1. Measures of Disease Occurrence
Unit 2:
Measures of Disease Occurrence

2. Unit 2 Learning Objectives:
Understand counts, ratios, proportions, and rates.
Define, calculate, and interpret incidence.
Understand the use of person-time denominators.
Distinguish between cumulative incidence and incidence rate.
Define, calculate, and interpret prevalence.
Distinguish between point and period prevalence.

3. Unit 2 Learning Objectives (cont.):
Understand special types of incidence and prevalence measures.
Understand the interrelationship between incidence, prevalence, and duration of disease.
Differentiate the use of incidence and prevalence measures.
Become familiar with methods used in survival analysis.

4. Assigned Readings:
Textbook (Gordis):
Chapter 3, pages (Measuring occurrence of morbidity and mortality
Chapter 6, pages (Person years and survival analysis)

5. Quantitative Measures of Health Status
Measures of health status convey information about the occurrence of disease. They include:
• Counts
• Proportions
• Ratios
• Rates

6. Counts • Simplest/most frequently performed measure in epidemiology
• Refers to the number of cases of a disease or
other health phenomenon being studied
i.e. cases of influenza in Allegheny county in January, 2002
i.e. Number of persons involuntarily referred for psychiatric crisis intervention
• Useful for allocation of health resources
• Limited usefulness for epidemiologic purposes without knowing size of the source population

7. Counts – Limited Interpretation
New Cases Reporting
Location of Disease Period Population
City A
City B
Annual Rate of Occurrence
City A: 20 / = 1 / 5
City B: 100 / = 1 / 10

8. Proportions
Persons included in the numerator are always included in the denominator: A
Proportion:
A + B
Indicates the magnitude of a part, related to the total.
In epidemiology, tells us the fraction of the population that is affected.

9. Proportions - Example A B Total (A + B) # persons with hypertension
# persons without hypertension
Total study population
1,400
9,650
11,050
P = A / (A + B) = (1,400 / 11,050) = 0.127

10. Proportions Numerical value of a proportion: 0 to 1.0
Linked to probability theory (i.e. risk of developing disease)
For ease of usage, can multiply a proportion by 100 to get a percentage
Example: p = = 12.7%

11. Ratios
Like a proportion, is a fraction, BUT without a specified relationship between the numerator and denominator
Example: Occurrence of Major Depression
Female cases =
= :1 female to male
Male cases =

12. Rates A ratio in which TIME forms part of the denominator
Epidemiologic rates contain the following elements:
• disease frequency (in the numerator)
• unit size of population
• time period during which an event occurs

13. Rates – Example Calculate crude annual death rate in the US:
Annual death count
Crude death rate = x 1,000
Reference population
(during midpoint of year)
Death count in U.S. during 1990: 2,148,463
U.S. population on June 30, 1990: 248,709,873
2,148,463
Crude death rate = x 1,000 = 8.64 per 1,000
248,709,873

14. What does a crude annual death rate of
Discussion Question 1
What does a crude annual death rate of
8.64 per 1,000 mean?

15. Discussion Question 1 It means that over the course of a year:
About 9 persons in 1,000 died.
About 864 persons per 100,000 died.
The risk of dying was about 0.9% (see below)
2,148,463
Crude death rate = = x 100 = 0.86%
248,709,873

16. Incidence
The development of new cases of a disease that occur during a specified period of time in previously disease-free or condition-free (“at risk”) individuals.

17. Incidence Incidence quantifies the “development” of
disease --- Most fundamental measure of disease frequency and leads to the development of the concept of risk (i.e transition from non-diseased to diseased state)
- Cumulative incidence (CI)
(“Incidence proportion”)
- Incidence rate (IR)
(“Incidence density”)

18. Cumulative Incidence (CI)
PROPORTION of individuals who become diseased during a specified period of time
(e.g. all new cases during 1998)
Range: 0 to 1.0
Also referred to as “incidence proportion.”

