Measures of Frequency - interfetpthailandTime Place Person Descriptive In Specific Population...
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Measures of Frequency
Thanit Rattanathumsakul, M.D., M.Sc.,
Bureau of Epidemiology, DDC, MOPH
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Type of Data
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Type of DataType of Data3
Data collection Characteristics of data Scale
Qualitative data (Categorical variables)
Counting
(Enumeration) e.g. sex, occupation,
address, grade (score)
1. Nominal scale
2. Ordinal scale
4. Ratio scale
Data
grade (score) stage of disease
Measurement
e.g. temperature, score, length, time
2. Ordinal scale
3. Interval scale
Quantitative data
Discrete variables
Continuous variables
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Data Characteristics according to Scale
Nominal scale
Ordinal scale
Scale Example Characteristics
Disease, sex,
occupation, race, district, Blood
group, risk factor
Severity, grade (score), education
level, shirt size
Grouping
Direction (unequal interval)
Statistics: Presentation
Frequency, proportion, ratio, mode: table, chart
Frequency, proportion, ratio, mode, median,
percentile: table, chart
same -
differ
same -
differ
less-
more
Difference(Grouping)
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Ordinal scale
Interval scale
Ratio scale
level, shirt size
Score, temperature,
time, IQ
Age, income, distance, weight, height, volume
interval)
Grouping Direction Equal int. No abs zero
Grouping Direction Equal int. Abs zero Ratio
percentile: table, chart-differ
-more
same -
differ
less-
more
() ()
same -
differ
less-
more
() () ()()
Frequency, proportion, ratio, mode, median, mean, S.D.: table,
chart
Grouping
Direction
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Measures in Measures in Epidemiology
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How epidemiologists work?
1. Counting: Counts cases or health events, and describes them in terms of time, place, and person
2. Dividing:
DescriptiveEpidemiology
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2. Dividing:Divides the number of cases by an appropriate denominator to calculate “rates”
3. Comparing:Compares these “rates” over time or for different groups of people
“Rates”, in this slide, simply means division of one number by another
AnalyticEpidemiology
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Number of cases“we have 4 cases of rabies”
Simple
Counting
How big of the population in which the cases occurred?These cases occurred in what length of period?
Simple but not informative!
Need to find appropriate denominatorand specify time period. 7
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EpidemiologyStudy
Distribution
Time
Place
Person
Descriptive
In Specific Population
Measures of Frequency”
Measures of Impact”
Attack Rate, Prevalence,
Incidence
Attributable Risk, Study
Determinants
Host
Agent
Environment
Analytic
Population
Measures of Association”
Impact”
OR, RR, PROD, RD
Risk, AFp, ARp
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Aims of Epidemiology• DESCRIBE
• How many cardiovascular disease (CVD) patients are there in Province A?
• Proportion of male and female among the CVD patients?
• EXPLAIN
• Why is CVD more common in men than women?• Does smoking increase the risk of developing CVD?
Measures of Frequency
Measures of Association
• Does smoking increase the risk of developing CVD?
• PREDICT
• If there is an effective smoking cessation campaign, how many new CVD patients can be reduced in next year?
Source: Morgenstern, 2001 (modified)
Measures of Impact
• CONTROL
• What are appropriate control measures for the community (under limitations)?
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Measures in Epidemiology
Measures of Risk* Summarizing data**
1. Measures of Frequency2. Measures of Association
4. Measures of Central Location (Tendency)2. Measures of Association
3. Measures of Public Health Impact
(Tendency)5. Measures of Spread
(Dispersion)
* Dichotomous variables such as:• Disease – case/non-case, • Exposed to disease – yes/no, • Test – positive/negative,
case/control,…
** Continuous quantitative variables
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Measures of RiskMeasures of Risk
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Reported Dengue cases in Ratchaburi Province, by district, 2015
Damnoen Saduak
Ban Pong
Mueang Ratchaburi
“Why we have to use Measures of Risk?”
