EPIDEMIOLOGY 200A
Drs. Olsen & Arah
Fall 2009
EXERCISE 2: DISEASE OCCURRENCE
Problem 1. For a population of 10,000 in steady-state you have been told the following
about a certain disease and an exposure of interest:



40% of your population reports exposure to the risk factor in a year
One-year risk of disease among the exposed is estimated to be 0.35
One-year risk of disease among the unexposed is estimated to be 0.15
Fill in the following 2 x 2 table based on the one-year information given above.
Disease
No Disease
Total
Exposure
No Exposure
Total
10,000
How many cases of this disease do you expect to see in one year?
What is the estimated prevalence of this disease among the population?
What is the risk ratio? Interpret your result in words.
What is the risk difference? Interpret your result in words.
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Among the exposed, what is the proportion of disease that can be attributed to the
exposure?
You work for the mayor of this community and she says to you, “What proportion of
disease could we eliminate from our population if we were to eliminate this exposure?”
What will you tell her?
Problem 2. What is the difference between incidence and prevalence?
Problem 3. How are prevalence and incidence related?
Problem 4. For each of the following scenarios, determine whether it more closely
resembles incidence or prevalence:

Number of campers who developed gastroenteritis within 24 hours after eating
potato salad at the dining hall

Number of persons who reported having hypertension as part of a national survey.

