Lab 2: Cumulative incidence and Incidence Density
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Drs. Olsen & Arah
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.
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.
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 |Areas |
| |City A |City B |
|Measles |70% |95% |
|Tetanus |80% |92% |
|Polio |90% |97% |
|Hepatitis B |85% |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
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%
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%
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%
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%
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?
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.
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?
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.
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?
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.
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 |Size of 1970 |Number of |
|1970 |Population |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 |
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. 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.
c. What additional assumptions are needed to estimate the risks in part b?
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).
| |EXPOSED |UNEXPOSED |
|Age |Nk |Ck |Ak |Nk |Ck |Ak |
|40-49 |35,000 |175 |70 |240,000 |600 |240 |
|50-59 |50,000 |1,220 |488 |230,000 |2,840 |1,136 |
|60-69 |60,000 |5,455 |2,182 |200,000 |9,525 |3,810 |
|70-79 |55,000 |11,000 |4,400 |130,000 |14,445 |5,778 |
|Total |200,000 |17,850 |7,140 |800,000 |27,410 |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
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.
|Subject |Months before |Subject |Months before |Subject |Months before |
| |improvement | |improvement | |improvement |
|1 | 4 |8 |18 |15 | 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!).
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 |SMR | N |Man years at risk |
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