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Probability
is an important concept in statistics. Both objective and subjective
probabilities are used in the medical field.- Basic definitions
include the concept of an event or outcome. A number of essential
rules tell us how to combine the probabilities of events.
- Bayes’ theorem
relates to the concept of conditional probability—the probability
of an outcome depending on an earlier outcome. Bayes’ theorem
is part of the reasoning process when interpreting diagnostic procedures.
- Populations
are rarely studied; instead, researchers study samples.
- Several methods
of sampling are used in medical research; a key issue is that any
method should be random.
- When researchers
select random samples and then make measurements, the result is
a random variable. This process makes statistical tests and inferences
possible.
- The binomial
distribution is used to determine the probability of yes/no
events—the number of times a given outcome occurs in a
given number of attempts.
- The Poisson
distribution is used to determine the probability of rare events.
- The normal distribution
is used to find the probability that an outcome occurs when the
observations have a bell-shaped distribution. It is used in many
statistical procedures.
- If many random
samples are drawn from a population, a statistic, such as the mean,
follows a distribution called a sampling distribution.
- The central
limit theorem tells us that means of observations, regardless of
how they are distributed, begin to follow a normal distribution
as the sample size increases. This is one of the reasons the normal
distribution is so important in statistics.
- It is important
to know the difference between the standard deviation, which describes
the spread of individual observations, from the standard error of
the mean, which describes the spread of the mean observations.
- One of the purposes
of statistics is to use a sample to estimate something about the
population. Estimates form the basis of statistical tests.
- Confidence intervals
can be formed around an estimate to tell us how much the estimate
would vary in repeated samples.
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Neisseria meningitidis, a gram-negative diplococcus, has as its
natural reservoir the human posterior nasopharynx where it can be
cultured from 2–15% of healthy individuals during
nonepidemic periods. The bacterial organism can be typed into at
least 13 serogroups based on capsular antigens. These serogroups
can be further subdivided by antibodies to specific subcapsular
membrane proteins. In the United States, sero groups B and C have
accounted for 90% of meningococcal meningitis cases in
recent decades. The major manifestations of meningo coccal disease
are acute septicemia and purulent meningitis. The age-specific attack
rate is greatest for children under 5 years of age.
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Epidemiologic surveillance data from the state of Oregon detected
an increase in the overall incidence rate of meningococcal disease
from 2 cases per 100,000 population during 1987–1992 to 4.5
cases per 100,000 population in 1994 (Diermayer et al, 1999). Epidemiologists
from Oregon and the Centers for Disease Control wanted to know if
the increased numbers ...