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

Special case:

Case-control study

100 matched pairs

n¼ 200

100 strata¼100 matched pairs

2 observations per stratum

1st

pair

2nd

pair

100th
pair
E E E E E E
D 1 D 1 D 1

D 1 D 1 D 1

Four possible forms:

E E

D 101 Wpairs

D 101

E E

D 101 Xpairs

D 011

E E

D 011 Ypairs

D 101

E E

D 011 Zpairs

D 011

WþXþYþZ¼total number of
pairs

Analysis: Two equivalent ways

As a special case, consider a pair-matched

case-control study involving 100 matched

pairs. The total number of observations, n,

then equals 200, and the data consists of 100

strata, each of which contains the two observa-

tions in a given matched pair.

If the only variables being controlled in the

analysis are those involved in the matching,

then the complete data set for this matched

pairs study can be represented by 100 2 2

tables, one for each matched pair. Each table is

labeled by exposure status on one axis and

disease status on the other axis. The number

of observations in each table is two, one being

diseased and the other (representing the con-

trol) being nondiseased.

Depending on the exposure status results for

these data, there are four possible forms that a

given stratum can take. These are shown here.

The first of these contains a matched pair for

which both the case and the control are exposed.

The second of these contains a matched pair

for which the case is exposed and the control is

unexposed.

In the third table, the case is unexposed and the

control is exposed.

And in the fourth table, both the case and the

control are unexposed.

If we letW, X, Y, andZdenote the number of

pairs in each of the above four types of table,

respectively, then the sumWplusXplusYplus

Z equals 100, the total number of matched

pairs in the study.

For example, we may haveW equals 30, X

equals 30,Yequals 10, andZequals 30, which

sums to 100.

The analysis of a matched pair dataset can then

proceed in either of two equivalent ways,

which we now briefly describe.

EXAMPLE

W¼ 30 ;X¼ 30 ;Y¼ 10 ;Z¼ 30

WþXþYþZ¼ 30 þ 30 þ 10 þ 30 ¼ 100



Presentation: III. Matched Analyses Using Stratification 395