Measures of Disease Frequency

Abstract

In epidemiologic studies, we use a measure of disease frequency to determine how often the disease or other health outcome of interest occurs in various subgroups of interest. We describe two basic types of measures of disease frequency in this chapter, namely, measures of incidence and measures of prevalence. The choice typically depends on the study design being used and the goal of the study.

Appendices

Homework Questions

1.1 ACE-1. Measures of Disease Frequency

• 1. What is the purpose of a measure of disease frequency?

• 2. What is the difference between incidence and prevalence?

• 3. How are incidence and prevalence interrelated?

• 4. What is the difference between cumulative incidence and incidence density?

• 5. What does it mean to say that a person’s 2-year risk is .03?

• 6. What does it mean to say that the rate in a certain population is .03/year?

• 7. Under what (design) circumstances would you want to measure risk?

• 8. Under what (design) circumstances would you want to measure rate?

• 9. Why do we carry out age-adjustment of risks or rates?

• 10. How does the direct method of age-adjustment work?

1.2 ACE-2. Person-time

What are two ways to calculate person-time in the estimation of a rate (i.e., incidence density)? Under what circumstances would you use each formula? Describe an example of the use of each formula.

1.3 ACE-3 Incidence vs. Prevalence

Determine whether each if the following statements requires measurement of INCIDENCE or PREVALENCE.

• a. A new oral vaccine, which is purported to prevent cholera, has been introduced into a certain health district. The district health officer wants to monitor an appropriate measure to determine whether the vaccine is working.

• b. A school psychologist wants to determine if there is an association between the reading of pornographic materials and teenage sexual violence. She is able to collect interview data on the amount of pornography regularly read and the number of violent sexual encounters experienced by the students.

• c. An HMO (Health Maintenance Organization) is considering offering a community-oriented diabetic clinic. It will be necessary to determine how many patients would be interested in utilizing the service.

• d. A pharmaceutical company has developed a new drug that is purported to cure asthma. The company wants to monitor the product’s effectiveness.

• e. A nurse-midwife decides to examine the relationship between home deliveries and post–partum infection. She is able to follow a group of women through the pregnancy and the first week after the birth of their children.

• f. Quaker Oats has an ad campaign claiming that a diet high in grains helps prevent colon cancer. An epidemiologist wants to evaluate the validity of this claim.

• g. A company is considering a new worksite smoking cessation program. A questionnaire is distributed among employees to determine how many people would be interested in taking part in such a program.

• h. School administrators are informed that the school system in a given state is obligated by law to provide Special Education classes for all public school children with learning disabilities. The board wants to estimate how many Special Education teachers will need to be hired in order to meet this obligation.

• i. An investigator is interested in assessing whether pregnant women exposed to environmental tobacco smoke are more likely to deliver low birth-weight babies.

1.4 ACE-4. Incidence and Prevalence: HIV

A study published in 1990 (Amer. J. Pub. Health 80:pp209-10) 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 2 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. Why can’t you obtain an estimate of risk based on the information provided?

• d. Why would estimating risk likely be inappropriate for these data?

• e. Calculate the prevalence of HIV infection among incoming prisoners in the Nevada prisoners under study.

• f. Why is the estimate of prevalence calculated in part e not necessarily equal to an appropriate measure of risk that might be calculated for these data?

1.5 ACE-5. Interpreting Incidence and Prevalence

The following graph indicates the changing incidence rate and prevalence for disease “X” over time:

For each statement below, indicate whether the statement is consistent (yes or no) with the information portrayed in the graph.

• a. Persons acquiring this disease are being cured quicker.

• b. Efforts to prevent this disease appear to be succeeding.

• c. The disease is becoming more chronic over time.

1.6 ACE-6. Calculate Measures of Disease Frequency

The following data were obtained in a study in which 1000 nurses were followed for 20 years to examine the hypothesis that use of a certain diet pill is a risk factor for heart attack.

	Diet Pill Use
Heart Attack	Yes	No	Total
Yes	30	11	41
No	470	489	959
Total	500	500	1000

• a. Estimate the number of woman-years contributed by the unexposed group.

• b. What information would you need in order to obtain a better estimate of the number of women-years?

• c. What is the 20-year risk of heart attack among those who used diet pills?

• d. What is the prevalence of diet pill use among those who did not have a heart attack?

• e. Do the data suggest that Diet Pill Use is a risk factor for heart attack? Explain.

1.7 ACE-7. Exercise vs. CHD

A group of epidemiologists was interested in investigating the relationship between exercise and development of coronary heart disease (CHD) among women. A healthy population of women aged 35 to 75 years was polled to assess their exercise habits. They were then followed for a period of 15 years to determine incidence of CHD. Here are the results:

	Frequency of Exercise – Times per week
	Twice	Once	No exercise
CHD	4	40	23
Person-Years	25,111	117,205	32,843
Rate per 10,000 Person-Years	__________	__________	__________

• a. What proportion of women who developed CHD had exercised once per week?

• b. Complete the table by calculating the rates per 10,000 and filling in the three empty cells. Express answers to two decimal places.

