Healthcare and Medicine Reference

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being treated by drugs, having surgery, having complications, suffering from

adverse effects of treatment and care, etc.) in various groups of individuals.

Events are presented and studied in two forms: frequencies or fractions.

Frequencies are simple numbers of events happening. Example: 250 cases

of chronic obstructive pulmonary disease (COPD) exist in our community. It is a

total of events as they were observed.
Frequencies
such as 1000 cases of cancer

or their
rates
(1,000 cases per 100,000 subjects in the community; i.e., a rate of

1/100 or 10/1,000, etc.) represent
absolute values
of what we observed, usually a

total of events as they were observed in a given category, set, or group.

Fractions are two related frequencies as expressions of relationship

between them. Frequencies of events are numerators presented as parts of

some whole. The whole is presented as the denominator. Example: 25 cases

of COPD occur in a community of 35,000 inhabitants (25 diseased
+
34,775

nondiseased). In epidemiology, they are usually presented as
rates
or
ratios
.

Fractions
are expressions of the relationship between two entities. In our

case, these expressions are most often rates (proportions) or ratios.

Rates are couplings of a set of observations in the numerator like disease

cases (a) with a set in the denominator including those same observations

(a) and some additional ones such as noncases (b) such as two sets creat-

ing a community:
a
/
a
+
b
. A rate in our example is then 25/(25
+
34,775). It

can be presented as such or multiplied by some coefficient like 100,000 for

comparability: 25/35,000
×
100,000, that is, 7142.85/100,000. For less frequent

phenomena like cancer, rates per 100,000 may be presented. For frequent

phenomena like diarrhea cases during a food born disease outbreak per

100, adverse drug effects may be reported per 1,000,000, and so on. As in

our COPD case, rates may also be presented as a percentage (07.14%) or as

decimal fractions (0,00714) for various computational purposes.

Ratios are relationships between different entities in the numerator

(a) and the denominator (b):
a
/
b
. In our case: 25/34,775. The entity in the

numerator is not reproduced in the denominator. For example, compar-

ing rates of events (incidence of events in one community) to other rates

of events (incidence of events in another community) yields
ratios
such as

cancer incidence rate in smokers/cancer incidence rate in nonsmokers (risk

ratio in this case). Odds (cross product ratio, relative odds) are ratios of

the probability of occurrence of an event to that of nonoccurrence of that

same event in another set of observations. In other words, it is the ratio of

the probability that something is one way to the probability that it is other

way.
64
Odds
, in fact, are fractions having an event in the nominator and non-

events in the denominator: There are 100 cases of cancer and 900 healthy

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