Statistical Methods in Medical Research 4ed

672 Statistical methods in epidemiology
where IE and INE are the incidence rates in the exposed and non-exposed,
respectively. This measure may also be referred to as the risk ratio.
In a cohort study the relative risk can be estimated directly, since estimates
are available of both IE and INE. In a case±control study the relative risk cannot
be estimated directly since neither IE nor INE can be estimated, and we now
consider how to obtain a useful solution.
Suppose that each subject in a large population has been classified as positive
or negative according to some potential aetiological factor, and positive or
negative according to some disease state. The factor might be based on a current
classification or (more usually in a retrospective study) on the subject's past
history. The disease state may refer to the presence or absence of a certain
category of disease at a particular instant, or to a certain occurrence (such as
diagnosis or death) during a stated periodÐthat is, to prevalence and incidence,
respectively.
For any such categorization the population may be enumerated in a 2 2
table, as follows. The entries in the table are proportions of the total population.
Factor
Disease
‡
‡ P1 P3 P1 ‡ P3
P2 P4 P2 ‡ P4
P1 ‡ P2 P3 ‡ P4 1
…19:14†
If these proportions were known, the association between the factor and the
disease could be measured by the ratio of the risks of being disease-positive for
those with and those without the factor.
Risk ratio ˆ
P1
…P1 ‡ P3†
ˆ P1…P2 ‡ P4†
P2…P1 ‡ P3† :
P2
…P2 ‡ P4†
…19:15†
Where the cases are incident cases the risk ratio is the relative risk.
Now, in many (although not all) situations in which aetiological studies are
done, the proportion of subjects classified as disease-positive will be small. That
is, P1 will be small in comparison with P3, and P2 will be small in comparison
with P4. In such a case, (19.15) will be very nearly equal to