2.epidemilogic measures

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Epidemiologic Measures

CHEN Yu-ming 陈裕明Prof., PhD

Dept. Medical Statistics & EpidemiologySun Yat-sen Univ.

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Example Someone conducted a study on diabetes in all

hospitals in a rural region in China. He found:

He thus concluded that normal subjects had a higher risk of having diabetes than obese individuals.

Do you agree with him? Why?

Obese Sub. Normal Sub. Totaln % n % n %

Diabetic patients 300 30 700 70 1000 100

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Objectives

By the end of this lesson, you shoud be able to:

Define and distinguish among ratios, proportions, and rates

State the meanings and applications of incidence rates and prevalence

Identify and calculate commonly used measures for morbidity and motality

Distinguish the difference between prevalence & incidence

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Main contents Definition and use of ratio, proportion and rate Measuring disease occurrence

Prevalence: point, period prevalence Incidence: cumulative incidence & incidence rate

Measuring Disease Mortality Total mortality rate Specific mortality rate Case-fatality rate Proportionate mortality rate

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Definition and use ofratio, proportion and rate

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What, who is in the Numerator & denominator?

• Count • Ratio• Proportion• Rate

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• The number of cases of a disease or other health conditions being studied

• Example:• Cases of AIDS reported in GZ in 2004• Stomach cancer patients who were female this

Hospital

1. Count

Female: 5

Male: 2

• Useful for allocation of health resources•Limited usefulness for epidemiologic purposes

without knowing size of the source population

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= 5 / 2 = 2.5 / 1

• The quotient of 2 numbers• Numerator NOT necessarily INCLUDED in the

denominator• Allows to compare quantities of different nature

2. Ratio

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Ratio, Examples # beds per doctor

850 beds/10 doctors R = 85 beds for 1 doctor

# nurses per doctor Pig to dog ratio

Sex ratio: Male / Female Female / Male

Odds ratio Rate ratio Prevalence ratio

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2--- = 0.5 = 50% 4

3. Proportion• The quotient of 2 numbers• Numerator NECESSARELY INCLUDED

in the denominator• Quantities have to be of same nature• Proportion always ranges between 0 and 1 • Percentage = proportion x 100

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Proportion, Examples What percentage of Hong Kong citizens

is in your class?

What percentage of female students in

is your class?

What percentage do heart diseases

account for total deaths in GZ in 2002?

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Rate• The quotient of 2 numbers• Be NOT a proportion• Speed of occurrence of an event OVER

TIME (events/unit time)

Three elements • Events or new cases• Unit size of population• Time period during which the events

occur

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Rate

2----- = 0.02 / year 100

Observed in 2005

Numerator - number EVENTS observed for a given time

Denominator- population in which the events occur

(Population at risk)- includes time

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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

Rates – Example

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Discussion QuestionDiscussion Question

What does a crude annual death rate of

8.64 per 1,000 mean?

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Discussion QuestionDiscussion Question

It means that over the course of a year:

1. About 9 persons in 1,000 died.

2. About 864 persons per 100,000 died.

3. The risk of dying was about 0.9% (see below)

2,148,463

Crude death rate = -------------- = 0.0086 x 100 = 0.86%

248,709,873

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Measuring the Occurrence of Disease

Morbidity

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Measures of Disease Occurence

Two types of measures : Prevalence (proportion)

Use: measures population disease status Types: Point & period

Incidence (rate or risk) Use: Assess frequency of disease onset Types : Cumulative incidence and

Incidence density or incidence rate

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1. Prevalence—definition

Number of cases of disease at a specific time

Population exposed at that time

• Definition: Proportion of a population affected by a disease at a specific time.

• Expressed as a percentage

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1. Prevalence—Example

Example of overweight in a town on

Jun 31, 2002:

Population 350,000

Cases 96,200 (BMI

24-27.9kg/m2)

Prevalence 96200/350000 = 27.6%

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1. Prevalence—three elements:

Numerator = existing cases of disease (old and newly diagnosed)

Denominator = population “at risk ” to have the condition

Time: point (or sometimes a period) in time to which the prevalence applies

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1. Prevalence—Types Point prevalence(时点患病率 ):

Proportion of a population affected by a disease at a point in time

Period prevalence (期间患病率 ) : Proportion of a population affected by a disease during a certain period of time How many people have had the disease at

any time during a certain period?

