Computation and Measurement of Risk - Mathematics and Statistics for the Environment - page 183

Number of womeninState Awho died fromheartdiseasein 2008
Number of womeninStateeAwhodiedin 2008
Number of womeninState Awho died fromlung cancer in 2004
Number of womeninState Awho died from cancerr(alltypes) in 2004
For a proportion, 10 n is usually 100 (or n = 2) and is often expressed as a percentage. Example 8.3
and Example 8.4 illustrate how proportion is calculated.
■ EXAMPLE 8.3
Problem: Calculate the proportion of men in the NHANES follow-up study who were diabetics.
Solution:
Numerator = 189 diabetic men
Denominator = Total number of men = 189 + 3151 = 3340
Proportion = (189/3340) × 100 = 5.66%
■ EXAMPLE 8.4
Problem: Calculate the proportion of deaths among men.
Solution:
Numerator = deaths in men
= 100 deaths in diabetic men + 811 deaths in non-diabetic men
= 911 deaths in men
Notice that the numerator (911 deaths in men) is a subset of the denominator.
Denominator = all deaths
= 911 deaths in men + 72 deaths in diabetic women + 511 deaths in non-diabetic women
= 1494 deaths
Proportion = (911/1494) × 100 = 60.98%, or 61%
8.2.2.1 Properties and Uses of Proportions
Proportions are common descriptive measures used in all fields. In environmental health and epide-
miology, proportions are used most often as descriptive measures. For example, one could calculate
the proportion of persons enrolled in a study among all those eligible (“participation rate”), the
proportion of children in a village vaccinated against measles, or the proportion of persons who
developed illness among all passengers of a cruise ship. Proportions are also used to describe the
amount of disease that can be attributed to a particular exposure. For example, on the basis of stud-
ies of smoking and lung cancer, public health officials have estimated that greater than 90% of the
lung cancer cases that occur are attributable to cigarette smoking. In a proportion, the numerator
must be included in the denominator. Thus, the number of apples divided by the number or oranges
is not a proportion, but the number of apples divided by the total number of fruits of all kinds is a
proportion. Remember, the numerator is always a subset of the denominator.
A proportion can be expressed as a fraction, a decimal, or a percentage. The statements “one
fifth of the residents became ill” and “twenty percent of the residents because ill” are equivalent.
Proportions can easily be converted to ratios. If the numerator is the number of women (179) who
attended a clinic and the denominator is all the clinic attendees (341), the proportion of clinic
attendees who were women is 179/341, or 53% (a little more than half). To convert to a ratio, subtract