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

Criticism:

 Information on 4,790
discordant pairs not used

 Pooling exchangeable matched
sets more appropriate analysis

 Frequency matching more
appropriate than individual
matching

How to modify the analysis to con-
trol for nonmatched variables

OBS and SMK?

If no other covariates are considered other

than the matching variables (and the expo-

sure), the data can be summarized in the

McNemar table shown at the left.

From this table, the estimated MRR, which

adjusts for AGE and YEAR equals 20/16 or

1.25. Notice that sinceP¼0 in this table, the

MRR equals thed MORd ¼Q=R.

The McNemar test statistic for these data is

computed to bew^2 MH¼ 0 : 44 ðdf¼ 1 Þ, which is

highly nonsignificant. Thus, from this analysis

we cannot reject the null hypothesis that the

risk ratio relating vasectomy to myocardial

infarction is equal to its null value (i.e., 1).

The analysis just described could be criticized

in a number of ways. First, since the analysis

only used the 36 discordant pairs information,

all of the information on the 4,790 concordant

pairs was not needed, other than to distinguish

such pairs from concordant pairs.

Second, since matching involved only two vari-

ables, AGE and YEAR, a more appropriate

analysis should have involved a stratified anal-

ysis based on pooling exchangeable matched

sets.

Third, a more appropriate design would likely

have used frequency matching on AGE and

YEAR rather than individual matching.

Assuming that a more appropriate analysis

would have arrived at essentially the same con-

clusion (i.e., a negative finding), we now con-

sider how the McNemar analysis described

above would have to be modified to take into

account two additional variables that were not

involved in the matching, namely obesity sta-

tus (OBS) and smoking status (SMK).

EXAMPLE (continued)

McNemar’s table:

VS = 0

P = 0Q = 20

R = (^16) S = 4790
VS = 1
MI = 1 MI = 0
MI = 1
MI = 0
MRRd ¼PþQ
PþR
¼
0 þ 20
0 þ 16
¼ 1 : 25
Note:P¼ 0 ) MRRd ¼MOR.d
w^2 MH¼
ðQRÞ^2
QþR
¼
ð 20  16 Þ^2
20 þ 16
¼ 0 : 44
Cannot rejectH 0 : mRR¼ 1
412 11. Analysis of Matched Data Using Logistic Regression