• c. What can you conclude from these data about the relationship between exercise and CHD?

1.8 ACE-8. Standardized Rates: Hypertension

An investigator is interested in comparing rates of hypertension in two populations. Which of the following should be taken into account when deciding whether it is necessary to standardize the rates by race? (There may be more than one correct answer here.)

• a. Whether the rate of hypertension differs by race.

• b. Whether the racial distribution differs in the two populations.

• c. Whether the rate of hypertension differs in the two populations.

• d. The rate of hypertension in the standard population.

1.9 ACE-9. Rates and Rate Adjustment

For each statement below, indicate whether it is true or false.

• a. Two populations with the same age-specific rates of death could have different crude (i.e., overall) rates of death.

• b. Two populations with the same crude (i.e., overall) rates of death could have different age-specific rates of death.

• c. The process of direct adjustment of rates utilizes stratum-specific rates from the standard population.

• d. A crude rate is a weighted average of stratum-specific rates.

1.10 ACE-10. Rate Adjustment: Standard Populations

Use the data provided below and, carrying all calculations to one decimal, complete the following:

• a. Obtain age-adjusted total leukemia incidence rates in Mesa and Weld Counties using their pooled population as the standard.

• b. Obtain age-adjusted total leukemia incidence rates in Mesa and Weld counties using the 1970 Colorado population (expressed in percentages) as the standard.

• c. Are the age-adjusted rates for each county the same in parts a and b above?

• d. Could a standard population be chosen such that the age-adjusted incidence rate for Weld county is higher than the age-adjusted incidence rate for Mesa county?

• e. Regardless of the standard population used above, the age-adjusted rate for Weld county is similar to the unadjusted (i.e., crude) rate. What can you conclude from this?

  • Age adjustment was necessary only for Mesa County, not for Weld county.

  • Leukemia incidence rates are similar in Weld county and the standard population.

  • The age structure is similar in Weld county and the standard population.

Age Group	Colorado 1970 Population (%)	Weld County		Mesa County
		1970 Pop.	Leukemia AAIR*	1970 Pop.	Leukemia AAIR*
< 5	8.4	7,491	9.5	3,754	7.6
5-19	30.6	28,452	3.0	16,852	4.2
20-34	22.5	20,382	1.4	9,253	4.6
35-49	17.2	13,859	1.0	9,329	3.1
50-64	12.8	11,219	6.4	8,685	11.5
65 + 8.5	7,894	12.7	6,501	43.9
Total	100.0	89,297	4.2	54,374	10.2

1. * Average annual leukemia incidence rates per 100,000 population for the interval 1970-76 based upon 1970 population enumeration.

Answers to Study Questions and Quizzes

• Q4.1

  • 1. Incidence – Here we are interested in the number of new cases after eating the potato salad.

  • 2. Prevalence – Here we are interested in the number of existing cases.

  • 3. Incidence – Here we are interested in the number of new cases that occur during the follow-up.

  • 4. Incidence – Here we are interested in the number of new deaths attributed to the hurricane.

  • 5. Prevalence – Here we are interested in the existing number of children who have immunity to measles.

  • 6. Incidence – Since rabies has a short duration, we would expect the prevalence on a particular day to be low relative to the incidence.

  • 7. Prevalence – The incidence of multiple sclerosis would be low, but since it has a long duration, we would expect the prevalence to be higher.

  • 8. Incidence – The incidence of influenza would be high, but since it is of short duration the prevalence would be low.

  • 9. Incidence – Since the duration of poison ivy is relatively short the prevalence would be low, and since it is a common occurrence, the incidence would be high.

  • 10. Prevalence – Since high blood pressure is common and of long duration, both incidence and prevalence would be high, however the prevalence would be higher.

• Q4.2

  • 1. The statement means that a 45-year-old male free of prostate cancer has a probability of .05 of developing prostate cancer over the next 10 years if he does not die from any other cause during the follow-up period.

  • 2. Smaller, because the 5-year risk involves a shorter time period for the same person to develop prostate cancer.

• Q4.3

  • 1. No, subjects should be counted as new cases if they were disease-free at the start of follow-up and became a case at any time during the follow-up period specified.

  • 2. Yes, there is a problem, since a subject followed for 2 years does not have the same opportunity for developing the disease as a subject followed for 4 years.

  • 3. No, but we have to assume that those subjects that do not develop the disease have the same amount of follow-up time. Otherwise, we can get a misleading estimate of CI because not all subjects will have the same opportunity to develop the disease over the follow-up period.

• Q4.4

  • 1. Dynamic

  • 2. Subject 2

  • 3. Subject 7

  • 4. Subject 9

  • 5. Subject 3

  • 6. Subject 5

  • 7. 5/12 = 42 %

  • 8. 4/12 = 33 %

  • 9. D

  • 10. No

  • 11. No

  • 12. Yes

  • 13. Yes

  • 14. Yes

  • 15. No

  • 16. Yes

• Q4.5

  • 1. 30/97

  • 2. 60/97

  • 3. 90/95

  • 4. True – The numerator of the CI formula is a subset of the denominator.

