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Chapter 6
EXERCISES
6.1 - 6.9 See text pp. 136 - 139.
6.10 Mortality and
life expectancy. This schematics illustrates the survival experience of a cohort:
Each line in this schematic
represents an individual. The symbol D represents death. This cohort has full
follow-up, with individuals followed until death.
(A) Calculate the mortality rate in the cohort
(B) Calculate average life span.
(C) Describe the mathematical relation between the mortality rate and life expectancy in this cohort (p. 130).
6.11 Mortality and life expectancy, part B.
(A) Calculate the mortality rate in the cohort
(B) Calculate life expectancy. How does the life expectancy in this cohort
compare to that of the cohort in question 6.10?
6.12 Person-time and % surviving. See exercise 6.10 for an explanation of the symbols in this schematic:
(A) Count the person-time in this cohort.
(B) The schematic has been modified to emulate a Kaplan-Meier survival curve. Based on this curve, what percent of the cohort survived for two years? What percentage survived four years?
(C) The area under the above Kaplan-Meier survival curve is equivalent to the person-time in the cohort. Because of the rectangular nature of various intervals on this “curve,” it is easy to determine areas associated with various units of time (Area of rectangle = base × height). For example, between year 0 and year 1, the “curve” comprises a rectangle with a base 1 and height 4, and thus has area = 1 year × 4 persons = 4 person-years. Determine the number of person- between year 1 and 2.
(D) Determine the number of person-years were between years 2 and 4?
(E) How many person years were there total? How does this compare to the total person-years in the cohort?
6.13 Breast cancer.
A study starts with
10,000 women. Of these, 500 had already experienced breast cancer. The
remaining 9,500 are followed for five-years. Two-hundred fifty breast cancer
incidents occurred during the 5 years of following.
(A) What is the five-year cumulative incidence (proportion) of breast cancer? Report the incidence per 1000 people.
(B) What is the incidence rate of breast cancer? No life-table adjustment of the denominator is necessary. Report the rate "per 1000 person-years".
6.14 Cohort study,
CHD. One-thousand
people are recruited for a study. Eight-hundred-fifty agree to participate.
Fifty have coronary heart disease upon examination. Over the next ten years,
100 develop coronary heart disease.
(A) What is the 10-year incidence proportion (average risk) of coronary heart disease in this cohort?
(B) What is the rate in the cohort?
6.15 Rates of
driving errors. "Every two miles, the average driver makes four hundred
observations, forty decisions, and one mistake. Once every five hundred miles,
one of those mistakes leads to a near collision, and once every sixty-one
thousand miles one of those mistakes leads to a crash." (New Yorker, Gladwell,
June 11, 2001, pp. 50-61.)
(A) What is the rate of mistakes per mile?
(B) What proportion of observations are mistaken?
(C) Why is the answer to Part A a rate and the answer to Part B a proportion?
(D) What is the odds of near collisions to actual collisions?
6.16 Open
population.
Here's a schematic in which "o" represents either the beginning or
end of a follow-up interval and "D" represents disease onset.
(A) Determine the total number of people in the population (N).
(B) Determine the average number of people (Ñ). [Ñ = PT / change in time]
(C) Determine the mortality rate
6.17 Another cohort. A cohort of 150 people begins with
10 cases. The cohort is followed for five years, during which time 16 new cases
arise.
(A) What is the prevalence of disease at the start of the study?
(B) Assume all cases survive. What is the prevalence at the end of the study?
(C) What is the incidence proportion over the interval?
(D) What is the incidence rate over the interval?
6.18 Just like Exercise 6.1. The
figure below represents a cohort of 7 individuals observed for a year. In this
figure, periods of disease are represented with a D and dashes represents
disease-free periods. There are no losses to
follow-up in the cohort, and we assume that recovery will confer life-long
immunity.
(A) What is the prevalence on Jan 1?
(B) What is the prevalence on Dec 31?
(C) Estimate the one-year risk of developing illness.Person 1 -|---------------------|--
Person 2 D|DDDDDDD--------------|--
Person 3 -|-----------------DDDD|DD
Person 4 -|---------------------|--
Person 5 -----DDDDDDDDDDDDDDDDDD|DD
Person 6 -|---------------------|--
Person 7 -|---------------------|--
| |
Jan1 Dec31
6.19 Just like
Exercise 6.3. A population demonstrates the following vital statistics:
Total midyear population 25,000
Population size, 65-years of age or older 2,500
Number of live births 300
Total deaths (all cause) 250
Deaths in under 1-year olds 3
Deaths in persons 65 and over 75(A) Calculate the crude birth rate per 1,000.
(B) Calculate the crude mortality rate per 1,000.
(C) Calculate the infant mortality rate per 1000.
(D) Calculate the age-specific mortality rate for those over 65 (per 1000).
6.20 In the schematic below, dashed lines
(--) represent disease-free person-time and D indicates a disease onset. There
are three (3) people in the cohort, labeled A, B, and C.
A|--------D
B|------------------------
C|------------------------
|---|----|----|----|----|
0 1 2 3 4 5
Year(A) What is the 5-year risk of disease in the cohort?
(B) What is the rate of the disease in the cohort?
6.21 Twice the
prevalence with the same risk. Suppose the prevalence of disease in population A is 20 per
100,000. The prevalence in population B is 10 per 100,000. The groups have
identical age distributions. Can we conclude that population A has twice the
risk compared to group B? Explain.