Quantitative Measures in Epidemiology DEFINITION OF EPIDEMIOLOGY - - PDF document

Quantitative Measures in Epidemiology

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DEFINITION OF EPIDEMIOLOGY

“The study of the distribution and determinants of disease frequency"

(MacMahon, 1970)

“The study of the occurrence

• f illness"

(Cole, 1979)

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QUANTITATIVE MEASURES OF DISEASE FREQUENCY

Basic elements of epidemiologic inference are defining, counting, and summarizing disease outcomes

Outcomes: expressed as either categorical (eg. Disease occurrence or severity) or continuous variables

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NOMINAL AND ORDINAL VARIABLES

• Both nominal and ordinal scale data can be

summarized in frequency distributions

• Nominal scale data are usually further

summarized as ratios, proportions and rates

• Ordinal scale data are usually further

summarized with measures of central location and measures of dispersion

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TYPES OF VARIABLES AND STATISTICS

Qualitative

Polychotomous (> 2 groups)

Categorical data

Variables

Quantitative Nominal Ordinal

Dichotomous (2 groups)

Continuous data Mean Median Mode Range Inter-quartile range Standard deviation Ratio Proportion Rate

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QUANTITATIVE MEASURES USED IN EPIDEMIOLOGY

• Measures of disease frequency reflect the relative
• ccurrence of the disease in a population.
• Measures of association reflect the strength or

magnitude of the statistical relationship between exposure status and disease occurrence.

• Measures of effect: Certain measures of association

involving disease incidence are also measures of the exposure effect.

• Measures of impact* are used to predict the impact of

an intervention on the disease occurrence in a population (extra number of cases attributable to, or prevented by, the exposure)

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EPIDEMIOLOGIC APPROACH

• Case Definitions:

– based on signs, symptoms and results of tests

• Numbers and Rates
• Descriptive Epidemiology
• Analytic Epidemiology

QUANTITATIVE METHODS

• Measurement of

variables

• Estimation of population

parameters

• Testing of statistical

hypothesis

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EPIDEMIOLOGIC DATA

• A common form of epidemiologic data is a

rectangular database.

• Each row contains information about one individual--

i.e., record, observation.

• Each column contains information about one

characteristic--i.e., variable.

• In an outbreak investigation, we usually create a

database called a “line listing”.

• In a line listing, each row represents a case. Columns

contain identifying information, clinical details, descriptive epidemiologic factors, and possible etiologic factors.

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Neonatal listeriosis, General Hospital A, Costa Rica, 1989

Symptom Delivery Admitting ID Sex Date DOB Type Outcome Symptoms 1 F 6/2 6/2 Vaginal Lived dyspnea 2 M 6/8 6/2 C-section Lived fever 3 F 6/15 6/8 Vaginal Died dyspnea 4 F 6/12 6/8 Vaginal Lived fever 5 F 6/15 6/11 C-section Lived pneumonia 6 F 6/20 6/14 C-section Lived fever 7 M 6/21 6/14 Vaginal Lived fever 8 F 6/18 6/15 C-section Lived fever 9 M 6/20 6/15 C-section Lived pneumonia 10 M 6/19 6/16 Forceps Lived fever 11 M 7/21 7/21 Vaginal Died dyspnea

Source: Schuchat 1991

An example of “line listing”.

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SUMMARIZING DIFFERENT TYPES OF VARIABLES

When categories are used, the measurement scale is called a nominal scale.

Vaccination Number Yes 76 No 125 Total 201

When points on a numerical scale are used, the scale is called an ordinal scale.

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FREQUENCY DISTRIBUTION

• With larger databases, we usually

summarize variables into tables called “frequency distribution”.

• A frequency distribution shows the

values a variable can take, and the number of people with each value.

Example

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Distribution of Students by Levels of Blood Sugar, n= 100

• Bl. sugar (mg% ) Number Relative freq Cumulative relative freq

52-55 4 4 4 56-59 12 12 16 60-63 16 16 32 64-67 27 27 59 68-71 13 13 72 72-75 19 19 91 76-79 4 4 95 80-83 5 5 100 Total 100 100 100

Example of “frequency distribution”.

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In what circumstance that we should measure by counting absolute number?

