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

Logistic model for matched data
includes control of variables not
matched

Stratified analysis inefficient:

Data is discarded

Matched data:

Use conditional ML estimation

(number of parameters large

relative ton)

Pair-matching:

ORdU¼ðORdCÞ^2

"

overestimate

Principle
Matched analysis)stratified
analysis

 Strata are matched sets, e.g.,
pairs

 Strata defined using dummy
(indicator) variables

E¼(0, 1) exposure

C 1 ,C 2 ,...,Cpcontrol variables

For example, one may match on AGE, RACE,

and SEX, but may also wish to control for

systolic blood pressure and body size, which

may have also been measured but were not

part of the matching.

In the remainder of the presentation, we describe

how to formulate and apply a logistic model to

analyze matched data, which allows for the con-

trol of variables not involved in the matching.

In this situation, using a stratified analysis

approach instead of logistic regression will

usually be inefficient in that much of one’s

data will need to be discarded, which is not

required using a modeling approach.

The model that we describe below for matched

data requires the use of conditional ML estima-

tion for estimating parameters. This is because,

as we shall see, when there are matched data,

the number of parameters in the model is large

relative to the number of observations.

If unconditional ML estimation is used instead

of conditional, an overestimate will be obtained.

In particular, for pair-matching, the estimated

odds ratio using the unconditional approach

will be the square of the estimated odds ratio

obtained from the conditional approach, the

latter being the correct result.

An important principle about modeling

matched data is that such modeling requires

the matched data to be considered in strata. As

described earlier, the strata are the matched

sets, for example, the pairs in a matched pair

design. In particular, the strata are defined

usingdummyor indicator variables, which we

will illustrate shortly.

In defining a model for a matched analysis, we

consider the special case of a single (0, 1) expo-

sure variable of primary interest, together with

a collection of control variablesC 1 ,C 2 , and so on

up throughCp, to be adjusted in the analysis for

possible confounding and interaction effects.

EXAMPLE

Match on AGE, RACE, SEX

also, control for SBP and BODYSIZE

398 11. Analysis of Matched Data Using Logistic Regression