Introductory Biostatistics

The interpretation above of the concept of an odds ratio as an odds can be
generalized as follows. The aim here is to present an e‰cient method for use
with ordered 2kcontingency tables, tables with two rows andkcolumns
having a certain natural ordering. The figure summarized is the generalized
odds formulated from the concept of odds ratio. Let us first consider an exam-
ple concerning the use of seat belts in automobiles. Each accident in this
example is classified according to whether a seat belt was used and to the
severity of injuries received: none, minor, major, or death (Table 1.13).
To compare the extent of injury from those who used seat belts with those
who did not, we can calculate the percent of seat belt users in each injury group
that decreases from level ‘‘none’’ to level ‘‘death,’’ and the results are:

None:

75

75 þ 65

¼54%

Minor:

160

160 þ 175

¼48%

Major:

100

100 þ 135

¼43%

Death:

15

15 þ 25

¼38%

What we are seeing here is atrendor anassociationindicating that the lower
the percentage of seat belt users, the more severe the injury.
We now present the concept ofgeneralized odds, a special statistic specifi-
cally formulated to measure the strength of such a trend and will use the same
example and another one to illustrate its use. In general, consider an ordered
2 ktable with the frequencies shown in Table 1.14.

TABLE 1.13

Extent of Injury Received

Seat Belt None Minor Major Death

Yes 75 160 100 15
No 65 175 135 25

TABLE 1.14

Column Level

Row 1 2  k Total

1 a 1 a 2  ak A
2 b 1 b 2  bk B

Total n 1 n 2  nk N

RATIOS 23