Example 1.16 A case–control study of the epidemiology of preterm delivery,
defined as one with less than 37 weeks of gestation, was undertaken at Yale–
New Haven Hospital in Connecticut during 1977. The study population con-
sisted of 175 mothers of singleton preterm infants and 303 mothers of singleton
full-term infants. Table 1.15 gives the distribution of mother’s age. We have
C¼ð 15 Þð 25 þ 62 þ 122 þ 78 Þþð 22 Þð 62 þ 122 þ 78 Þ
þð 47 Þð 122 þ 78 Þþð 56 Þð 78 Þ
¼ 23 ; 837
D¼ð 16 Þð 22 þ 47 þ 56 þ 35 Þþð 25 Þð 47 þ 56 þ 35 Þ
þð 62 Þð 56 þ 35 Þþð 122 Þð 35 Þ
¼ 15 ; 922leading to generalized odds of
y¼C
D
¼
23 ; 837
15 ; 922
¼ 1 : 50
This means that the odds that the younger mother has a preterm delivery is 1.5.
In other words, the younger mothers would be more likely to have a preterm
delivery.
The next example shows the use of generalized odds for contingency tables
with more than two rows of data.
Example 1.17 Table 1.16 shows the results of a survey in which each subject
of a sample of 282 adults was asked to indicate which of three policies he or she
favored with respect to smoking in public places. We have
TABLE 1.15
Age Cases Controls
14–17 15 16
18–19 22 25
20–24 47 62
25–29 56 122
b 30 35 78RATIOS 25