Lesson 3: Measures of Risk

Exercise 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

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

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

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
   Total	14,095		291,020
   0–4	12	2.5	62.5	750
   5–10	25	10	55	1,375
   15–24	178	20	45	8,010
   25–34	1,839	30	35	64,365
   35–44	5,707	40	25	142,675
   45–54	4,474	50	15	67,110
   55–64	1,347	60	5	6,735
   65+	509	–	–	–
   Not stated	4	–	–	–

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
   

   	Leukemia	HIV
   # cause-specific deaths, all ages	21,498	14,095
   cause-specific death rate, all ages (per 100,000 pop)	7.5	4.9
   # deaths, < 65 years	6,221	13,582
   death rate, < 65 years	2.5	5.4
   YPLL65	117,033	291,020
   YPLL65 rate	0.5	1.2

   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.