Measures of Frequency

Thanit Rattanathumsakul, M.D., M.Sc.,

Bureau of Epidemiology, DDC, MOPH

1

Type of Data

2

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

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)

4

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

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

6

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

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

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

8

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

10

Measures of RiskMeasures of Risk

11

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

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

Fraction in Epidemiology

• When you divide a number by another

Numerator

• You will get either Rate, Ratio, and Proportion

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Denominator

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

15

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)

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

16

A

B

Any quantities

Any quantities

females

males= 30/20 = 1.5/1 = 1.5

beds

doctors120/6= = 20/1 = 20

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%

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

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

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

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

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

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!

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%

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

Appropriate Denominator for Cervical Carcinoma?

0-25

Total populationAll women

(all age groups)Population at risk

(specific age group)

34

Men Women

0-25 years

25-69 years

70+ years

25-69 years

Source: Basic Epidemiology, 2nd Ed., R Bonita, 2006

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

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 =

36

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

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

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

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

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

Example: Seven-Years Follow-up

1

2

3

4

Person

Healthy

Disease

DeathD

DD

47

4

5

6

7

0 1 2 3 4 5 6 7 Years of F/U

Loss F/U

DeathDL

D

L

Example: Point Prevalence

1

2

3

4

Person

Healthy

Disease

DeathD

DD

48

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

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

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

Example: Incidence RateTime-at-risk Followed

(Year)

7

3

0

6

1

2

3

4

Person

Healthy

Disease

DeathD

DD

51

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

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

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

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

55

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%

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%

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

57

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%

58

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

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

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

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?