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

Matched pairs model:

logit PðXÞ¼aþbEþ~g 1 iV 1 i
þ~g 2 jV 2 jþE~dkWk

ROR¼expbþ~dkWk



Note: Two types ofVvariables are
controlled

V. An Application

Alternatively, using the above dummy variable

definition, a person in the first matched set will

haveV 11 equal to 1 and the remaining dummy

variables equal to 0; a person in the 99th

matched set will haveV1, 99equal to 1 and the

other dummy variables equal to 0; and a person

in the 100th matched set will have all 99

dummy variables equal to 0.

For the matched analysis model we have just

described, the odds ratio formula for the effect

of exposure status adjusted for covariates is

given by the expression ROR equals e to the

quantitybplus the sum of thedjtimes theWj.

This is exactly the same odds ratio formula

given in our review for theE,V,W model.

This makes sense because the matched analy-

sis model is essentially anE,V,Wmodel con-

taining two different types ofVvariables.

As an application of a matched pairs analysis,

consider a case-control study involving 2-to-1

matching which involves the following variables:

Thedisease variableis myocardial infarction

status, as denoted by MI.

Theexposure variableis smoking status, as

defined by a (0, 1) variable denoted as SMK.

There are sixCvariables to be controlled.

The first four of these variables, namely age,

race, sex, and hospital status, are involved in

the matching.

The last two variables, systolic blood

pressure, denoted by SBP, and

electrocardiogram status, denoted by ECG,

are not involved in the matching.

EXAMPLE (continued)

1st matched set

V 11 ¼ 1 ;V 12 ¼V 13 ¼¼V 1 ; 99 ¼ 0

99th matched set

V 1 ; 99 ¼ 1 ;V 11 ¼V 12 ¼¼V 1 ; 98 ¼ 0

100th matched set

V 11 ¼V 12 ¼¼V 1 ; 99 ¼ 0

EXAMPLE

Case-control study

2-to-1 matching

D¼MI 0 ; 1

E¼SMK 0 ; 1

C|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 1 ¼AGE;C 2 ¼RACE;C 3 ¼SEX;C 4 ¼HOSPITAL

matched

C|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 5 ¼SBPC 6 ¼ECG

not matched

400 11. Analysis of Matched Data Using Logistic Regression