Introductory Biostatistics

w^2 ES¼

4 ^1  210



þ 17 ^2  520



þ 11 ^3  512



þ 9 ^4  510



þ 1 ^1  41



þ 3 ^2  43

  2

1

25 ½ð^1 ^10 ^4 Þþð^2 ^20 ^3 Þþð^3 ^12 ^2 Þþð^4 ^10 ^1 ފþ

1

16 ½^1 ^1 ^3 þ^2 ^3 ^2 Š

¼ 27 : 57

Mantel–Haenszel’s estimate for the odds ratio is

dORMH¼

½ð 4 Þð 4 Þþð 3 Þð 17 Þþð 2 Þð 11 Þþð 1 Þð 9 ފþ½ð 3 Þð 1 Þþð 2 Þð 3 Þþð 1 Þð 0 ފ

½ð 1 Þð 6 Þþð 2 Þð 3 Þþð 3 Þð 1 Þþð 4 Þð 1 ފþ½ð 1 Þð 0 Þþð 2 Þð 0 Þþð 3 Þð 0 ފ

¼ 5 : 63

11.7 CONDITIONAL LOGISTIC REGRESSION

Recall from Chapter 9 that in a variety of applications using regression analy-
sis, the dependent variable of interest has only two possible outcomes and
therefore can be represented by an indicator variable taking on values 0 and 1.
An important application is the analysis of case–control studies where the
dependent variable represents the disease status, 1 for a case and 0 for a con-
trol. The methods that have been used widely and successfully for these appli-
cations are based on the logistic model. In this section we also deal with cases
where the dependent variable of interest is binary, following a binomial dis-
trubution—the same as those using logistic regression analyses but the data are
matched. Again, the termmatchingrefers to the pairing of one or more con-
trols to each case on the basis of their similarity with respect to selected vari-
ables used asmatching criteria, as seen earlier. Although the primary objective of
matching is the elimination of biased comparison between cases and controls,
this objective can be accomplished only if matching is followed by an analysis
that corresponds to the design matched. Unless the analysis accounts properly
for the matching used in the selection phase of a case–control study, the results
can be biased. In other words, matching (which refers to the selection process)
is only the first step of a two-step process that can be used e¤ectively to control
for confounders: (1) matching design, followed by (2) matched analysis. Sup-
pose that the purpose of the research is to assess relationships between the dis-
ease and a set of covariates using a matched case–control design. The regres-
sion techniques for the statistical analysis of such relationships is based on the
conditional logistic model.
The following are two typical examples; the first one is a case–control study
of vaginal carcinoma which involves two binary risk factors, and in the second
example, one of the four covariates is on a continuous scale.

Example 11.10 The cases were eight women 15 to 22 years of age who were
diagnosed with vaginal carcinoma between 1966 and 1969. For each case, four
controls were found in the birth records of patients having their babies deliv-

CONDITIONAL LOGISTIC REGRESSION 413