Number of cases Morbidity rate
(per 100,000 population)
Pak Tho
Bang Phae
Wat Phleng
Suan Phueng
Photharam
Chom Bueng10203040 0 10 20 30 40 12
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Measures of Risk
1. Measures of Frequency
1.1 Morbidity Frequency Measures
1.2 Mortality Frequency Measures
1.3 NatalityMeasures
Incidence
Prevalence
Deaths and cause of deaths
Maternal and child deaths
YLL, YLD
Births or Fertility
“SIZE”
“SEVERITY”
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2. Measures of Association
3. Measures of Public Health Impact
1.3 NatalityMeasures
Births or Fertility
Births problems (LBW, teenage pregnancy)
Ratio scale
Difference scale
Causal factor
Protective factor
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Fraction in Epidemiology
• When you divide a number by another
Numerator
• You will get either Rate, Ratio, and Proportion
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Denominator
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Rate
• By definition, rate is ratio representing relative change in two quantities
• In Epidemiology, rate is measure of change per unit of time, where time might be expressed or just implied in denominator
• It is speed of occurrence of an event over time
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A
time
Number of events (e.g. # cases)
Sum of follow-up time contributed by the people at risk of the event (person-time)
Note: The term “Rate” is wrongly, and commonly, used as a synonym for ratio (e.g. fertility rate or infant mortality rate), or proportion (e.g. case-fatality rate, mortality rate, or attack rate)
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Ratio• Ratio is the relationship of one quantity
(numerator) to another quantity (denominator)
• The quantities may be related or unrelated, and are not necessary in the same units.
A Any quantities
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A
B
Any quantities
Any quantities
females
males= 30/20 = 1.5/1 = 1.5
beds
doctors120/6= = 20/1 = 20
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Proportion• Proportion is a ratio in which the numerator is included in
the denominator
• It has no dimension because the unit of the numerator cancels out the unit of the denominator
• Proportion always ranges between 0 and 1
• Percentage = proportion x 100 • Percentage = proportion x 100
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A
A+B
A part of denominator
Always Includes numerator
females
total population= 30 / 50= 0.6 = 60%
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Rate vs. Ratio vs. Proportion
• Rate
– Denominator = population at risk
– Rate of subgroups can not be directly summation
• Ratio
– Has no unit. (the lower value usually be 1) – Has no unit. (the lower value usually be 1)
– The quantities may be related or unrelated, and are not necessary in the same units
• Proportion
– Proportion is a ratio in which the numerator is included in
the denominator
– Proportion always ranges between 0 and 1
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Measure of Frequency
Exposure Disease
Measure of Disease frequency
Measure of Exposure frequency
? ?
Smoking
Smoking in Community A in 20151. Prevalence of smoking
• In Male = 30%• In Female =10%
2. Incidence of new smokers• 5/1,000 population
Heart disease in Community A in 2015
1. Prevalence of heart disease • In Male = 5% • In Female = 2%
2. Incidence of new heart disease• 3/1,000 population
Smoking Ischemic Heart disease
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Prevalence and Incidence
Incidence (I)New cases
IxDP D = average disease duration
Prevalence (P)New + old cases
Resolution•Cures•Deaths
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Longer duration of the disease
High case fatality rate
Decrease in incidence
Improved diagnostic facilities
Factors affected to PrevalencePrevalence
Increase/Decrease?
Increase
Decrease
Decrease
Increase
Out-migration of cases
In-migration of healthy people
Improved diagnostic facilities
Better reporting
Improved cure rate
Decrease
Decrease
Increase
Increase
Decrease
Source: WHO, 1994 21
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Prevalence and Incidence
• Prevalence
– Point prevalence
– Period prevalence
• Incidence• Incidence
– Incidence proportion
– Incidence rate
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Prevalence
• Point prevalence
– Amount of disease in the population at a given point in time
= Number of cases of the disease present at given point in time
total population at that time Population at risk
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Population at risk
• On Jan 1st , 2015, company A has 5000 employees, • 100 of which have hypertension • Point Prevalence on Jan 1st, 2015 = ?
• Point prevalence = 100/5000 = 0.02 = 20 per 1000
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Prevalence
• Period prevalence
– Amount of disease in the population during a specific time period
– = Number of cases presenting anytime during specific time interval
average population during the time interval or mid-interval population
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Population at risk
• In 2015, company X has total employees of 5000 in Jan and 4900 in Dec • Of these 100 cases were diagnosed prior to Jan 1st , 2015 and 5 new
cases were diagnosed in 2015• Of these 105 cancer cases, 10 died in 2015• Period Prevalence in 2015 = ?
