Computation and Measurement of Risk - Mathematics and Statistics for the Environment - page 199

To eliminate the distortion caused by different underlying age distributions in different popula-
tions, statistical techniques are used to adjust or standardize the rates among the populations to
be compared. These techniques take a weighted average of the rate-specific mortality rates and
eliminate the effect of different age distributions among the different populations. Mortality rates
computed with these techniques are age-adjusted or age-standardized mortality rates . Alaska's
2002 age-adjusted mortality rate (794.1 per 100,000) was higher than Florida's (787.8 per 100,000),
which is not surprising given that 7 of 13 age-specific mortality rates were higher in Alaska than
Florida.

8.4.2 d eath - to -C ase r atio
The death-to-case ratio is the number of deaths attributed to a particular disease during a specified
time period divided by the number of new cases of that disease identified during the same time
period. The death-to-case ratio is a ratio but not necessarily a proportion, because some of the
deaths that are counted in the numerator might have occurred among persons who developed the
disease in an earlier period and are therefore not counted in the denominator.

8.4.2.1 Method for Calculating Death-to-Case Ratio

Number of deaths attributed to aparticular disease duringspecified period
Number of new cases of thediseaseidentified during thespecified period

×10 n

■ EXAMPLE 8.16
Problem: Between 1940 and 1949, a total of 143,497 incident cases of diphtheria were reported.
During the same decade, 11,228 deaths were attributed to diphtheria. Calculate the death-to-case
ratio.
Solution:

Death-to-case ratio = 11,228/143,497 × 1 = 0.0783

or

Death-to-case ratio = 11,228/143,497 × 100 = 7.83 per 100

■ EXAMPLE 8.17
Problem: The following table provides the number of reported cases of diphtheria and the number
of diphtheria-associated deaths in the United States by decade. Calculate the death-to-case ratio by
decade. Describe the data in the table, including your results (CDC, 1999, 2001, 2003).

Number of Cases and Deaths from Diphtheria
by Decade—United States, 1940-1999

Number of
New Cases

Number
of Deaths

Death-to-Case Ratio
( × 100) Decade

1940-1949 143,497 11,228 7.62

1950-1959 23,750 1710

1960-1969 3679 390

1970-1979 1956 90

1980-1989 27 3

1990-1999 22 5