Occurrence of Acute Myocardial Infarction in participants during the first 10
years of follow up in Framingham Heart Study.
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Problem 5
In a survey to evaluate the vaccination program among children less than 5 years
old in two cities A and B, the coverage is:
Diseases
Measles
Tetanus
Polio
Hepatitis B
Areas
City A
70%
80%
90%
85%
City B
95%
92%
97%
90%
We can conclude that:
a. The number of children vaccinated for measles in City B is greater than in
City A
b. The number of children vaccinated for measles in City A is greater than in
City B
c. Hepatitis B vaccination program was best done (in coverage aspect) in both
areas
d. Overall, vaccination program was more successful (in coverage) in city B than
in city A
e. None of the above
Problem 6
A community is a steady-state population in which 2000 persons at any given
time are at risk for a specific incurable disease, and there is no net migration of
cases into or out of the community. If 240 new cases of that disease occur each
year and if the mean duration of the disease is 10 months, then the prevalence of
the disease in the community is:
a. 9%
b. 10%
c 12%
d 33%
e. 55%
Problem 7
A fixed cohort of 20 persons is followed for 1 year from Jan 1. During the follow-up time
4 deaths occurred (at the start of each month -- Feb, March, May and June). Assume there
was no loss to follow-up. The one year risk of dying in that cohort population is:
a. 10%
b. 20%
c. 21%
d. 5%
e. 25%
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Problem 8
A closed cohort of 100 subjects was examined for a disease at baseline and 2 years later.
20 subjects had the disease at baseline. Additionally, 30 new cases had the disease at
follow-up; however, 18 existing cases (among the 20 cases at baseline) were accidentally
counted again as part of the 30 cases at follow-up. The actual two-year risk of disease is:
a. 0%
b. 12%
c. 13%
d. 15%
e. 20%
Problem 9
20 new cases of STDs occurred during a 5 year follow-up period in a closed cohort of
100 women aged 20-30 years old, who were screened as non-cases of STDs at the
beginning of the follow-up. The 5 years risk of STDs in this cohort is:
a. 10%
b. 18%
c. 20%
d. 24%
e. 27%
Problem 10
During the period 1930-1970, the annual number of deaths due to cancer in the United
States increased from 118,000 to 331,000. One explanation for this steep increase could
be an increased exposure of the population to carcinogenic substances. What are some
other possible explanations?
Problem 11
A study published in 1990 (Am J Pub Health 80:p. 209-210) investigated the occurrence
of HIV infection among prisoners in Nevada. Of 1105 prison inmates who were tested
for HIV upon admission to the prison system, 36 were found to be infected. All
uninfected prisoners were followed for a total of 1207 person-years and retested for HIV
upon release from prison. Two of the uninfected inmates demonstrated evidence of new
HIV infection. Assuming that the two prisoners were infected during their time in prison:
a. Based on the above information, calculate the incidence rate of HIV infection among
prisoners in the Nevada prisons.
b. Express the incidence rate calculated in part a in terms of cases per 1000 person-years.
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c. Calculate the prevalence of HIV infection among the incoming prisoners in the Nevada
prisoners at the start of the study.
d. What is the size of the population at risk for HIV at the beginning of the study?
Problem 12
You are interested in determining the incidence, mortality, and case-fatality due to AIDS
in Los Angeles County. You assemble a group of 110 men, who are HIV positive, of
whom 100 are at risk of developing AIDS (the other 10 already met the case definition of
AIDS due to their low CD4 count and high viral load), and follow them (all 110 of them)
for a period of 10 years. During the 10 year follow-up period, 5 of them die of AIDS, and
30 of them meet the case definition of AIDS. Among the 20 of whom were newly
diagnosed with AIDS, 4 die within 1 year after infection. Assume that the subjects either
died or recovered within 1 year of meeting the AIDS definition, and that the outcome was
observed for all incident cases of AIDS. Assume that there are no losses to follow-up and
there are no competing risks.
a. Estimate the 10 year risk of developing AIDS in this group of subjects.
b. During the 10 year follow-up period, 5 of them die of AIDS. Estimate the 10 year
mortality risk in the base population.
c. Estimate the 1 year fatality risk of dying from AIDS in this group of subjects.
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Problem 13
For the following problem, assume that the disease does not result in lasting immunity
after recovery (i.e. persons are at risk again as soon as they recover) and that this is a
closed cohort (i.e. membership in the cohort is permanent based on its definition).
a. What is the prevalence of the disease in February 1997?
b. What is the size of the population at the beginning of 1996?
c. What is the number of new cases during 1996?
d. What is the cumulative incidence of the disease for 1996?
e. What is the mid-year size of the population in 1996 (i.e. as of July 1996)?
f. In practice, calculating the total number of people at risk in a population is
difficult, so a mid-year tally is used to estimate the total number at risk during
the entire time period. Calculate the cumulative incidence of the disease in
1996, using the 1996 mid-year, at-risk population as an estimate for the
number at risk?
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g. What is the total number of person-months at risk during 1996?
h. What is the incidence rate (or incidence density) of the disease during 1996?
i. Convert the incidence density estimate from question h to the # of cases per
100 person-years.
Problem 14
The table below, taken from a paper by Warshauer and Monk (Am J Public Health 1978;
68:383-388), gives the number of suicides in East Harlem and the South Bronx between
1968 and 1970 (36 months) among white females, by age in 1970. Assume that the
population of white females in this area is stable.
Age in
1970
Size of 1970
Population
Number of
Suicides
18-24
34,714
26
25-34
42,489
23
35-54
59,762
31
55-84
63,306
39
Total
200,271
119
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a. Estimate the average suicide rate for each age interval and describe the observed age
trend– i.e., how the estimated suicide rate varies with age.
b.
c.
Estimate the following risks of committing suicide (using the exponential formula):
i. The 1-year risk for a 20-year-old white woman,
ii. The 10-year risk for a 20-year-old white woman,
iii. The 67-year risk for an 18-year-old white woman.
What additional assumptions are needed to estimate the risks in part b?
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Problem 15
The table below gives prevalent (C) and incident (A) cases during a 2-year follow-up of a
hypothetical stable population (size N), by exposure status and age (k=1,…, 4).
Age
40-49
50-59
60-69
70-79
Total
Nk
35,000
50,000
60,000
55,000
200,000
EXPOSED
Ck
175
1,220
5,455
11,000
17,850
Ak
70
488
2,182
4,400
7,140
Nk
240,000
230,000
200,000
130,000
800,000
UNEXPOSED
Ck
600
2,840
9,525
14,445
27,410
Ak
240
1,136
3,810
5,778
10,964
Estimate the following parameters for the exposed group:
a.
the 2-year risk for a 55-year-old person
b.
the 10-year risk for a 55-year-old person
c.
the 20-year risk for a 55-year-old person
Problem 16
Tardive dyskinesia (TD) is an abnormal involuntary movement disorder caused in part by
the use of antipsychotic medication. A study was conducted to estimate the probability
of improvement in symptom severity (the outcome event), following discontinuation of
antipsychotics in a group of 20 psychiatric outpatients with TD. Subjects were
reexamined monthly from time of discontinuation in 2001 until December 2002 (the end
of follow-up). Improvement in TD symptoms was defined as a 50 percent or more
reduction in a quantitative severity score, relative to the patient's prediscontinuation
value. The table below gives the duration of follow-up (in months) from discontinuation
until improvement for each subject.
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Subject
1
Months
Subject
Months
before
before
improvement
improvement
4
8
18
Subject
15
Months
before
improvement
8
2
14
9
13
16
22
3
5
10
8
17
15
4
9
11
13
18
11
5
13
12
19
19
14
6
10
13
15
20
16
7
6
14
17
a. Estimate the average improvement rate for all TD cases during the entire follow-up
period.
b. Assuming the improvement rate remains constant, calculate the “risk” of improving,
by each time interval after discontinuation (make sure you choose appropriate interval
sizes!).
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c. Assess whether the improvement rate changed during the two-year follow-up period
(as assumed in part b) by comparing the average improvement rate in the first 12 months
after discontinuation with the average rate in the second 12 months after discontinuation.
Problem 16: Vinyl Chloride – Revisited
The following table is from your lecture notes after Duck et al. Lancet 1973, Dec13:
1197-1199.
Duration of work
O
E
<10 years
10-14 years
15+ years
83
28
25
74.01
26.91
41.30
SMR
112
107
61
N
1538
246
336
Man years at
risk
13697
3271
6084
How many man-years at risk should there be in each stratum? Show your work.

<10 years:

10-14 years:

15+ years:
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Using your new values for man-years at risk, what will be the expected deaths for each
stratum?

<10 years:

10-14 years:

15+ years:
Now calculate a new Standardized Mortality Ratio (SMR) for each stratum.

<10 years:

10-14 years:

15+ years:
Finally, refill the table with your new values.
Duration of work
O
<10 years
10-14 years
15+ years
83
28
25
E
SMR
N
Man years at
risk
1538
246
336
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