8.6 Relative Risk and Odds Ratio 139perspective, Friis and Sellers ( 1999 ). Both concepts are germane to
contingency tables where proportions are considered. Relative risk is
used in cohort studies. Suppose we have a population of subjects who
have different exposure to risk factors for a particular disease.
We have a record of their medical history and information on past
exposure. Then we follow these patients to see if they get the disease.
The occurrences of new cases of the disease, in this population, are
compared between groups with different exposure to see if the exposure
affects the incidence rates. Table 8.10 shows the concept of relative risk
in a 2 × 2 table.
The relative risk can vary from 0 to ∞. It is the ratio of the propor-
tion of the cases where the disease occurs, given the factor is present
to the proportion of cases where the disease occurs, given the factor is
absent. It shows how many times the risk increases or decreases accord-
ing to whether or not the factor is present. So a relative risk of 2 for
lung cancer when the subject is a smoker compared with a nonsmoker
is interpreted as smoking doubles your risk of getting lung cancer. Table
8.11 shows a 2 × 2 table for lung cancer with smoking as a factor from
a cohort study.
So we see from Table 8.11 that the relative risk is 6.53, which
means that you are over 6.5 times more likely to get lung cancer if you
smoke than if you don ’ t smoke. So a relative risk greater than 1 in this
case means that the factor increases your chances of getting the disease.
Consequently we often test that the relative risk is different from
1 or perhaps greater than 1 if we anticipate a negative effect from the
factor. In Chapter 10 , when we cover survival analysis, we will see how
the survival models allow us to obtain tests of hypotheses on the rela-
tive risk or construct confi dence intervals for it. This is often done when
the Cox proportional hazard model is fi t to the survival data. In such a
Table 8.10
Assessment of Relative Risk in a 2 × 2 Table
Outcome
Factor Present Absent Total
Yes a b a + b
No c d c + d
RR (relative risk) = [ a /( a + b ])/[ c /( c + d )] = a ( c + d )/[ c ( a + b )]