1. Prevalence
The presence (proportion) of disease or condition in a population (generally irrespective of the duration of the disease)
Prevalence: Quantifies the “burden” of disease.
- Point Prevalence
- Period Prevalence

2. “Point” Prevalence Number of existing cases
Total population
At a set point in time
(i.e. September 30, 1999)

3. “Point” Prevalence Example: On June 30, 1999, neighborhood A has:
• population of 1,600
• 29 current cases of hepatitis B
So, P = 29 / = or 1.8%

4. “Period” Prevalence Number of existing cases
Pp =
Total population
During a time period
(i.e. May 1 - July 31, 1999)
Includes existing cases on May 1, and those
newly diagnosed until July 31.

5. “Period” Prevalence Example:
Between June 30 and August 30, 1999, neighborhood A has:
• average population of 1,600
• 29 existing cases of hepatitis B on June 30
• 6 incident (new) cases of hepatitis B between July 1 and August 30
So, Pp = (29 + 6) / = or 2.2%

6. Prevalence
AXIOM:
In general, a person’s probability of being captured as a prevalent case is proportional to the duration of his or her disease.
Thus, a set of prevalent cases tends to be skewed toward cases with more chronic forms of the disease.

7. Mathematical Notation: A few measures used in Epidemiology render decimal numbers
Prevalence: 58 cases of diabetes
25,000 Subjects
Prevalence =
Incidence: 34 new cases of breast cancer
54,037 Person-Years
Incidence =

8. = 232 cases of diabetes/100,000 Population
So that those numbers have a meaning, we add a population unit:
Usually a power of 10 (10N)
101 = 10
102 = 100
103 = 1000
104 = 10000
Prevalence = * 105
= 232 cases of diabetes/100,000 Population
Incidence = * 105
= 63 New cases of breast cancer/100, Person Years

9. Special Types of Incidence and
Prevalence Measures
INCIDENCE
Mortality Rate # of Deaths over specified time
Total Population
Case Fatality Rate # of Deaths from a Disease
# of Cases from that Disease
Attack Rate # of Cases of a Disease
Total Population at Risk for
a Limited Period of Time
PREVALENCE
Birth Defect Rate # of Babies w/Given Abnormality
# of Live Births

10. prevalence of disease related?
Discussion Question 4
How are incidence and
prevalence of disease related?

11. Prevalence depends on: - Incidence rate - Disease duration
Discussion Question 4
Prevalence depends on:
- Incidence rate
- Disease duration

12. Relationship between prevalence and incidence
WHEN (the steady state is in effect):
a) Incidence rate (I) has been constant over time
b) The duration of disease (D) has been constant over time:
ID = P / (1 – P)
P = ID / (1 + ID)
c) If the prevalence of disease is low
(i.e. < 0.10): P = ID .

13. Uses of Incidence & Prevalence Measures
Prevalence: Snap shot of disease or
health event
Help health care providers plan to deliver services
Indicate groups of people who should be targeted for control measures
May signal etiologic relationships, but also reflects determinants of survival

14. Uses of Incidence & Prevalence Measures
Incidence: Measure of choice to:
--- Estimate risk of disease development
--- Study etiological factors
--- Evaluate primary prevention programs

15. Why is incidence preferred over prevalence when studying the
Discussion Question 5
Why is incidence preferred over
prevalence when studying the
etiology of disease?

16. Discussion Question 5
Because, in the formula: P = I x D
D is related to : - The subject’s constitution
- Access to care
- Availability of treatment
- Social support
- The severity of disease

17. Discussion Question 5
So prevalent cases reflect factors related to the incidence of disease (Etiological factors), AND factors related to the duration of disease (Prognostic factors)
Thus, they are not adequate for studies trying to elucidate Disease Etiology

18. PROBLEMS WITH INCIDENCE AND PREVALENCE MEASURES
Problems with Numerators:
• Frequently, the diagnosis of cases is not straightforward
• Where to find the cases is not always straightforward

19. PROBLEMS WITH INCIDENCE AND PREVALENCE MEASURES
Problems with Denominators:
• Classification of population subgroups may be ambiguous (i.e race/ethnicity)
• It is often difficult to identify and remove from the denominator persons not “at risk” of developing the disease.

20. Summary of Incidence and Prevalence
PREVALENCE: Estimates the risk (probability) that an individual will BE ill at a point in time
very useful to plan for health-related services and programs

21. INCIDENCE:
- Estimates the risk (probability) of developing illness
- Measures the change from “healthy” status to illness.
Useful to evaluate prevention programs
Useful to forecast need for services & programs
Useful for studying causal factors.

