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

Category matching: Combined

set of cate-

gories for

case and its

matched

control

Factor A:

Factor B:

Factor Q:

AGE:20–29 30–39 40–49 50–59 60–69

SEX:

Race:

Control has same age–race–sex

combination as case

WHITE

MALE FEMALE

NONWHITE

EXAMPLE

Case

No. of

controls Type

1 1 1–1 or pair

matching

1 R

e.g.,R¼ 4

R-to-1

!4-to-1

Rmay vary from case to case

e:g:;

R¼ 3 for some cases

R¼ 2 for other cases

R¼ 1 for other cases

8

><

>:

Not always possible to find exactly
Rcontrols for each case

To matchornot to match

Advantage:

Matching can be statistically

efficient, i.e., may gainprecision

using confidence interval

The most popular method for matching is

called category matching. This involves first

categorizing each of the matching factors and

then finding, for each case, one or more con-

trols from the same combined set of matching

categories.

For example, if we are matching on age, race,

and sex, we first categorize each of these three

variables separately. For each case, we then

determine his or her age–race–sex combination.

For instance, the case may be 52 years old, white,

and female. We then find one or more controls

with the same age–race–sex combination.

If our study involves matching, we must decide

on the number of controls to be chosen for

each case. If we decide to use only one control

for each case, we call this one-to-one or pair-

matching. If we chooseRcontrols for each

case, for example,Requals 4, then we call this

R-to-1 matching.

It is also possible to match so that there are differ-

ent numbers of controls for different cases; that is,

Rmay vary from case to case. For example, for

some cases, there may be three controls, whereas

for other cases perhaps only two or one control.

This frequently happens when it is intended to do

R-to-1 matching, but it is not always possible to

find a full complement ofRcontrols in the same

matching category for some cases.

As for whether to match or not in a given study,

there are both advantages and disadvantages

to consider.

The primary advantage for matching over ran-

dom sampling without matching is that match-

ing can often lead to a more statistically

efficient analysis. In particular,matching may

lead to a tighter confidence interval, that is, more

precision, around the odds or risk ratio being

estimated than would be achieved without

matching.

Presentation: II. Basic Features of Matching 393