Prevalence The presence (proportion) of disease or condition in a population (generally irrespective...

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.