(a) m¼P
xfðxÞ
(b)s^2 ¼P
ðxmÞ^2 fðxÞFor example, we have for the binomial distribution,m¼nps^2 ¼npð 1 pÞand for the Poisson distribution,
m¼ys^2 ¼y3.5.2 Pair-Matched Case–Control Study
Data from epidemiologic studies may come from various sources, the two fun-
damental designs beingretrospectiveandprospective(orcohort). Retrospective
studies gather past data from selected cases (diseased individuals) and controls
(nondiseased individuals) to determine di¤erences, if any, in the exposure to a
suspected risk factor. They are commonly referred to ascase–control studies.
Cases of a specific disease, such as lung cancer, are ascertained as they arise
from population-based disease registers or lists of hospital admissions, and
controls are sampled either as disease-free persons from the population at risk
or as hospitalized patients having a diagnosis other than the one under investi-
gation. The advantages of a case–control study are that it is economical and
that it is possible to answer research questions relatively quickly because the
cases are already available. Suppose that each person in a large population has
been classified as exposed or not exposed to a certain factor, and as having or
not having some disease. The population may then be enumerated in a 2 2
table (Table 3.12), with entries being the proportions of the total population.
Using these proportions, the association (if any) between the factor and the
disease could be measured by the ratio of risks (or relative risk) of being disease
positive for those with or without the factor:
TABLE 3.12
DiseaseFactor þTotal
þ P 1 P 3 P 1 þP 3
P 2 P 4 P 2 þP 4
Total P 1 þP 2 P 3 þP 4 1
138 PROBABILITY AND PROBABILITY MODELS