary
coding

 Ordinal or intervalE

 PolytomousE

 SeveralEs

Chapter 2 –E, V, Wmodel:

 (0, 1) exposure

 Confounders

 Effect modifiers

The variables in theE, V, Wmodel:

E: (0, 1) exposure

Cs: control variables

Vs: potential confounders

Ws: potential effect modifiers
(i.e., go into model asEW)

TheE, V, Wmodel:

logit PðÞ¼X aþbEþ~

p 1

i¼ 1

giVi

þE~

p 2

j¼ 1

djWj

This presentation describes how to compute

the odds ratio for special cases of the general

logistic model involving one or more exposure

variables. We focus on models that allow for

theassessmentofanexposure–diseaserela-

tionship that adjusts for the potential con-

founding and/or effect modifying effects of

control variables.

In particular, we consider dichotomous expo-

sure variables with arbitrary coding, that is, the

coding of exposure may be other than (0, 1).

We also consider single exposures that are ordi-

nalorintervalscaledvariables.And,finally,we

consider models involving several exposures, a

special case of which involves a single polyto-

mous exposure.

In the previous chapter we described the logit

form and odds ratio expression for theE, V, W

logistic model, where we considered a single

(0, 1) exposure variable and we allowed the

model to control several potential confounders

and effect modifiers.

Recall that in defining theE, V, Wmodel, we

start with a single dichotomous (0, 1) exposure

variable, E, and p control variablesC 1 , C 2 ,

and so on, up throughCp. We then define a

set of potential confounder variables, which

are denoted asVs. TheseVs are functions of

theCs that are thought to account for con-

founding in the data. We then define a set of

potential effect modifiers, which are denoted

asWs. Each of theWs goes into the model as

product term withE.

Thelogit formof theE, V, Wmodel is shown

here. Note thatbis the coefficient of the single

exposure variableE, the gammas (gs) are coef-

ficients of potential confounding variables

denoted by theVs, and the deltas (ds) are coef-

ficients of potential interaction effects involv-

ingEseparately with each of theWs.

76 3. Computing the Odds Ratio in Logistic Regression