California from 1971 to 1975, each disease person was matched withR¼ 4
controls who were alive and living in the community at the time the case was
diagnosed, who were born within one year of the case, who had the same mar-
ital status, and who had entered the community at approximately the same
time. The risk factor was previous use of estrogen (yes/no) and the data in
Table 11.9 were obtained from the first-found matched control (the complete
data set with four matched controls will be given later). An application of the
methods above yields
dOROR¼^29
3
¼ 9 : 67and a 95% confidence interval for OR isð 2 : 95 ; 31 : 74 Þ.
11.6 MULTIPLE MATCHING
One-to-one matching is a cost-e¤ective design. However, an increase in the
number of controls may give a study more power. In epidemiologic studies,
there are typically a small number of cases and a large number of potential
controls to select from. When the controls are more easily available than cases,
it is more e‰cient and e¤ective to select more controls for each case. The e‰-
ciency of anM:1 control–case ratio for estimating a risk relative to having
complete information on the control population (i.e.,M¼y)isM=ðMþ 1 Þ.
Hence, a 1:1 matching is 50% e‰cient, 4:1 matching is 80% e‰cient, 5:1
matching is 83% e‰cient, and so on. The gain in e‰ciency diminishes rapidly
for designs withMb5.
11.6.1 Conditional Approach
The analysis of a 1:1 matching design was conditional on the number of pairs
showing di¤erences in exposure history:ð;þÞandðþ;Þpairs. Similarly,
considering anM:1 matching design, we use a conditional approach, fixing the
numbermof exposed persons in a matched set, and the sets withm¼0or
TABLE 11.9
CaseControl þTotal
þ 27 3 30
29 4 33
Total 66 7 73
MULTIPLE MATCHING 409