• Period prevalence = 105/[(5000+4900)/2] = 0.021 = 21 per 1000
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Interpretation of Prevalence
• Because prevalence depends on both incidence and disease duration, it is not as useful as incidence for studying causes of a disease (Etiologic study).
• It is useful for measuring disease burden on a population, especially if those who have the disease require specific medical attention.
• Suitable with chronic diseases or diseases that can not clearly identify the onset
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Example: Prevalence
Year 2002 2003 2004 2005 2006 2007 2008 2009
No. 1
No. 2
No. 3
Prevalence of DM in 6 persons, 2002 - 2009
No. 3
No. 4
No. 5
No. 6
Period prevalence from 2006 to 2007 =
Point prevalence at mid-year of 2005 = 2/6 = 0.33 = 33%
3/6 = 0.50 = 50% 26
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Incidence
• Incidence proportion
Syn: incidence risk, risk, cumulative incidence, attack rate (in an epidemic)
• Incidence rate
Syn: incidence density, force of morbidity/force of mortality, hazard rate, person-time rate, disease intensity
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Incidence Proportion • Incidence proportion is the proportion of people in a population who
became diseased or ill or experienced an event during the specified period of time
• = Number of new cases of disease or events during time period
Total population at risk at the beginning of the time period
• = Probability, or “risk”, of developing the disease during the time interval• = Probability, or “risk”, of developing the disease during the time interval
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•On Jan 1st , 2015 company X has 5000 employees free of cancer
•During the course of the year, 5 employees are diagnosed with cancer
•Incidence proportion during 2015 = ?
•Incidence proportion = 5/5000 =0.001 = 0.1% = 1 per 1000
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Assumptions for Incidence Proportion
Two assumptions required when calculating incidence proportion:
• Entire population at risk has been followed from the beginning of the study till the endfrom the beginning of the study till the end
• All participants are at risk of the outcome of interest
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1. The only way to interpret incidence proportion, or risk, is to know the length of the time period over which the risk applies
2. Useful for studying causes of a disease (Etiologic study) or evaluate implemented
Interpretation of Incidence Proportion
2. Useful for studying causes of a disease (Etiologic study) or evaluate implemented control measure.
3. Suitable with acute diseases or diseases that can clearly identify the onset
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Attack Rate
• Attack rate (AR) is a probability, or “risk”, of getting a disease during an epidemic period, applied to a defined population observed for a limited time.
• = Number of incident cases during an epidemic period
Population at risk at the beginning of the epidemic periodPopulation at risk at the beginning of the epidemic period
– Overall attack rate: Attack rate among total population at risk
– Specific Attack rate: Attack rate among subpopulation• Age-specific attack rate • Gender-specific attack rate• Food-specific attack rate
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Differences among specific attack rates are important for
generating hypotheses!
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Attack Rate: Example
• The district health officer was called in to investigate more than 20 reports of people being ill with gastroenteritis after eating at a large food festival party during the first week of May 2015.
• An investigator was conducted interviewing all visitors who ate at the festival during that week
• They found 2,000 visitors ate at the festival that week and 400 became sick.
• Overall attack rate = 400/2000 = 20%
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•700 ate food item “A”, 200 became sick
•1,200 ate food item “B, 250 became sick
•500 ate food item “C”, 300 became sick
Food-specific Attack rate
•A: 200/700 = 29%
•B: 250/1,200 = 21%
•C: 300/500 = 60%
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Secondary Attack Rate
• is the attack rate among susceptible people who come into direct contact with primary cases
• Example:– 7 sick students from 7
families (black circle) families (black circle) – Total 25 household
contacts, 5 out of them became sick later (black square)
• Primary attack rate =
• Secondary attack rate =
33N = 70
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Appropriate Denominator for Cervical Carcinoma?
0-25
Total populationAll women
(all age groups)Population at risk
(specific age group)
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Men Women
0-25 years
25-69 years
70+ years
25-69 years
Source: Basic Epidemiology, 2nd Ed., R Bonita, 2006
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Incidence Rate
• The incidence rate is the number of new cases in a
population divided by the total time units each individual in
the population at risk was observed.