19. Cumulative Incidence (CI)
No. of new cases of disease during a given period
CI =
Total population at risk during the given period
Example: During a 1-year period, 10 out of “at risk” persons develop the disease of interest. 10
CI = = or 10.0%
100

20. Cumulative Incidence (CI)
To accurately calculate cumulative incidence, we need to follow the entire population for the specified time interval. Often times, this does not fully occur.
Cumulative incidence provides an estimate of the probability (risk) that an individual will develop a disease during a specified period of time.

21. Cumulative Incidence (CI)
Keep in mind that over any appreciable period of time, it is usually technically impossible to measure risk.
This is because if a population is followed over a period of time, some people in the population will die from causes other than the outcome under study
The phenomenon of being removed from a study through death from other causes is referred to as ”competing risks”.

22. Incidence Rate (IR) No. new cases of disease during a given period
Total “person-time” of observation
Range = 0 to Infinity
Since the number of cases is divided by a measure of time of observation, rather than people, this helps address the problem of competing risks.

23. Incidence Rate (IR) What is person time?
When we observe a group of individuals for a period of time in order to ascertain the DEVELOPMENT of an event….
- The actual time each individual
is observed will most likely
vary.

24. In a 2-year study of the development of
Discussion Question 2
In a 2-year study of the development of
disease X, why might the actual
time each individual is observed vary?

25. Discussion Question 2 Subjects may be recruited at different times
Because:
Subjects may be recruited at different times
Subjects may emigrate
Subjects may choose to leave study
Subjects may die
Subjects may get the disease we are studying

26. Person-Time
Each subject contributes a specific person-time of observation (days, months, years) to the denominator
Person Follow-up Time on Study Person Yrs.
1 < > 2
2 < D
3 < WD
4 < > 3
5 < > 2
Jan. Jan. Jan. Jan.

27. Person-Time Study Period: 3 Years Study Participants: 5
Person Follow-up Time on Study Person Yrs.
1 < > 2
2 < D
3 < WD
4 < > 3
5 < > 2
Jan. Jan. Jan. Jan.
Study Period: 3 Years
Study Participants: 5
Person Years of Observation: 10
Average Duration of Follow-Up: 2.0 Years

28. Incidence Rate (IR) No. new cases of disease during a given period
Total “person-time” of observation
So,
1 case
IR = = 1 case per 10 years follow-up
10 years
Whereas,
CI = = 0.20 = 20.0%
5 persons

29. Comparison of IR and CI
If we multiply by 0.2, the IR of 1 case per 10 years is equivalent to 0.2 cases per 2 years:
which suggests a 20% risk of disease development
within 2 years of follow-up.
Whereas, the CI risk estimate of 20% (1 case per 5 persons) was based on a period of 3 years of follow-up.
The CI calculation of risk of disease development differs from the IR calculation, in part, because it assumed that for incomplete follow-up, no cases of disease occurred.

30. Previously, we said that the incidence rate
Discussion Question 3
Previously, we said that the incidence rate
can range from 0 to infinity!
How can this be?

31. Discussion Question 3 Consider the following:
McDonald’s shooting lasting 1/2 hour with 50
patrons in the restaurant.
29 survivors: at risk period of 1/2 hr = 14.5 person hrs.
21 deaths: at risk period of avg. 1/4 hr = 5.25 person
hrs. =21 deaths / 20 person hours
This translates to 919,800,000 / 100,000 person years
Therefore, as time increases, IR approaches infinity.

32. Incidence Rate (IR) NOTE: The selection of the time unit for the
denominator is arbitrary, and is not
directly interpretable:
Example: 100 cases / person year
can also be expressed as:
10,000 cases / person century
8.33 cases / person month
1.92 cases / person week
0.27 cases / person day

33. Incidence Rate (IR)
Incidence rate: - Incidence density Force of morbidity
Measure of the instantaneous rate of development of disease in a population

34. Comparison of IR and CI
In general:
Risk estimates derived from IR and CI calculations will be similar when:
• Follow-up loss is minimal
• The disease of interest occurs infrequently.
CI is most useful if interest centers on the probability than an individual will become ill over a specified period of time.
IR is preferred if interest centers on how fast the new cases are occurring in the population.