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

Presentation

FOCUS

Form

Characteristics

Applicability

I. The Multivariable
Problem

E? D

E, C 1 , C 2 , C 3? D

independent dependent

This presentation focuses on the basic features

of logistic regression, a popular mathematical

modeling procedure used in the analysis of

epidemiologic data. We describe theformand

keycharacteristicsof the model. Also, we dem-

onstrate theapplicabilityof logistic modeling in

epidemiologic research.

We begin by describing the multivariable prob-

lem frequently encountered in epidemiologic

research. A typical question of researchers is:

What is the relationship of one or more expo-

sure (or study) variables (E) to a disease or

illness outcome (D)?

To illustrate, we will consider a dichotomous

disease outcome with 0 representingnot dis-

easedand 1 representingdiseased. The dichot-

omous disease outcome might be, for example,

coronary heart disease (CHD) status, with sub-

jects being classified as either 0 (“without

CHD”) or 1 (“with CHD”).

Suppose, further, that we are interested in a

single dichotomous exposure variable, for

instance, smoking status, classified as “yes” or

“no”. The research question for this example is,

therefore, to evaluate the extent to which

smoking is associated with CHD status.

To evaluate the extent to which an exposure,

like smoking, is associated with a disease, like

CHD, we must often account or “control for”

additional variables, such as age, race, and/or

sex, which are not of primary interest. We have

labeled these three control variables asC 1 ,C 2 ,

andC 3.

In this example, the variableE(the exposure

variable), together withC 1 ,C 2 , andC 3 (the con-

trol variables), represents a collection ofinde-

pendent variables that we wish to use to

describe or predict thedependentvariableD.

EXAMPLE

D(0, 1)¼CHD

E(0, 1)¼SMK

SMK CHD

“control for”

C 1 ¼AGE

C 2 ¼RACE

C 3 ¼SEX

4 1. Introduction to Logistic Regression