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Ratio males/women=2/8 Point Prevalence: Mar 1 =3/10Proportion of women=2/10=2% Period Prevalence Mar-Jul =7/10

0

1

2

3

4

5

6

7

8

9

10

Jan Feb Mar Apr May Jun Jul

Prevalence

3 P-mo

3 P-mo

2 P-mo

4 P-mo

4 P-mo2 P-mo

D

D

D

D

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Examples Interview Question 1 “Do you currently

have asthma?” 14 of 200 subjects answered “yes”, 7% Is this a point or period prevalence?

Interview Question 2 “Have you had asthma during the last (n) year(s)?” 30 of 200 subjects answered “yes”, 15% Is this a point or period prevalence?

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Limitation of Prevalence

Can be viewed as a slice through the Pop. at a point in time

Not take into account the duration of disease

Only answer “who has and who do have”, “How often”, “How many” at present,

Not answer “when & How likely the disease develop”. Be Not suit for etiological studies

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2. Incidence—Definition

Definition: the number of new cases of a disease that occur during a specified period of time in a population at risk for developing the disease.

n10period timeaover riskat Pop.

casesnew of No. Incidence

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2. Incidence —Three elements

Three elements

A numerator: the No. of NEW cases

A denominator: the population at risk for

developing the disease

Time: the period during which the cases

accrue

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New case

New onset, or

Initial definitive diagnosis over the

period of time

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Population at risk (PAR)

The denominator for incidence is the population at risk

Not including Existing cases Individuals who are not capable of

developing the disease.

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Factors affecting population at risk Populations are dynamic

births and deaths (with different risk) immigration, emigration and other losses

Affected by immunity status Removal from at-risk population

Cases Lost to follow up Death due to other causes (competing risks) Change in risk status (hysterectomy and uterine

cancer)

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Calculating population at risk Exact

Sum each person’s contribution to time-at-risk

Must know exact times of entry, disease onset, or withdrawal for every individuals

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Calculating population at risk Mid-point population

Assume onset/withdrawal random over time

Use population at the mid-point of study to estimate average PAR (most recent census figure)

Mean of start and end populations

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Specification of a time period

Incidence entails the designation of a time period, e.g. a week, month, year, or n years

The time of onset or initial definitive diagnosis must be within the period

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Incidence

Incidence rate (IR)

Incidence density (ID)

Rate (speed)

For open population

Cumulative incidence (CI)

Incidence proportion (IP)

Risk (probability)

For closed population

2. Incidence — Types

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No units Theoretical range 0 to 1 Probability that an individual will become

diseased over the specified period CI in population = average risk for

individuals

0

casesnew

N

NCI

2. Incidence —Cumulative Incidence

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Risk

CI assumes that entire population at risk followed up for specified time period

xx

x

x

x

x

xx disease onset

lost to followupMonth 1 Month12

CI = 7/12 per year

= 0.58 per year

2. Incidence —Cumulative Incidence (CI)

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Closed population

Population at risk

Deaths

Cases

Emigration/losses

time

2. Incidence —Cumulative Incidence

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Closed populationKey points

Defined at start of study and has no new entrants

Be perfect if no losses other than deaths Cohort size decreases over time (with

“die-off”) Average age increases over time Example: people born in 1980

2. Incidence —Cumulative Incidence

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Attack Rate Be an alternative form of CI

Usually used for an outbreak or other acute diseases as a result of a specific exposure (ie, poisoning food, virus, etc)

Observed for a short time period

Usually expressed for the entire epidemic period (for outbreak), from the first to the last case

2. Incidence —Cumulative Incidence

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Attack Rate, example

Ex: Outbreak of cholera in country X in March 1-31, 1999

Number of new cases = 490

Population at risk = 18,600

Attack rate = 2.6%

2. Incidence —Cumulative Incidence

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CI vs Prevalence

CI implies probability that a similar individual will DEVELOP the condition in future. Risk

Prevalence implies probability that a individual to HAVE the disease in a Pop. It describes current situation of a disease in a population.

