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

REFERENCE

Chapter 11: Analysis of Matched
Data Using Logistic Regression

In contrast, consider a case-control study

involving 100 matched pairs. Suppose that the

outcome variable is lung cancer and that con-

trols are matched to cases on age, race, sex, and

location. Suppose also that smoking status, a

potential confounder denoted as SMK, is not

matched but is nevertheless determined for

both cases and controls, and that the primary

exposure variable of interest, labeled asE,is

some dietary characteristic, such as whether or

not a subject has a high-fiber diet.

Because the study design involves matching, a

logistic model to analyze this data must control

for the matching by using dummy variables

to reflect the different matching strata, each

of which involves a different matched pair.

Assuming the model has an intercept, the

model will need 99 dummy variables to incor-

porate the 100 matched pairs. Besides these

variables, the model contains the exposure var-

iableE, the covariable SMK, and perhaps even

an interaction term of the formESMK.

To obtain the number of parameters in the

model, we must count the one intercept,

the coefficients of the 99 dummy variables,

the coefficient ofE, the coefficient of SMK,

and the coefficient of the product termE

SMK. The total number of parameters is 103.

Because there are 100 matched pairs in the

study, the total number of subjects is, there-

fore, 200. This situation requiresconditional

ML estimationbecause the number of para-

meters, 103, is quitelargerelative to the num-

ber of subjects, 200.

A detailed discussion of logistic regression for

matched data is provided in Chap. 11.

EXAMPLE: Conditional Preferred

Case-control study

100 matched pairs

D¼lung cancer

Matching variables:

age, race, sex, location

Other variables:

SMK (a confounder)

E(dietary characteristic)

Logistic model for matching:

 uses dummy variables for

matching strata

 99 dummy variables for 100

strata

 E, SMK, andESMK also in

model

Number of parameters¼

1 þ 99 þ 3 ¼ 103

"""

intercept dummy E, SMK,ESMK

variables

largerelative to 100 matched

pairs) n = 200

Presentation: III. Unconditional vs. Conditional Methods 109