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!