  • 5. True – Because the incubation period is short, subjects are not likely to be lost to follow-up.

  • 6. True – The long incubation period means subjects are likely to be lost to follow-up, and hence cases may not be detected. For a dynamic cohort, the denominator in the CI formula does not reflect the continually changing population size.

  • 7. False – the estimated CI will underestimate the true risk of disease.

• Q4.6

  • 1. C

  • 2.  

    • a. Yes

    • b. Yes

    • c. No

    • d. Yes

    • e. No

• Q4.7

  • 1. No, the denominator of 25 does not describe 25 persons, but rather the accumulated follow-up time for 12 persons.

  • 2. No, the risk in this example would be calculated as 5/12 or 0.42. However, using risk would be questionable here because different subjects have different follow-up times.

  • 3. C

• Q4.8

  • 1. N* is the average size of the disease-free cohort and Δt is the time length of the study period. Therefore, a rough estimate of the total amount of person-years contributed by the study is 6,500 *6 = 39,000 person-years.

  • 2. The incidence rate is 66/39,000 = 0.0017, or 1.7 per 1,000 person-years.

• Q4.9

  • 1. True – For questions 1 & 2: a rate can range from 0 to infinity, whereas a risk (which is a proportion) ranges from 0 to 1 (or 0 % to 100 %).

  • 2. False

  • 3. False – There are alternative ways to calculate person-time information when individual follow-up time is unavailable.

  • 4. False – A rate can be calculated for either a dynamic cohort or fixed cohort, depending on the person-time information available.

• Q4.10

  • 1. Risk

  • 2. Both

  • 3. Both

  • 4. Rate

  • 5. Risk

  • 6. Rate

  • 7. Risk

  • 8. Rate

  • 9. Risk

  • 10. Both

• Q4.11

  • 1. Yes, its value can range from 0 to 1 and it is often expressed as a percentage

  • 2. C. The prevalence of disease is 13/406,245 = 0.000032

  • 3. B. 3.2 per 100,000 is an equivalent expression and is easier to interpret

• Q4.12

  • 1. True – Prevalence considers existing cases rather than incident cases.

  • 2. True – Since the numerator is contained in the denominator, prevalence is a proportion and must range from 0 to 1 (or 0 % to 100 %).

  • 3. False – Cross-sectional studies are carried out at essentially a single (or short) point in time.

  • 4. True – Prevalence may concern a health outcome or any other characteristic of a subject.

  • 5. d

• Q4.13

  • 1. B

  • 2. A

  • 3. B

• Q4.14

  • 1. The estimate of LC incidence is calculated as CI = 15/900 = .017 or 1.7 %

  • 2. The 5 % mortality estimate counts the 40 prevalent LC cases and does not count the 5 new LC cases that did not die. Furthermore, the denominators are different.

  • 3. The LC incidence and mortality risks would be about equal if the disease was quickly fatal, so that there would be few if any prevalent cases in the initial cohort and all new cases would have died before the end of follow-up.

• Q4.15

  • 1. True

  • 2. True

  • 3. False – The denominator of a disease-specific mortality risk is the size of the initial cohort regardless of disease status.

  • 4. True

  • 5. True

• Q4.16

  • 1. The two rates are crude rates because they represent the overall mortality experience in 1996 for the entire population of each state. Crude rates do not account for any differences in these populations on factors such as age, race, or sex that might have some influence on mortality. Without consideration of such factors, it would be premature to make such a conclusion.

  • 2. Arizona. The dry, warm climate of Arizona attracts many older persons than does Alaska.

  • 3. There are relatively older persons living in Arizona, and older persons are at high risk of dying.

• Q4.17

  • 1. Controlling for any age differences in the two populations, the overall mortality rate is higher in Alaska with a cold, damp climate, then in Arizona where the climate is warm and dry.

  • 2. The population of Alaska must be much younger than the US population since the age-adjusted rate was so much higher than the crude rate.

  • 3. The rate for Arizona did not change much from crude to adjusted because Arizona’s age distribution was only slightly younger than that of the entire US in 1996.

• Q4.18

  • 1. True – If age-adjustment is not used, then a difference in risk or rates between two populations may be primarily due to age differences in the two populations.

  • 2. False – There is no guarantee that two adjusted measures will be either closer or further from each other than were corresponding crude measures.

  • 3. False – The choice of standard population depends on the characteristics of the populations being considered.

  • 4. True – There is no limitation on the number populations that could be age-adjusted.

  • 5. False – For questions 5 & 6: If the crude rates are quite different whereas the age distributions are similar, then the adjusted rates are likely to be quite different.

  • 6. True

  • 7. 44

  • 8. 9.1

  • 9. older – Women must be older than men in this case. The mortality rate drops substantially in women when we standardize the rate using the age distribution of men. In other words, if we take age out of the picture, the rates for women drop. If the women were younger we would expect to see the adjusted rate increase once we remove age as a factor.

Author Queries

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