Prevalence data guides clinical decision making, interpretation of diagnostic tests

2. Incidence —Cumulative Incidence

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Limitation of CI

Can only be calculated in closed cohorts Fail to explicitly account for the passage

of time

0 25 50 75 100y

x

x

0 25 50 75 100y

x

x

CI = 2/2=100%

Mean life span=37.5 y

CI = 2/2=100%

Mean life span=87.5 y

2. Incidence —Cumulative Incidence

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Limitation of CI

Risk

May under- or over-estimate the risk when a high loss rate

xx

x

x

x

x

xx disease onset

lost to followupMonth 1 Month12

CI = 7/12 per year

= 0.58 per year

2. Incidence —Cumulative Incidence

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Incidence rate

Units of cases/person-time Theoretical range zero to infinity Numerical value has no meaning at the

individual level

TimePerson

casesnew of No.

IR

2. Incidence — Incidence Rate (IR)

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Incidence rate Rate

Instantaneous concept (like speed)

Denominator:

- is a measure of time

- the sum of each individual’s time at risk

and free from disease

- IR = No. of new cases/ total time

= news cases / unit time

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A

B

C

D

E

90 91 92 93 94 95 96 97 98 99 00 Time at risk

x

x

6.0

6.0

11.0

9.5

5.0

Total years at risk 37.5

-- time followedx disease onset

lost-to-followup

ID = 2 / 37.5 person- years

= 0.053 person-year

2. Incidence — Incidence Rate

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Open population

Population at risk

births deaths

cases

Immigration Emigration/losses

time

2. Incidence — Incidence Rate

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Open Populations Dynamics

Inflow = immigration & birth Outflow = emigration, lost-to-followup & death

Average age may increase, decrease, or stay the same. depends on what?

Size may increase, decrease, or stay the same

Stable population = an open population in which inflow balances outflow to maintain constant size and age structure

2. Incidence — Incidence Rate

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Open population

Open population Has new entrants: births, immigrants,

new recruitments Has losses other than cases:

emigrations, deaths, lost-to-followup

Example: students in this Univ.

2. Incidence — Incidence Rate

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Cumulative Incidence vs Incidence rate

CI can be calculated from IR

When incidence is very low or the time of observation is very short

CI = IR x time Assumes the Pop. at risk is constant

Homicide in GZ: 8.7/100,000 person-years Annual risk: 8.7/100,000

2. Incidence — Incidence Rate

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Relationship of CI and IR

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.161 3 5 7 9

11 13 15 17 19 21

Age

Cu

mu

lati

ve in

cid

ence

Incidence rate

Cumulative incidence

1-14 years

Cumulative incidence

1-7 years

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Relationship of CI and IR

time

Cu

mu

lati

ve in

cid

enc

e

0.2

0.4

0.6

0.8

1.0

Slope=

Incidence rate

If IR is constant, CI = IR time

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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 average risk of 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.

Comparison of IR and CI

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Discussion QuestionDiscussion Question

How are incidence and

prevalence of disease related?

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Relationship of CI and prevalence

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Under somewhat special conditions,

P / (1-P) = IR x D

Prevalence depends on incidence rate (IR) and duration (D) of disease (duration lasts from onset of disease to its termination)

If incidence is low but duration is long - prevalence is

relatively high

If incidence is high but duration is short - prevalence is

relatively low

Relationship between Relationship between CI and prevalenceCI and prevalence

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Special condition

Steady state (inflow outflow)

IR constant Distribution of durations constant

Note that if the prevalence of disease is low (less

than 10%), the equation simplifies to P IR x D

Conditions for equation to be true:Conditions for equation to be true:

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Factors affecting the relation of incidence and prevalence

Virulence of the disease – Is it rapidly fatal?

Health care – When do cases come to medical attention? Can cases be cured? Does earlier detection alter prognosis?

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Factors affecting the relation of incidence and prevalence (cont’d)

Behavior – Do people recognize and act promptly on symptoms? Do patients comply with treatment?

Competing causes of death – Are people with the disease likely to die of other causes?

Migration – Are people with the disease likely to leave the area? Are people with the disease like to migrate to the area?

