Introductory Biostatistics

Suppose that each subject in a large study, at a particular time, is classified
as positive or negative according to some risk factor, and as having or not
having a certain disease under investigation. For any such categorization the
population may be enumerated in a 22 table (Table 1.11). The entriesA,B,
CandDin the table are sizes of the four combinations of disease presence/
absence and factor presence/absence, and the numberNat the lower right cor-
ner of the table is the total population size. The relative risk is

RR¼

A

AþB

o

C

CþD

¼

AðCþDÞ

CðAþBÞ

In many situations, the number of subjects classified as disease positive is
small compared to the number classified as disease negative; that is,

CþDFD

AþBFB

and therefore the relative risk can be approximated as follows:

RRF

AD

BC

¼

A=B

C=D

¼

A=C

B=D

where the slash denotes division. The resulting ratio,AD=BC, is an approxi-
mate relative risk, but it is often referred to as anodds ratiobecause:

1.A=BandC=Dare the odds in favor of having disease from groups with

or without the factor.

TABLE 1.11

Disease

Factor þ
Total

þ AB AþB

CD CþD
Total AþCBþDN¼AþBþCþD

20 DESCRIPTIVE METHODS FOR CATEGORICAL DATA