• = No. new cases during the specified time period• = No. new cases during the specified time period
Sum of person-time at risk during the time period
• Denominator for incidence rate is the sum of disease-free
time contributed to by each at-risk individual
• Incidence rate ranges from 0 to infinity (it is not a proportion!)
• Dimension = case per unit of time (or case/time)35
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Total Person Time at Risk
• Example: 40 workers worked in Battery Factory A with vary durations.
8 workers works for 10 years person-time at risk = 8 x 10 = 80 person-years
25 workers works for 5 years person-time at risk = 8 x 10 = 125 person-years25 workers works for 5 years person-time at risk = 8 x 10 = 125 person-years
6 workers works for 2 years person-time at risk = 6 x 2 = 12 person-years
1 workers works for 6 months person-time at risk = 1 x 0.5 = 0.5 person-years
Total person-years at risk = 80 + 125 + 12 + 0.5 = 217.5 person-years
If there were 6 new neurologic disease occurred during past 10 years
6 x 1,000217.5 = 27.6 per 1000 person-yearsIncidence Rate =
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Person-Time Calculation (1)
• There are two ways to calculate “person-time”, i.e. denominator of incidence rate
1. Using individual data
• Sum of each person-time at risk, one-by-one• Sum of each person-time at risk, one-by-one
• Accurate
• Requires resources (time, staff, money)
• Appropriate for small population or in well-planned prospective research
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Example: Incidence
Year 2002 2003 2004 2005 2006 2007 2008 2009
No. 1 1
No. 2 7
No. 3 7
Incidence of DM in 6 persons, 2002 - 2009
Year at risk
No. 3 7
No. 4 3
No. 5 5
No. 6 7
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Total = 30
Incidence Rate =
Incidence Proportion = 4/6 = 0.67 case in 7 years
4/30 = 0.13 Person-years
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Person-Time Calculation (2)
2. Using aggregated data
• Assume that the occurrence of new cases and loss-to-follow-up are spread uniformly throughout the time period
• Denominator is “average population at risk” multiply with “follow-up period”
“Average population at risk” can be calculated by• “Average population at risk” can be calculated by– Average of the population at the beginning and at the end of the
period, or
– Subtracting one half of the events and losses from the initial population, or
– Number of people free of the disease in the middle of the time period
• Not very accurate but can be use for larger population
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100
Population
90
80
Incomplete F/U = 10 PY
Assumption: the occurrence of new cases and loss-to-follow-up is spread uniformly throughout the time period
Total F/U= 90 PY
0 0.5 1
Follow-up time (year)
Complete F/U = 80 PY
• Average Population at Risk = (100+80)/2 = 90 persons
• Person-time at risk = 90 x 1 = 90 PY 40
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3
4
6
2
1
4
l
l
l
l
l
l
Person 1
Person 2
Person 3
Person 4
Person 5
Person 6
Person-time
Example: A follow-up study
Incidence Rate = 3 cases / [(6+1)/2] x 6 person-years
= 3 cases / 3.5 x 6 person-year
= 3 case /21 person-years
= 0.14 person-year = 14 cases / 100 person-years
4Total = 20 PY
1997 1998 1999 2000 2001 2002 2003
lPerson 6
= Loss F/U = Getting disease
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Interpretation of Incidence Rate
• It describes how quickly disease occurs in a population
• There are two ways to interpret it
1. It is the speed of occurrence of new cases from time zero to time t, per unit of time, relative to the size of the population at risk during that interval
• Incidence rate of 12 cases per person-year means “on average during study period, for each person-year passed, 12 cases would during study period, for each person-year passed, 12 cases would occur”
2. Under steady-state conditions, a situation in which rates do not change with time, the reciprocal of the incidence rate equals the average time until an event occurs, i.e. incidence time or waiting time
• An incidence rate of 12 cases per person-year can be interpreted as “an average incidence time of 1/12 years or 1 month” or “on average, one case will occur every one month of follow-up”
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Incidence VS Prevalence
Incidence Prevalence
Numerator Number of new cases of diseaseduring a specified period of time
Number of existing cases of diseaseat a given point of time
