X, which isBðn;pÞ. In situations where the infection ratelis very small, the
Poisson distribution could be used as an approximation, withy¼mlbeing the
expected number of infected insects in a pool. The Poisson probability of this
number being zero is
p¼expðyÞand we have the same binomial distributionBðn;pÞ. It is interesting to note that
testing for syphilis (as well as other very rare diseases) in the U.S. Army used to
be done this way.
Example 10.2 For the year of 1981, the infant mortality rate (IMR) for the
United States was 11.9 deaths per 1000 live births. For the same period, the
New England states (Connecticut, Maine, Massachusetts, New Hampshire,
Rhode Island, and Vermont) had 164,200 live births and 1585 infant deaths. If
the national IMR applies, the mean and vaiance of the number of infant deaths
in the New England states would be
ð 164 : 2 Þð 11 : 9 Þ¼ 1954From thezscore,
z¼1585 1954
ffiffiffiffiffiffiffiffiffiffi
1954p¼ 8 : 35
it is clear that the IMR in the New England states is below the national aver-
age.
Example 10.3 Cohort studies are designs in which one enrolls a group of
healthy persons and follows them over certain periods of time; examples
include occupational mortality studies. The cohort study design focuses atten-
tion on a particular exposure rather than a particular disease as in case–control
studies. Advantages of a longitudinal approach include the opportunity for
more accurate measurement of exposure history and a careful examination of
the time relationships between exposure and disease.
The observed mortality of the cohort under investigation often needs to be
compared with that expected from the death rates of the national population
(served as standard), with allowance made for age, gender, race, and time
period. Rates may be calculated either for total deaths or for separate causes of
interest. The statistical method is often referred to as theperson-years method.
The basis of this method is the comparison of the observed number of deaths,
d, from the cohort with the mortality that would have been expected if the
group had experienced death rates similar to those of the standard population
352 METHODS FOR COUNT DATA