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

Analysis for R-to-1 and mixed
matching use stratified analysis

R-to-1 or mixed matching

usew^2 MHandMORd
for stratified data

IV. The Logistic Model for
Matched Data

1. Stratified analysis


2. McNemar analysis
   ü3. Logistic modeling

Advantage of modeling
can control for variables other
than matched variables

This statistic has approximately a chi-square

distribution with one degree of freedom

under the null hypothesis that the odds ratio

relating exposure to disease equals 1.

From chi-square tables, we find this statistic to be

highly significant with aP-value well below 0.01.

The estimated odds ratio, which adjusts for the

matching variables, can be computed from the

above table using the MOR formula XoverY

which in this case turns out to be 3. The computed

95% confidence interval is also shown at the left.

We have thus described how to do a matched

pair analysis using stratified analysis or an

equivalent McNemar’s procedure. If the match-

ing isR-to-1 or even involves mixed matching

ratios, the analysis can also be done using a

stratified analysis.

For example, ifRequals 4, then each stratum

contains five subjects, consisting of the one

case and its four controls. These numbers can

be seen on the margins of the table shown here.

The numbers inside the table describe the

numbers exposed and unexposed within each

disease category. Here, we illustrate that the

case is exposed and that three of the four con-

trols are unexposed. The breakdown within the

table may differ with different matched sets.

Nevertheless, the analysis forR-to-1 or mixed

matched data can proceed as with pair-match-

ing by computing a Mantel–Haenszel chi-

square statistic and a Mantel–Haenszel odds

ratio estimate based on the stratified data.

A third approach to carrying out the analysis of

matched data involves logistic regression mod-

eling.

The main advantage of using logistic regres-

sion with matched data occurs when there are

variables other than the matched variables that

the investigator wishes to control.

EXAMPLE

R¼4: Illustrating one stratum

E E

D 101

D 134

5

EXAMPLE (continued)

w^2 chi square 1 df

underH 0 :OR¼ 1

P<<0.01, significant

MORd ¼X

Y¼^3 ;^95 %CI: ð^2 :^31 ;^6 :^14 Þ

Presentation: IV. The Logistic Model for Matched Data 397