Denominator Population at risk Population at risk
Focus •Dynamic concept, i.e. “follow-up”•Focuses on time of onset of the
•Static concept, i.e. “snapshot”•Focuses on presence or absence
disease •Unaffected by cure or death
of a disease; time period is arbitrary•Affected by cure or death
Uses •Expresses the risk or speed of becoming ill
•The main measure of acutediseases or conditions, but alsoused for chronic diseases
•More useful for studies of causation
•Estimates the probability of thepopulation being ill at the period oftime being studied
•Inappropriate for diseases with short duration
•Useful in the study of the burden ofchronic diseases and implication forhealth services 43
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Incidence Proportion vs. Incidence Rate
Incidence Proportion Incidence Rate
Simple proportion with no units Rate expressed per person-time unit
Range from 0-1 Range from 0 - Infinity
Measures average risk of disease development
Measures speed of disease development
Appropriate with fixed populations or closed cohort where follow-up times are uniform
Appropriate with dynamicpopulations or open cohort where follow-up times vary
Assume no deaths due to competing risks or loss to follow up
Account for deaths due to competing risks or loss to follow up
Easily interpreted Not easily interpreted
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Relationship:
Incident Proportion (IP) & Incident Rate (IR)
IP = IR x Time
•This simplest formula is an approximation that works well as long as both of following condition satisfied
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as long as both of following condition satisfied• Small incidence e.g. Incident proportion < 10-20%• Incidence rate remains constant over the time period
•In other conditions
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Relationship:
Prevalence (P) & Incidence (I)
Assuming steady-state condition…
• the population is closed (no immigration, no death
from other causes, and no loss follow up)
• Prevalence and incidence are unchanging
P Average disease durationD
IxDP
P
1
If P is smalle.g. < 10-20%
Average disease duration
I
P
D
Point Prevalence
Incidence Rate
IxDP 46
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Example: Seven-Years Follow-up
1
2
3
4
Person
Healthy
Disease
DeathD
DD
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4
5
6
7
0 1 2 3 4 5 6 7 Years of F/U
Loss F/U
DeathDL
D
L
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Example: Point Prevalence
1
2
3
4
Person
Healthy
Disease
DeathD
DD
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Point Prevalence at the Beginning = 2/7 = 0.28 = 28%
4
5
6
7
0 1 2 3 4 5 6 7 Years of F/U
Loss F/U
DeathDL
D
L
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Example: Period Prevalence
1
2
3
4
Person
Healthy
Disease
DeathD
DD
49
7-year Period Prevalence = 4 / 7 = 0.57 = 57%= 4 / 5 =
0.80= 80%
4
5
6
7
0 1 2 3 4 5 6 7 Years of F/U
Loss F/U
DeathDL
D
L
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Example: Incidence Proportion
1
2
3
4
Person
Healthy
Disease
DeathD
DD
50
year Incidence Proportion = 2/5 = 0.4 = 40%
4
5
6
7
0 1 2 3 4 5 6 7 Years of F/U
Loss F/U
DeathDL
D
L
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Example: Incidence RateTime-at-risk Followed
(Year)
7
3
0
6
1
2
3
4
Person
Healthy
Disease
DeathD
DD
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6
1
0
3
• Person-time at risk = 7+3+0+6+1+0+3 = 20 person-year
• Incidence Rate (during 7-years study period)= 2 / 20 = 0.10 case/ person-year
4
5
6
7
0 1 2 3 4 5 6 7 Years of F/U
Loss F/U
DeathDL
D
L
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Severity
• Mortality
– Crude death (mortality) rate
– Specific death (mortality) rate
– Proportional mortality rate– Proportional mortality rate
– Survival rate
– Case-fatality rate
• Complication rate
• Burden of Disease (YPLL, DALY, QALY)
• Effect on economics and social loss52
= Number of those who developed the complication
among total patients with that disease
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Crude Death Rate
• It is a proportion of total deaths by all causes among total population in a given period
= Total number of deaths from all causes during calendar year
total midyear population
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In 2015, City A: 131,044 deaths; total population = 12,335,000
Crude death rate = 131,044 / 12,335,000 = 0.01062 or 10.62 deaths per 1,000or 1062 deaths per 100,000
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Specific Death Rate
