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

IV. The logistic model for matched data(pages

397–400)

A. Advantage: Provides an efficient analysis when

there are variables other than matching

variables to control.

B. Model uses dummy variables in identifying

different strata.

C. Model form:

logit PðXÞ¼aþbEþ~g 1 iV 1 iþ~g 2 jV 2 j

þE~dkWk;

whereV 1 iare dummy variables identifying

matched strata,V 2 jare potential confounders

based on variables not involved in the matching,

andWkare effect modifiers (usually) based on

variables not involved in the matching.

D. Odds ratio expression ifEis coded as (0, 1):

ROR¼expbþ~dkWk



:

V. An application(pages 400–403)

A. Case-control study, 2-to-1 matching,D¼MI

(0, 1),E¼SMK (0, 1),

four matching variables: AGE, RACE, SEX,

HOSPITAL,

two variables not matched: SBP, ECG,

n¼117 (39 matchedsets,3 observations per set).

B. Model form:

logit PðXÞ¼aþbSMKþ~

38

i¼ 1

g 1 iV 1 iþg 21 SBP

þg 22 ECGþSMKðd 1 SBPþd 2 ECGÞ:

C. Odds ratio:

ROR¼expðbþd 1 SBPþd 2 ECGÞ:

D. Analysis: Use conditional ML estimation;

interaction not significant

No interaction model:

logit PðXÞ¼aþbSMKþ~

38

i¼ 1

g 1 iV 1 iþg 21 SBP

þg 22 ECG:

Odds ratio formula:

ROR¼expðbÞ;

416 11. Analysis of Matched Data Using Logistic Regression