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2 4 6 8 10 18 - 24 M ay 25 - 31 M ay 1 - 7 Jun 8 - 14 Jun 15 - 21 Jun 22 - 28 Jun 29 Jun - 5 Jul 6 - 12 Jul 13 - 19 Jul 20 - 26 Jul 27 Jul - 2 A ug 3 - 9 A ug 10 - 16 A ug 17 - 23 A ug 24 - 30 A ug 31 A ug - 6 Sep 7 - 13 Sep 14 - 20 Sep 21 - 27 Sep 28 Sep - 4 Oct 5 - 11 Oct

Weekly interval NS 1 NS 2 2 / 2 Kit.

Epidemic curve and spot map

• f mumps cases, kindergarten “A” ,May–September 1999

(N= 38)

1 child case 1 officer case

1 / 1 1 / 2 3 / 2 3 / 1 2 / 1

Laosirithaworn, 1999

Distribution

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Example: Investigation of increasing death from unintentional fall, Thailand

• The injury surveillance (IS) data from

Lampang regional hospital showed increasing number of death from unintentional fall after 1998

• FETP was notified and went to investigate
• IS report and medical records were

reviewed and relatives of the deaths were interviewed

Source: Jiraporn Plaitho, 2002

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Number of deaths from unintentional fall by year and age-group, Lampang hospital 1997-2001

Source: Jiraporn Plaitho, 2002

Age 1997 1998 1999 2000 2001 0-14 yr 1 1 1 1 15-59 yr 12 7 15 12 20 > = 60 yr 15 10 16 17 22

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Population of Lumpang province 1997-2001

Age 1997 1998 1999 2000 2001 0-14 yr

161,221 162,430 159,550 158,160 153,343

15-59 yr

479,933 493,553 500,146 509,278 513,012

> = 60 yr

90,002 93,184 94,983 82,914 99,441

Source: Jiraporn Plaitho, 2002

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Number of deaths from unintentional fall by age- group, Lampang hospital 1997-2001

5 10 15 20 25 1997 1998 1999 2000 2001 0-14 yrs 15-59 yrs >=60 yrs

0-14yr 3% >=60yr 53% 14-59yr 44%

Number

N=150

Source: Jiraporn Plaitho, 2002

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Death rate of unintentional fall by age-group, Lumpang hospital 1997-2001

5 10 15 20 25 1997 1998 1999 2000 2001 0-14 yrs 15-59 yrs >=60 yrs

14-59yr 44% >=60yr 53% 0-14yr 3%

Rate per 100,000 pop

N=150

Source: Jiraporn Plaitho, 2002

rate ?

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DISEASE FREQUENCY

Disease frequency is usually measured as a proportion or rate in which:

• Numerator reflects the number of cases
• r events of interest
• Denominator reflects the size of a

population from which those cases or events are identified

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TYPES OF FREQUENCY MEASURES Distinguished by type of numerator

• Incidence: the numerator reflects

the number of new cases identified during a given period.

• Prevalence: the numerator reflects

the number of existing cases identified at a point in time.

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Incidence and Prevalence

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PREVALENCE MEASURES Prevalence is the frequency

• f existing cases

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Prevalence is calculated by: Number of people with the disease or condition at a specific time P = Total population at a specific time

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1 existing case at a point in time in a population of 5 babies

1 Prevalence = = 0.2 = 20% 5

• Point prevalence is:

The proportion of the population affected by a disease at a specific point in time

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PERIOD PREVALENCE

• Period prevalence is calculated by:

Number of incident and prevalent cases identified during a given period

• P =

Size of the total population during the period

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3 existing case during a period of time in a population of 5 babies

3 Period revalence = = 0.6 = 60% 5

• Period prevalence is:

The proportion of the population affected by a disease anytime during a given period

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INTERPRETATION OF PREVALENCE

• Because prevalence reflects both

incidence rate and disease duration, it is not as useful as incidence for studying causes of disease.

• It is useful for measuring disease

burden on a population, especially if those who have the disease require specific medical attention.

