Ratio

Method for calculating a ratio

Number or rate of events, items, persons,
etc. in one group
Number or rate of events, items, persons,
etc. in another group

Example A: A city of 4,000,000 persons has 500 clinics. Calculate the ratio of clinics per person.
500 ⁄ 4,000,000 × 10n = 0.000125 clinics per person
TEST: Delaware's infant mortality rate in 2001 was 10.7 per 1,000 live births.(2) New Hampshire's
infant mortality rate in 2001 was 3.8 per 1,000 live births. Calculate the ratio of the infant mortality
rate in Delaware to that in New Hampshire.

ANSWER 10.7 ⁄ 3.8 × 1 = 2.8:1

Thus, Delaware's infant mortality rate was 2.8 times as high as New Hampshire's infant mortality rate
in 2001.

Proportion
Method for calculating a proportion
Number of persons or events with a
particular characteristic × 10 n
Total number of persons or events, of which
the numerator is a subset

Example A: Calculate the proportion of men in the NHANES follow-up study who were diabetics.
Numerator = 189 diabetic men
Denominator = Total number of men = 189 + 3,151 = 3,340
Proportion = (189 ⁄ 3,340) × 100 = 5.66%
TEST: Calculate the proportion of deaths among men.

ANSWER Numerator = deaths in men

= 100 deaths in diabetic men + 811 deaths in nondiabetic 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 nondiabetic women
= 1,494 deaths
Proportion = 911 ⁄ 1,494 = 60.98% = 61%
Your Turn: What proportion of all study participants were men? (Answer = 45.25%)

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 Incidence Proportion (risk)
Method for calculating incidence proportion (risk)
Number of new cases of disease or injury during
specified period

Size of population at start of period

Example A: In the study of diabetics, 100 of the 189 diabetic men died during the 13-year follow-up
period. Calculate the risk of death for these men.
Numerator = 100 deaths among the diabetic men
Denominator = 189 diabetic men
10n = 102 = 100
Risk = (100 ⁄ 189) × 100 = 52.9%
TEST: In an outbreak of gastroenteritis among attendees of a corporate picnic, 99 persons ate
potato salad, 30 of whom developed gastroenteritis. Calculate the risk of illness among persons who
ate potato salad. Numerator = 30 persons who ate potato salad and developed gastroenteritis
Denominator = 99 persons who ate potato salad
10n = 102 = 100
ANSWER Risk = "Food-specific attack rate" = (30 ⁄ 99) × 100 = 0.303 × 100 = 30.3%

Incidence rate
Method for calculating incidence rate
Number of new cases of disease or injury during specified period

Time each person was observed, totaled for all persons

Example B: The diabetes follow-up study included 218 diabetic women and 3,823 nondiabetic
women. By the end of the study, 72 of the diabetic women and 511 of the nondiabetic women had
died. The diabetic women were observed for a total of 1,862 person years; the nondiabetic women
were observed for a total of 36,653 person years. Calculate the incidence rates of death for the
diabetic and non-diabetic women.

TEST: In 2003, 44,232 new cases of acquired immunodeficiency syndrome (AIDS) were reported in
the United States. The estimated mid-year population of the U.S. in 2003 was approximately
290,809,777. Calculate the incidence rate of AIDS in 2003.

ANSWER Numerator = 44,232 new cases of AIDS

Denominator = 290,809,777 estimated mid-year population
10n = 100,000
Incidence rate = (44,232 ⁄ 290,809,777) × 100,000
= 15.21 new cases of AIDS per 100,000 population

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NAMES OF MEMBERS

EXAMPLE: Calculating Prevalence

In a survey of 1,150 women who gave birth in Maine in 2000, a total of 468 reported taking a
multivitamin at least 4 times a week during the month before becoming pregnant.(7) Calculate the
prevalence of frequent multivitamin use in this group.

Numerator = 468 multivitamin users

Denominator = 1,150 women

Prevalence = (468 ⁄ 1,150) × 100 = 0.407 × 100 = 40.7%

TEST: Out of 54 students who took an exam 5 got an F grade. Calculate the prevalence of
students who failed the exam.

5÷54×100= 9 %

EXAMPLES: Incidence versus Prevalence

Figure below represents 10 new cases of illness over about 15 months in a population of 20
persons. Each horizontal line represents one person. The down arrow indicates the date of onset of
illness. The solid line represents the duration of illness. The up arrow and the cross represent the
date of recovery and date of death, respectively.

Figure New Cases of Illness from October 1, 2004–September 30, 2005

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 Example A: Calculate the incidence rate from October 1, 2004, to September 30, 2005, using the
midpoint population (population alive on April 1, 2005) as the denominator. Express the rate per 100
population.
Incidence rate numerator = number of new cases between October 1 and September 30
= 4 (the other 6 all had onsets before October 1, and are not included)

Incidence rate denominator = April 1 population

= 18 (persons 2 and 8 died before April 1)

Incidence rate = (4 ⁄ 18) × 100

= 22 new cases per 100 population

TEST: Calculate the point prevalence on April 1, 2005. Point prevalence is the number of persons ill
on the date divided by the population on that date. On April 1, seven persons (persons 1, 4, 5, 7, 9,
and 10) were ill.
Point prevalence = (7 ⁄ 18) × 100
= 38.89%

TEST: Calculate the period prevalence from October 1, 2004, to September 30, 2005. The
numerator of period prevalence includes anyone who was ill any time during the period. In Figure ,
the first 10 persons were all ill at some time during the period.
Period prevalence = (10 ⁄ 20) × 100
= 50.0%

Mortality rate
Deaths occurring during a given time period × 10 n
Size of the population among which
the deaths occurred

EXAMPLE: In the United States in 2003, a total of 2,419,921 deaths occurred. The estimated
population was 290,809,777. The mortality rate in 2003 was, therefore, (2,419,921 ⁄ 290,809,777) ×
100,000, or 832.1 deaths per 100,000 population.

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 TEST: In 2001, a total of 15,555 homicide deaths occurred among males and 4,753 homicide
deaths occurred among females. The estimated 2001 midyear populations for males and females
were 139,813,000 and 144,984,000, respectively.

1. Calculate the homicide-related death rates for males and for females.
2. Homicide-related death rate (males)
= (# homicide deaths among males ⁄ male population) × 100,000
= 15,555 ⁄ 139,813,000 × 100,000
= 11.1 homicide deaths ⁄ 100,000 population among males
3. Homicide-related death rate (females)
= (# homicide deaths among females ⁄ female population) × 100,000
= 4,753 ⁄ 144,984,000 × 100,000
= 3.3 homicide deaths ⁄ 100,000 population among females

4. What type(s) of mortality rates did you calculate in Question 1?

These are cause- and sex-specific mortality rates.

5. Calculate the ratio of homicide-mortality rates for males compared to females.

Homicide-mortality rate ratio

homicide death rate (males) ⁄ homicide death rate (females)

= 11.1 ⁄ 3.3
= 3.4 to 1

6. Interpret the rate you calculated in Question 3 as if you were presenting information to a
policymaker.

Because the homicide rate among males is higher than the homicide rate among females, specific
intervention programs need to target males and females differently.