22. SUMMARY
Cumulative incidence (CI): estimates the risk that an individual will develop disease over a given time interval
Incidence rate (IR): estimates the instantaneous rate of development of disease in a population

23. OTHER MORTALITY MEASURES
Proportionate Mortality: Proportion of all deaths attributed to a specific cause of death:
No. of deaths from disease X in 1999
All deaths in the population in 1999
Can multiple by 100 to get a percent.

24. Why isn’t proportionate mortality a direct measure of risk?
Discussion Question 6
Why isn’t proportionate mortality
a direct measure of risk?

25. Discussion Question 6
Because:
The proportion of deaths from disease X tells us nothing about the frequency of deaths in the population ---- the overall risk of death in the population may be low.

26. OTHER MORTALITY MEASURES
Years of Potential Life Lost (YPLL): Measure of the loss of future productive years resulting from a specific cause of death.
YPLL are highest when:
• The cause of mortality is common or relatively common, AND
• Deaths tends to occur at an early age.

27. Some Problems with Mortality Data
• Cause of death reporting from death certificates is notoriously unreliable
• Changing criteria for disease definitions can make analyses over time problematic

28. Survival Analysis
• A technique to estimate the probability of “survival” (and also risk of disease) that takes into account incomplete subject follow-up.
• Calculates risks over a time period with changing incidence rates.
• Wide application in a variety of disciplines, such as engineering.

29. Survival Analysis
• With the Kaplan-Meier method (“product-limit method”), survival probabilities are calculated at each time interval in which an event occurs.
• The cumulative survival over the entire follow-up period is derived from the product of all interval survival probabilities.
• Cumulative incidence (risk) is the complement of cumulative survival.

30. K-M formula: S =  ------------- # of time k = 1 Nk
intervals (Nk – Ak)
S = 
k = Nk
Where: k = sequence of time interval
Nk = number of subjects at risk
Ak = number of outcome events

31. Survival Analysis Example:
• Assume a study of 10 subjects conducted over a 2-year period.
• A total of 4 subjects die.
• Another 2 subjects have incomplete follow-up (study withdrawal or late study entry).
What is the probability of 2-year survival, and the corresponding risk of 2-year death?

32. Time to Death from Entry No. Lost to FU Prior to Next Time
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20 ?

33. Time to Death from Entry No. Lost to FU Prior to Next Time
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20 ?

34. Time to Death from Entry No. Lost to FU Prior to Next Time
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20
0.143
0.857
0.675
0.325 22 ?

35. Time to Death from Entry No. Lost to FU Prior to Next Time
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20
0.143
0.857
0.675
0.325 22
0.20
0.80
0.54
0.46

36. Time to Death from Entry No. Lost to FU Prior to Next Time
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20
0.143
0.857
0.675
0.325 22
0.20
0.80
0.54
0.46 24 4
0.0
1.0

37. Time to Death from Entry No. Lost to FU Prior to Next Time
Interpretation: What is the 2-year risk of death?
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20
0.143
0.857
0.675
0.325 22
0.20
0.80
0.54
0.46 24 4
0.0
1.0

38. Time to Death from Entry No. Lost to FU Prior to Next Time
Interpretation: What is the 1-year risk of death?
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20
0.143
0.857
0.675
0.325 22
0.20
0.80
0.54
0.46 24 4
0.0
1.0

39. Time to Death from Entry No. Lost to FU Prior to Next Time
Interpretation: Is the risk of death constant over
follow-up?
(1)
Time to Death from Entry
(Mo)
(2)
No. Alive at Each Time
(3)
No. Who Died at Each Time
(4)
No. Lost to FU Prior to Next Time
(5)
Prop. Died at That Time
(3) / (2)
(6)
Prop. Survive
At That Time
1 – (5)
(7)
Cumul. Survival
To that Time
(8)
Cumul.
Risk to That Time
1 – (7) 5 10 1
0.10
0.90 7 8
0.125
0.875
0.788
0.212 20
0.143
0.857
0.675
0.325 22
0.20
0.80
0.54
0.46 24 4
0.0
1.0

40. Survival Analysis
• With the Kaplan-Meier method, subjects with incomplete follow-up (FU) are “censored” at their last known time of (FU).
• An important assumption (often not upheld) is that censoring is “non-informative” (survival experience of subjects censored is the same as those with complete FU).
• Non-fatal outcomes can also be studied.

41. Survival Analysis
• The Life-Table method is conceptually similar to the Kaplan-Meier method.
• The primary difference is that survival probabilities are determined at pre- determined intervals (i.e. years), rather than when events occur.