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RELATIONSHIP BETWEEN PREVALENCE AND INCIDENCE

Prevalence is less useful than incidence in etiologic studies, because it is a function of incidence rate ( ) and duration of disease ( )

Assumption: prevalence, incidence rate and mortality rate remain constant over time, no in- and out-migration

( )

T I P P = − 1

T

I

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RELATIONSHIP BETWEEN PREVALENCE AND INCIDENCE

If the disease is rare, = mean duration of disease

Assumption: prevalence, incidence rate and mortality rate remain constant over time, no in- and out-migration

( )

T I P ≈

T

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FACTORS INFLUENCING OBSERVED PREVALENCE

Increase/Decrease

Out-migration of cases Longer duration of the disease High case fatality rate Decrease in incidence In-migration of healthy people Improved diagnostic facilities Better reporting Improved cure rate

Source: WHO, 1994

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The proportion of infants who are born alive with a defect of the ventricular septum of the heart is a prevalence or incidence?

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Risk and Rate

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INCIDENCE MEASURES: RISK AND RATE Distinguished by type of denominator

• Risk (cumulative incidence, incidence

proportion): probability of the event

• Incidence rate (incidence density): rate

estimate expresses the “rate” at which the events occur in the population at risk at any given point in time

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RISK AND INCIDENCE PROPORTION

• Risk is measured on the same scale and

interpreted in the same way as a probability.

• We use risk to describe the probability that a

person will develop a given disease.

• Risk is used in reference to a single person
• Incidence proportion is often used in

reference to a group of people

• We use average taken from population to

estimate the risk experience by individuals

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RISK ESTIMATION (SIMPLE METHOD)

• Risk (R) is:

The probability of an individual at risk developing the disease during a given period Number of incident cases of disease

• ccurring in a specified period

R = A/N = Number of people at risk at the start

• f the specified period
• Assumption: all N people are followed for the

entire time period, i.e., follow up is complete

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When did your last health check up?

If you can choose to have either total cholesterol equal 7 or 8 mmol/l*, which level do you want? Why?

*High total cholesterol defined as a total cholesterol level of 6.2 mmol/l or higher mmol/l = mg% X 0.02586

If you interview SARS patients, will you wear full PPE (personal protection equipments), compared to interview measles patients? Why?

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HYPOTHETICAL COHORT Incidence is best understood in the context of prospective (cohort) studies

• In a typical cohort, censored
• bservations can occur when individuals

dying from other diseases or recruited later in the accrual period of the study,

• r migration

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Hypothetical cohort of 10 persons followed for up to 24 months, Jan 96-Dec 98

Modified from fig. 2-1 in M. Szklo, F. Nieto. Epidemiology Beyond the Basics. Maryland: Aspen Publishers; 2000

Individuals 1 2 3 4 5 6 7 8 9 10

J a n -9 6 M a r-9 6 M a y -9 6 J u l-9 6 S e p -9 6 N o v -9 6 J a n -9 7 M a r-9 7 M a y -9 7 J u l-9 7 S e p -9 7 N o v -9 7 J a n -9 8

• Death

Censored

• bservation

Follow-up time

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The same hypothetical cohort, started from the beginning of the study

4 8 12 16 20 24

1 2 3 4 5 6 7 8 9 10 Individuals Months of follow-up

• 1

17 20 9 24 16 2 13 10 3 Total time under observation

Death Censored

• bservation

Follow-up time

Modified from fig. 2-1 in M. Szklo, F. Nieto. Epidemiology Beyond the Basics. Maryland: Aspen Publishers; 2000

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4 8 12 16 20 24

1 2 3 4 5 6 7 8 9 10 Individuals Months of follow-up

• 1

17 20 9 24 16 2 13 10 3 Total time under observation

Death Censored

• bservation

Follow-up time

Death = 6

• Pop. at start = 10

Risk estimated from simple method

Risk of dying = 6/10 = 0.6 in 2 years

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INTERPRETATION OF RISK

• The only way to interpret a risk is to know

the length of the time period over which the risk applies.

• This time period may be short or long, but

without identifying it, risk values are not meaningful

• Over a very short time period, the risk of any

particular disease is usually extremely low. What is the probability that a given person will develop a disease in the next 5 minutes?

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ATTACK RATE

An attack rate (AR) is a risk of becoming afflicted with a condition during an epidemic period, applied to a defined population observed for a limited time.

