Computation and Measurement of Risk - Mathematics and Statistics for the Environment - page 200

Solution:

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 7.20

1960-1969 3679 390 10.60

1970-1979 1956 90 4.60

1980-1989 27 3 11.11

1990-1999 22 5 22.72

The number of new cases and deaths from diphtheria declined dramatically from the 1940s through
the 1980s but remained roughly level at very low levels in the 1990s. The death-to-case ratio was
actually higher in the 1980s and 1990s than in 1940s and 1950s. From these data one might con-
clude that the decline in death is a result of the decline in cases—that is, from prevention rather than
from any improvement in the treatment of cases that do occur.

8.4.3 C ase -F atality r ate
The case-fatality rate is the proportion of persons with a particular condition (cases) who die from
that condition. It is a measure of the severity of the condition. The formula is

Number of cause-specificdeaths among theincident cases
Number of incident cases

×10 n

The case-fatality rate is a proportion, so the numerator is restricted to deaths among people included
in the denominator. The time periods for the numerator and the denominator do not need to be the
same; the denominator could be cases of HIV/AIDS diagnosed during the calendar year 1990, and
the numerator, deaths among those diagnosed with HIV in 1990, could be from 1990 to the present.

■ EXAMPLE 8.18
Problem : In an epidemic of hepatitis A traced to green onions from a restaurant, 555 cases were iden-
tified. Three of the case-patients died as a result of their infections. Calculate the case-fatality rate.

Solution:

Case-fatality rate = (3/555) × 100 = 0.5%

The concept behind the case-fatality rate and the death-to-case ratio is similar, but the formu-
lations are different. The death-to-case ratio is simply the number of cause-specific deaths that
occurred during a specified time divided by the number of new cases of that disease that occurred
during the same time. The deaths included in the numerator of the death-to-case ratio are not
restricted to the new cases in the denominator; in fact, the deaths included in the numerator are
restricted to the cases in the denominator.

DID YOU KNOW?

The case-fatality rate is a proportion, not a true rate. As a result, some environmental practi-
tioners prefer the term case-fatality ratio .