Introductory Biostatistics

2. The odds ratio due to a 1-unit increase ifXis continuous (X¼xþ 1
   versusX¼x).

Afterbb^and its standard error have been obtained, a 95% confidence interval
for the odds ratio above is given by

exp½bb^G 1 :96 SEðbb^ފ

Special Case Consider now the simplest case of a pair matched (i.e., 1:1
matching) with a binary covariate: exposedX¼1 versus unexposedX¼0.
Let the data be summarized and presented as in Section 5.2 (Table 11.15). For
example,n 10 denotes the number of pairs where the case is exposed but the
matched control is unexposed. The likelihood function above is reduced to

LðbÞ¼

1

1 þ 1

n 00

expðbÞ

1 þexpðbÞ

n 10

1

1 þexpðbÞ

n 01

expðbÞ

expðbÞþexpðbÞ

n 11

¼

expðbn 10 Þ

½ 1 þexpðbފn^10 þn^01

From this we can obtain a point estimate:

bb^¼n^10

n 01

which is the usual odds ratio estimate from pair-matched data.

Tests of Association Another aspect of statistical inference concerns the test of
significance; the null hypothesis to be considered is

H 0 :b¼ 0

The reason for interest in testing whether or notb¼0 is thatb¼0 implies that
there is no relation between the binary dependent variable and the covariateX
under investigation. We can simply appply a McNemar chi-square test (if the
covariate is binary or categorical or a pairedttest or signed-rank Wilcoxon test

TABLE 11.15

Case

Control 1 0

1 n 11 n 01

0 n 10 n 00

CONDITIONAL LOGISTIC REGRESSION 417