Introductory Biostatistics

ratio¼

a

b

whereaandbaresimilar quantitiesmeasured fromdi¤erent groupsor under
di¤erent circumstances. An example is the male/female ratio of smoking rates;
such a ratio is positive but may exceed 1.0.

1.3.1 Relative Risk

One of the most often used ratios in epidemiological studies isrelative risk,a
concept for the comparison of two groups or populations with respect to a
certain unwanted event (e.g., disease or death). The traditional method of
expressing it in prospective studies is simply the ratio of the incidence rates:

relative risk¼

disease incidence in group 1

disease incidence in group 2

However, the ratio of disease prevalences as well as follow-up death rates
can also be formed. Usually, group 2 is under standard conditions—such as
nonexposure to a certain risk factor—against which group 1 (exposed) is mea-
sured. A relative risk greater than 1.0 indicates harmful e¤ects, whereas a rela-
tive risk below 1.0 indicates beneficial e¤ects. For example, if group 1 consists
of smokers and group 2 of nonsmokers, we have arelative risk due to smoking.
Using the data on end-stage renal disease (ESRD) of Example 1.12, we can
obtain the relative risks due to diabetes (Table 1.10). All three numbers are
greater than 1 (indicating higher mortality for diabetics) and form a decreasing
trend with increasing age.

1.3.2 Odds and Odds Ratio

Therelative risk, also called therisk ratio, is an important index in epidemio-
logical studies because in such studies it is often useful to measure theincreased
risk (if any) of incurring a particular disease if a certain factor is present. In
cohort studies such an index is obtained readily by observing the experience of
groups of subjects with and without the factor, as shown above. In a case–
control study the data do not present an immediate answer to this type of
question, and we now consider how to obtain a useful shortcut solution.

TABLE 1.10

Age Group Relative Risk

1–45 3.74

46–60 1.81

61 þ 1.69

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