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Lesson 3: Measures of Risk

Pencil graphicExercise Answers

Exercise 3.1

  1. B
  2. C
  3. A
  4. B
  5. A

Exercise 3.2

  1. A; denominator is size of population at start of study, numerator is number of deaths among that population.
  2. B; denominator is person-years contributed by participants, numerator is number of death among that population.
  3. C; numerator is all existing cases.
  4. A; denominator is size of population at risk, numerator is number of new cases among that population.
  5. B; denominator is mid-year population, numerator is number of new cases among that population.
  6. C; numerator is total number with attribute.
  7. D; this is a ratio (heart disease:smokers)

Exercise 3.3

  1. 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
    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
  2. These are cause- and sex-specific mortality rates.
  3. Homicide-mortality rate ratio
    = homicide death rate (males) ⁄ homicide death rate (females)
    = 11.1 ⁄ 3.3
    = 3.4 to 1
    = (see below, which is the answer to question 4).
  4. Because the homicide rate among males is higher than the homicide rate among females, specific intervention programs need to target males and females differently.

Exercise 3.4

DecadeNumber of
New Cases
Number of
Deaths
Death-to-case
Ratio (×100)
1940–1949
143,497
11,228
7.82 (Given)
1950–1959
23,750
1,710
7.20
1960–1969
3,679
390
10.60
1970–1979
1,956
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 conclude that the decline in deaths 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.

Exercise 3.5

Proportionate mortality for diseases of heart, 25–44 years

= (# deaths from diseases of heart ⁄ # deaths from all causes) × 100

= 16,283 ⁄ 128,294 × 100

= 12.6%

Proportionate mortality for assault (homicide), 25–44 years

= (# deaths from assault (homicide) ⁄ # deaths from all causes) × 100

= 7,367 ⁄ 128,924 × 100

= 5.7%

Exercise 3.6

  1. HIV-related mortality rate, all ages
    = (# deaths from HIV ⁄ estimated population, 2002) × 100,000
    = (14,095 ⁄ 288,357,000) × 100,000
    = 4.9 HIV deaths per 100,000 population
  2. HIV-related mortality rate for persons under 65 years
    = (# deaths from HIV among <65 years year-olds ⁄ estimated population < 65 years, 2002) × 100,000
    = (12 + 25 + 178 + 1,839 + 5,707 + 4,474 + 1,347 ⁄ 19,597 + 41,037 + 40,590 +39,928 + 44,917 + 40,084 + 26,602) × 100,000
    = 13,582 ⁄ 252,755,000 × 100,000
    = 5.4 HIV deaths per 100,000 persons under age 65 years
  3. HIV-related YPLL before age 65
    Deaths and years of potential life lost attributed to HIV by age group — United States, 2002
    Column 1
    Age Group (years)
    Column 2
    Deaths
    Column 3
    Age Midpoint
    Column 4
    Years to 65
    Column 5
    YPLL
    Total14,095291,020
    0–4122.562.5750
    5–102510551,375
    15–2417820458,010
    25–341,839303564,365
    35–445,7074025142,675
    45–544,474501567,110
    55–641,3476056,735
    65+509
    -
    -
    -
    Not stated4
    -
    -
    -
  4. HIV-related YPLL65 rate
    YPLL65 rate = (291,020 ⁄ 252,755,000) × 1,000 = 1.2 YPLL per 1,000 population under age 65.
  5. Compare mortality rates and YPLL for leukemia and HIV
    LeukemiaHIV
    # cause-specific deaths, all ages21,49814,095
    cause-specific death rate, all ages (per 100,000 pop)7.54.9
    # deaths, < 65 years6,22113,582
    death rate, < 65 years2.55.4
    YPLL65117,033291,020
    YPLL65 rate0.51.2
    An advocate for increased leukemia research funding might use the first two measures, which shows that leukemia is a larger problem in the entire population. An advocate for HIV funding might use the last four measures, since they highlight HIV deaths among younger persons.

Exercise 3.7

  1. Rate ratio comparing current smokers with nonsmokers
    = rate among current smokers ⁄ rate among non-smokers
    = 1.30 ⁄ 0.07
    = 18.6
  2. Rate ratio comparing ex-smokers who quit at least 20 years ago with nonsmokers
    = rate among ex-smokers ⁄ rate among non-smokers
    = 0.19 ⁄ 0.07
    = 2.7
  3. The lung cancer rate among smokers is 18 times as high as the rate among non-smokers. Smokers who quit can lower their rate considerably, but it never gets back to the low level seen in never-smokers. So the public health message might be, "If you smoke, quit. But better yet, don't start."

Exercise 3.8

Odds ratio = ad ⁄ bc

= (28 × 133) ⁄ (129 × 4)
= 7.2

The odds ratio of 7.2 is somewhat larger (18% larger, to be precise) than the risk ratio of 6.1. Whether that difference is "reasonable" or not is a judgment call. The odds ratio of 7.2 and the risk ratio of 6.1 both reflect a very strong association between prison wing and risk of developing tuberculosis.

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