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subjects in a community of 1,000. Odds of having cancer are 100/900. Odds
in one group of subjects/odds in another group yield an odds ratio.
Ratios and odds give us an idea about relative values of what we see and
Odds ratio (syn. cross-product ratio, relative odds) is the ratio of two
odds. 64
Likelihood means the general state of being likely or probable that
an event has already occurred would yield a specific outcome. Formally, it
differs from probability , which refers to the occurrence of future events.
Statistically speaking, a likelihood ratio is the ratio of the values of the
likelihood function at two different parameter values or under two different
data models. 64 In the domain of diagnostic methods and tests evaluation, it
is the probability that a given test result would occur in a person with the
target disorder divided by the probability that the same result would occur
in a person without that disorder. 64
Figure 2.13 represents a basic model of comparison of two groups of
events from which an event frequency is derived. It serves with other con-
siderations to assess causality, what it represents, and to what it applies
(target population or patients as individuals). A subset (sample) of indi-
viduals representing a larger (target) population to which the results of the
study should apply and be representative of is selected. Groups exposed
and nonexposed to the event (noxious factor, treatment, or other beneficial
intervention) are formed. They are compared for their “initial state” or state
before the event of interest. Then, the “intervention,” “event,” “maneuvre,”
“exposures” as they are called across the literature are compared to their
alternatives: nonevent, alternative event. Additional events (like co-morbidity
or co-treatments) may be considered. “Subsequent states,” event outcomes,
in groups are then compared for their differences and distinctions. Causality
and the role of the actions under study are clarified. Findings are then evalu-
ated based on what they actually apply to: The original target population,
individuals beyond the original target population (further generalizations),
particular and specific patients or individuals in the community, and so on.
To study and explain the cases, we need disease frequency , a total of
events as they were observed, and its expression in fractions explaining
relationships between two entities (series of observations). Fractions appear
in two forms, either as rates (disease or event frequency in the numerator,
population in which they occur, cases and noncases, events and nonevents
included in the denominator) or ratios (events in the numerator, nonevents
or other events in the denominator).
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