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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
“Point” Prevalence
Number of existing cases
P = --------------------------------
Total population
At a set point in time
(i.e. September 30, 1999)
“Point” Prevalence
Example:
On June 30, 1999, neighborhood A has:
• population of 1,600
• 29 current cases of hepatitis B
So, P = 29 / 1600 = 0.018 or 1.8%
“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.
“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) / 1600 = 0.022 or 2.2%
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.
Mathematical Notation:Mathematical Notation:A few measures used in Epidemiology A few measures used in Epidemiology
render decimal numbersrender decimal numbers
Prevalence: 58 cases of diabetes
25,000 Subjects
Prevalence = 0.00232
Incidence: 34 new cases of breast cancer
54,037 Person-Years
Incidence = 0.00063
So that those numbers have a meaning, we add a population unit:
Usually a power of 10 (10N)101 = 10102 = 100103 = 1000104 = 10000Prevalence = 0.00232 * 105
= 232 cases of diabetes/100,000 Population
Incidence = 0.00063 * 105
= 63 New cases of breast cancer/100,000 Person Years
Special Types of Incidence and Prevalence Measures
INCIDENCEMortality 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
PREVALENCEBirth Defect Rate # of Babies w/Given Abnormality
# of Live Births
Discussion Question 4Discussion Question 4
How are incidence and
prevalence of disease related?
Discussion Question 4Discussion Question 4
Prevalence depends on:
- Incidence rate
- Disease duration
Relationship between prevalence and incidenceRelationship 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
.
Uses of Incidence & Uses of Incidence & Prevalence MeasuresPrevalence 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
Uses of Incidence & Uses of Incidence & Prevalence MeasuresPrevalence Measures
Incidence: Measure of choice to:
--- Estimate risk of disease development
--- Study etiological factors
--- Evaluate primary prevention programs
Discussion Question 5Discussion Question 5
Why is incidence preferred over
prevalence when studying the
etiology of disease?
Discussion Question 5Discussion 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
Discussion Question 5Discussion 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
PROBLEMS WITH INCIDENCE AND PROBLEMS WITH INCIDENCE AND PREVALENCE MEASURESPREVALENCE MEASURES
Problems with Numerators:
• Frequently, the diagnosis of cases is not straightforward
• Where to find the cases is not always straightforward
PROBLEMS WITH INCIDENCE AND PROBLEMS WITH INCIDENCE AND PREVALENCE MEASURESPREVALENCE 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.
Summary of Incidence Summary of Incidence and Prevalence 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
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.
SUMMARYSUMMARY
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
OTHER MORTALITY MEASURESOTHER 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.
Discussion Question 6Discussion Question 6
Why isn’t proportionate mortality
a direct measure of risk?
Discussion Question 6Discussion 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.
OTHER MORTALITY MEASURESOTHER 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.
Some Problems with Mortality DataSome 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
Survival AnalysisSurvival 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.
Survival AnalysisSurvival 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.
K-M formula:K-M formula:
# of time
intervals (Nk – Ak)
S = -------------
k = 1 Nk
Where: k = sequence of time intervalNk = number of subjects at risk
Ak = number of outcome events
Survival AnalysisSurvival AnalysisExample:
• 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?
(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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 ? 1 1 ? ? ? ?
(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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 7 1 1 ? ? ? ?
(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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 7 1 1 0.143 0.857 0.675 0.325
22 5 1 0 ? ? ? ?
(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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 7 1 1 0.143 0.857 0.675 0.325
22 5 1 0 0.20 0.80 0.54 0.46
(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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 7 1 1 0.143 0.857 0.675 0.325
22 5 1 0 0.20 0.80 0.54 0.46
24 4 0 0 0.0 1.0 0.54 0.46
(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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 7 1 1 0.143 0.857 0.675 0.325
22 5 1 0 0.20 0.80 0.54 0.46
24 4 0 0 0.0 1.0 0.54 0.46
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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 7 1 1 0.143 0.857 0.675 0.325
22 5 1 0 0.20 0.80 0.54 0.46
24 4 0 0 0.0 1.0 0.54 0.46
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 1 0.10 0.90 0.90 0.10
7 8 1 0 0.125 0.875 0.788 0.212
20 7 1 1 0.143 0.857 0.675 0.325
22 5 1 0 0.20 0.80 0.54 0.46
24 4 0 0 0.0 1.0 0.54 0.46
Interpretation: Is the risk of death constant overfollow-up?
Survival AnalysisSurvival 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.
Survival AnalysisSurvival 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.