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Ratio males/women=2/8 Point Prevalence: Mar 1 =3/10Proportion of women=2/10=2% Period Prevalence Mar-Jul =7/10

Incidence Proportion Mar-Jul =4/7 Incidence density Mar-Jul = 4/18 person-month

0

1

2

3

4

5

6

7

8

9

10

Jan Feb Mar Apr May Jun Jul

Prevalence and incidence

3 P-mo

3 P-mo

2 P-mo

4 P-mo

4 P-mo2 P-mo

D

D

D

D

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Prevalence vs incidence Point

prevalencePeriod

prevalenceCI IR

Numerator Existing cases

(old and new)

Existing and new cases

New cases New cases

Denominator Initial Pop. Mid-point Pop.

Initial or

Midyear Pop.

Person-time

Time One point A period A period A period

Unit None None None No./PT

Type proportion proportion proportion rate

Example question

Do you currently have asthma?

Have you had asthma during the last year?

Have you ever had asthma last

year?

Study types Cross-sectional studies

surveillance

closed

Cohort studies

Open Cohort studies

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Dealing with recurrent cases Count only first event

remove case from PAR Count all events

don’t remove case from PAR Count secondary etc. events only after

biologically based recovery period remove temporarily from PAR

Count all events - stratify Remove case from PAR for primary case enter case in PAR for secondary case

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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

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Uses of Incidence & Prevalence Measures

Incidence: Measure of choice to:

--- Estimate risk of disease development

--- Study etiological factors

--- Evaluate primary prevention programs

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Discussion QuestionDiscussion Question

Why is incidence preferred over

prevalence when studying the

etiology of disease?

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Discussion QuestionDiscussion Question

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

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Discussion QuestionDiscussion Question

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

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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

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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.

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Measuring the disease occurrence

Mortality

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Mortality rates

Annual mortality rate for all causes =

n10midyearat population in the persions of No.

y1in causes allfrom deaths of No. Total

Because the pop. Changes over time, the number of persons in the Pop. At midyear is generally used as an approximation.

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Mortality rates

Is mortality rate a risk or rate?

Application An indication of risk of death of a

population, health status, or healthcare

level

Evaluation of a intervention of measure

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Specific Mortality Rates

Population-specified rate Age-specified rate Sex-specified rate Job, race, country, … …

Cause-specified rate Lung cancer mortality rate Heart disease mortality rate … …

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Cause-specific death rates

Annual mortality rate for lung cancer =

n10midyearat population in the persions of No.

y1in cancer lungfrom deaths of No. Total

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Top 10 causes of death in USA美国前十位死因

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Case-fatality rates

Case-fatality rate (%) =

100diseasespecified with the persions of No.

diagnosisor onset diseaseafter timeof

period specified a during deaths of No.

What percentage of people diagnosed as having a certain disease die within a certain time after diagnosis?

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Case-fatality rates

Numerator: Should be restricted to deaths from that disease

Denominator: individuals who already have the disease

Application: Measuring the severity of a disease Evaluating any benefits of a new therapy

Is this a proportion or rate?

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Survival rate

Survival rate = 1- case-fatality rate

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Comparison of mortality rate and case-fatality rate

Assume a pop. Of 100,000 people of whom 20 are sick with lung cancer, and in 1y, 18/20 die

from lung cancer

Lung cancer mortality rate in that year = 18/100,000 = 0.018%

The lung case-fatality rate = 18/20 = 90%

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Proportionate mortality

Proportionate mortality from disease X in year Y (%) =

100Yin year deaths Total

Yin year X disease

from deaths of No.

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Injuries (9.1%)Noncommunicableconditions (59.0%)

Communicable diseases, maternal and perinatal

conditions and nutritional deficiencies (31.9%)

Total deaths: 55,694,000Total deaths: 55,694,000

Source: WHO, World Health Report 2001

Death, by broad cause group in 2000

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References

Greenberg RS, et al. Medical Epidemiology (4th ed.) Medical Publishing Division, Lange Medical Books/McGraw-Hill, New York. 2005

Gordis L. Epidemiology (3rd Ed.) Elsevier Inc. (USA), 2004

Friis RH & Sellers TA. Epidemiology for public health practice. Jones & Bartlett Publishers, Sudbruy, Massachusetts. 2004

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Thanks!