Introductory Biostatistics

2.A=CandB=Dare the odds in favor of having been exposed to the factors

from groups with or without the disease. These two odds can easily be

estimated using case–control data, by using sample frequencies. For

example, the oddsA=Ccan be estimated bya=c, whereais the number of

exposed cases andcthe number of nonexposed cases in the sample of

cases used in a case–control design.

For the many diseases that are rare, the termsrelative riskandodds ratioare
used interchangeably because of the above-mentioned approximation. Of
course, it is totally acceptable to draw conclusions on an odds ratio without
invoking this approximation for disease that is not rare. The relative risk is an
important epidemiological index used to measure seriousness, or the magnitude
of the harmful e¤ect of suspected risk factors. For example, if we have

RR¼ 3 : 0

we can say that people exposed have a risk of contracting the disease that is
approximately three times the risk of those unexposed. A perfect 1.0 indicates
no e¤ect, and beneficial factors result in relative risk values which are smaller
than 1.0. From data obtained by a case–control or retrospective study, it is
impossible to calculate the relative risk that we want, but if it is reasonable to
assume that the disease is rare (prevalence is less than 0.05, say), we can calcu-
late the odds ratio as a stepping stone and use it as an approximate relative risk
(we use the notationFfor this purpose). In these cases, we interpret the odds
ratio calculated just as we would do with the relative risk.

Example 1.14 The role of smoking in the etiology of pancreatitis has been
recognized for many years. To provide estimates of the quantitative signifi-
cance of these factors, a hospital-based study was carried out in eastern Mas-
sachusetts and Rhode Island between 1975 and 1979. Ninety-eight patients
who had a hospital discharge diagnosis of pancreatitis were included in this
unmatched case–control study. The control group consisted of 451 patients
admitted for diseases other than those of the pancreas and biliary tract. Risk
factor information was obtained from a standardized interview with each sub-
ject, conducted by a trained interviewer.
Some data for the males are given in Table 1.12. For these data for this
example, the approximate relative risks or odds ratios are calculated as follows:

(a) For ex-smokers,

RReF

13 = 2

80 = 56

¼

ð 13 Þð 56 Þ

ð 80 Þð 2 Þ

¼ 4 : 55

RATIOS 21