• It is a proportion of deaths from a specific disease and/or in specific population in a given period such as
• Cause specific Death Rate
= total number of deaths from a specific disease during calendar year
total population at risk
e.g. Lung cancer deaths rate of Thai populatione.g. Lung cancer deaths rate of Thai population
• Age-gender specific Death Rate
= total number of deaths in age-gender specific group during calendar year
total population in age-gender specific group
e.g. Lung cancer deaths rate among Thai male aged > 45 years
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Proportional Mortality Rate
• It is a proportion of deaths by a specific disease among all deaths in a given period
= total number of deaths due to specific disease during calendar year
total deaths due to all causes during calendar year
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In 2015, Country A: Population = 1,000,000400 deaths from all causes, 60 deaths from cancer,
Crude death rate = 40 per 100,000
Cancer death rate = 6 per 100,000
Proportional Mortality ratio = 60/400 = 0.15 or 15%
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Case-Fatality Rate (CFR)• It is a proportion of deaths by a specific disease
among all cases of that disease in a given period
• Expresses severity of the disease
= Number of deaths due to the disease during specific periodNumber of cases of the disease during the same period
Specific death rate = Incidence proportion x CFR
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In 1981, US: 23,400 leukemia cases, 15,900 deaths from leukemia
Case fatality rate = 15,900/23,400 = 0.679 = 67.9%
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Survival Rate
• Probability of remaining alive for a specific length of time for or a chronic disease such as cancer
• Like CFR, it is a proportion and expresses • Like CFR, it is a proportion and expresses disease severity
• 1-year survival and 5-year survival rates are often used as indicators of the severity of disease and the prognosis
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Ex: Survival curve for patients diagnosed with any type of leukemia
Median survival time
= 2.5 years
5-year survival= 47%
1-year survival= 68%
Source: Raymond 2004
= 47%50%
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Mortality Rate1. Crude death (mortality) rate (CDR)
> Determine the overall health status of the community > The real death rate occurred in the community
2. Specific death (mortality) rate (SDR)> Identify special characteristics or risk of dying from
that disease that disease
3. Case-fatality rate (CFR)> Identify the severity of the disease > Identify the quality of medical treatment
4. DALY = YLL (Year of Life Lost due to premature death) + YLD (Year Lost due to Disability)
> Determine the burden of disease (BOD) 59
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Causes Cases Deaths CDR(per 100,000 pop)
(%) CFR(%)
Accident 3,215 194 37.86 5.58 6.03
Cancers 2,381 313 61.08 9.01 13.14
HT 647 96 18.73 2.76 14.84
Example: Mortality rateNumber of deaths and causes of deaths, Province A, 2012
HT 647 96 18.73 2.76 14.84
TB 517 17 3.32 0.49 3.29
Diarrhea 9,880 37 7.22 1.06 0.37
Others N/A 2,817 549.69 81.09
Total - 3,474 677.89 100.0 -
Remarks: Mid-year population = 512,473 60
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Top ten: DALYsTop ten: DALYs
Rank DiseaseDALY
('000)% %
DALY
('000)Disease
1 HIV/AIDS 645 11.3 7.4 313 Stroke2 Traffic accidents 584 10.2 6.9 291 HIV/AIDS3 Stroke 332 5.8 6.4 271 Diabetes
Male Female
DALY
% of Total 52.61 42.83
3 Stroke 332 5.8 6.4 271 Diabetes4 Alcohol dependence/harmful use 332 5.8 4.6 191 Depression5 Liver and bile duct cancer 280 4.9 3.4 142 Ischaemic heart disease6 COPD 187 3.3 3.0 125 Traffic accidents7 Ischaemic heart disease 184 3.2 3.0 124 Liver and bile duct cancer8 Diabetes 175 3.1 2.8 118 Osteoarthritis9 Cirrhosis 144 2.5 2.7 115 COPD
10 Depression 137 2.4 2.6 111 Cataracts
From: Burden of Disease Research Program Thailand (BOD Thailand), 2004 61
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Further Readings
• Basic Epidemiology, 2nd Ed., R. Bonita et al.
• Principles of Epidemiology in Public Health Practice, 3rd Ed., US CDC.
• A Dictionary of Epidemiology, 5th Ed., M. Porta.• A Dictionary of Epidemiology, 5 Ed., M. Porta.
• Epidemiology: Concepts and Methods, 1st Ed., WA. Oleckno.
• Modern Epidemiology, 3rd Ed., KJ. Rothman et al.
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63Any Question?Any Question?