# Lesson 3: Measures of Risk

## Answers to Self-Assessment Quiz

- A, B, C, D. Frequency measures of health and disease include those related to birth, death, and morbidity (incidence and prevalence).
- A, B. All fractions are ratios. This fraction is also a proportion, because all of the deaths from lung cancer in the numerator are included in the denominator. It is not an incidence proportion, because the denominator is not the size of the population at the start of the period. It is not a mortality rate because the denominator is not the estimated midpoint population.
- A. All fractions are ratios. This fraction is not a proportion, because lung cancer deaths in the numerator are not included in the denominator. It is not an incidence proportion, because the denominator is not the size of the population at the start of the period. It is not a mortality rate because the denominator is not the estimated midpoint population.
- A, D. All fractions are ratios. This fraction is not a proportion, because some of the deaths occurred before July 1, so those women are not included in the calculation. It is not an incidence proportion, because the denominator is not the size of the population at the start of the period. It is a mortality rate because the denominator is the estimated midpoint population.
- A. All fractions, including proportions, are ratios. But only ratios in which the numerator is included in the denominator is a proportions.
- C. Probability or risk are estimated by the incidence proportion, calculated as the number of new cases during a specified period divided by the size of the population at the start of that period.
- B. The secondary attack rate is calculated as the number of cases among contacts (4) divided by the number of contacts (10).
- D. During year 1, 92 returning patients contributed 92 person-years; 8 patients lost to follow-up contributed 8 × ½ or 4 years, for a total of 96. During the second year, 78 disease-free patients contributed 78 person-years, plus ½ years for the 2 with newly diagnosed eye disease, the 2 who had died, and the 10 lost to follow-up (all events are assumed to have occurred randomly during the year, or an average, at the half-year point), for a total of 78 + 14 × ½ years, for another 85 years. During the third year, returning healthy patients contributed 60 years; the 3 with eye disease, the 4 who died, and the 11 lost to follow-up contributed 18 × ½ years or 9 years, for a total of 69 years during the 3
^{rd}year. The total person-years is therefore 96 + 85 + 69 = 250 person-years. - C, D. The person-time rate presented in Question 8 should be reported as 5 cases per 250 person-years. Usually person-time rates are expressed per 1,000 or 10,000 or 100,000, depending on the rarity of the disease, so the rate in Question 8 could be expressed as 2 cases per 100 person-years of follow-up. One could express this more colloquially as 2 new cases of eye disease per 100 diabetics per year.
- A. Measure of risk

B. Generally preferred for chronic diseases without clear date of onset

A. Used in calculation of risk ratio

B. Affected by duration of illness

Incidence reflects new cases only; incidence proportion is a measure of risk. A risk ratio is simply the ratio of two incidence proportions. Prevalence reflects existing cases at a given point or period of time, so one does not need to know the date of onset. Prevalence is influenced by both incidence and duration of disease — the more cases that occur and the longer the disease lasts, the greater the prevalence at any given time.Ill Well Total Total 54 25 79 Ate wedding cake? Yes 50 3 53 No 4 22 26 - B, C, D. The fraction 54 ⁄ 79 (see bottom row of the table) reflects the overall attack rate among persons who attended the wedding and were interviewed. Attack rate is a synonym for incidence proportion.
- D. The fraction 50 ⁄ 54 (under the Ill column) is the proportion of case-patients who ate wedding cake. It is not an attack rate, because the denominator of an attack rate is the size of the population at the start of the period, not all cases.
- A, B, C, D. The fraction 50 ⁄ 53 (see top row of table) is the proportion of wedding cake eaters who became ill, which is a food-specific attack rate. A food-specific attack rate is a type of attack rate, which in turn is synonymous with incidence proportion.
- C. Investigators were able to interview almost everyone who attended the wedding, so incidence proportions (measure of risk) were calculated. When incidence proportions (risks) can be calculated, the best measure of association to use is the ratio of incidence proportions (risks), i.e., risk ratio.
- A. The risk ratio is calculated as the attack rate among cake eaters divided by the attack rate among those who did not eat cake, or (50 ⁄ 53) ⁄ (4 ⁄ 26), or 94.3% ⁄ 15.4%, which equals 6.1.
- D. The attributable proportion is calculated as the attack rate among cake eaters minus the attack rate among non-eaters, divided by the attack rate among cake eaters, or 94.3 – 15.4) ⁄ 94.3, which equals 83.7%. This attributable proportion means that 83.7% of the illness might be attributable to eating the wedding cake (note that some people got sick without eating cake, so the attributable proportion is not 100%).
- D. A total of 8 cases are present at some time during the month of July.
- C. Five new cases occurred during the month of July.
- A, D. The fraction shown is the infant mortality rate. It is a ratio, because all fractions are ratios. It is not a proportion because some of the children who died in early 2004 may have been born in late 2003, so some of those in the numerator are not in the denominator. Technically, the mortality rate for infants is the number of infants who died in 2004 divided by the estimated midyear population of infants, so the fraction shown is not a mortality rate in that sense. However, the fraction is known throughout the world as the infant mortality rate, despite the technical inaccuracy.
- E. The data shown in the table are numbers of deaths. No denominators are provided from which to calculate rates. Neither is the total number of deaths given, so proportionate mortality cannot be calculated. However, calculation of potential life lost need only the numbers of deaths by age, as shown.
- C, D. Only crude and cause-specific mortality rates use the estimated total mid-year population as its denominator. The denominator for an age-specific mortality rate is the estimated mid-year size of that particular age group. The denominator for a sex-specific mortality rate is the estimated mid-year male or female population.
- A, C, D. The fraction is the mortality rate due to septicemia (cause) among men (sex) aged 65–74 years (age). Age-specific mortality rates are narrowly defined (in this fraction, limited to 10 years of age), so are generally valid for comparing two populations without any adjustment.
- C. Vaccine efficacy measures the proportionate reduction in disease among vaccinees.
- C. The results of this study could be summarized in a two-by-two table as follows:

The odds ratio is calculated as ad⁄bc, or (32 × 60) ⁄ (8 × 20), which equals 1,920 ⁄ 160 or 12.0.Cases Controls Total Total40 80 120 Stored maize inside? Yesa = 32 c = 20 52 Nob = 8 d = 60 68 - C. The crude mortality rate reflects the mortality experience and the age distribution of a community, whereas the age-adjusted mortality rate eliminates any differences in the age distribution. So if Community A's age-adjusted mortality rate was lower than its crude rate, that indicates that its population is older.

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