• Attack rate is calculated by:

Number of incident cases during an epidemic period AR = Population at risk at the beginning

• f the epidemic period

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SECONDARY ATTACK RATE

Is the attack rate among susceptible people who come into direct contact with primary cases

• Secondary attack rate is calculated by:

Number of incident cases among contacts of primary cases during the epidemic period = Total number of contacts

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RATE (INCIDENCE DENSITY)

• The occurrence of new cases at a point

in time t, per unit of time, relative to the size of the population at risk at time t

• Denominator for incidence rate is total

person-time for the study period (the sum of person-time contributed to by each individual)

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INCIDENCE RATE ESTIMATION

When data on the timing of events or losses are available from a defined cohort

• We used incidence rate to measure

disease occurrence by dividing number of cases by a measure of time

• Because the instantaneous rate for each

individual cannot be directly calculated, average incidence over a period of time for a population is used

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TIME MEASURE IN INCIDENCE RATE

• This time measure is the summation,

across all individuals, of time experienced by population being followed

• This denominator should include all of the

time that each person was at risk of getting the outcome

• Average incidence rate can be calculated

based on individual data or aggregate FU data

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Rate: the occurrence of an event in a population over time

Number of incident cases of disease

• ccurring in a specified period

I = Amount of person-time experienced by population at risk in the same period

INCIDENCE RATE ESTIMATION BASED ON INDIVIDUAL DATA

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4 8 12 16 20 24

1 2 3 4 5 6 7 8 9 10 Individuals Months of follow-up

• 1

17 20 9 24 16 2 13 10 3 Total time under observation

Death Censored

• bservation

Follow-up time

Total number of event = 6 Total amount of FU time for all individuals is = 115 Rate = 6/115 = 0.052 per person-month = 5.2 per 100 person-month = 0.63 per person-year

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INCIDENCE RATE ESTIMATION BASED ON AGGREGATE DATA

Using the estimated average population as the denominator Number of event Rate = Average population Typically used to estimate mortality based on vital statistics information

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ESTIMATE AVERAGE POPULATION

Assume that the period is not long and population and its demographic composition in the area of interest are stable

• Population at the middle of the period
• Average of the population at the

beginning and at the end of the period

• Subtracting one half of the events and

losses from the initial population

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4 8 12 16 20 24

1 2 3 4 5 6 7 8 9 10 Individuals Months of follow-up

• 1

17 20 9 24 16 2 13 10 3 Total time under observation

Death Censored

• bservation

Follow-up time

n = (10+1)/2 = 5.5 n = 10 - 0.5(6+3) = 5.5 Rate = 6/5.5 = 1.09 per 2 person-year

• r

0.55 per person-year

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4 8 12 16 20 24

1 2 3 4 5 6 7 8 9 10 Individuals Months of follow-up

• 1

17 20 9 24 16 2 13 10 3 Total time under observation

Death Censored

• bservation

Follow-up time

Why rate from individual data = rate from aggregate data?

Rate in 1st 12 months = 3/85 = 0.035 or 0.42 per person-year Rate in 2nd 12 months = 3/30 = 0.1 or 1.2 per person-year

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COMPARISON OF INCIDENCE PROPORTION (RISK) AND INCIDENCE RATE

Property Risk Rate Smallest value Greatest value 1 Infinity Units None 1/time Interpretation Probability Inverse of waiting time

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In Thailand, speed limit for 4-wheel cars

• n an express way is 110 km/hr

What measure? Compute to meters per minute

The unit of time in the denominator is arbitrary and has no implication for any period of time over which the rate is measured or applies

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INTERPRETATION OF RATE

• Incidence rate is a measure of occurrence that

takes the ratio of events to the total time in which the events occur. Unit is the reciprocal of time (time-1)

• 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.

• An incidence rate of 3.57 cases per person-year.

This value can be interpreted as an average waiting time of 0.28 years until the occurrence of the first case. (1/3.57 years = 0.28 years)

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RELATION BETWEEN RISK AND RATE Risk = Incidence Rate X Time

• This simplest formula is an

approximation that works well as long as risk is < 20%

• Assumption: Incidence rate remains

constant over the time period

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Suppose we have a population of 1000 people who experience a mortality rate

• f 12 deaths per 1000 person-year for a

20-year period At the end of 20-year period, how many deaths occur?

• The previous formula predicts that the risk of death over 20

years would be (12/1000)*20 = 0.24

• This calculation neglects that size of population at risk

decreases as deaths occur.

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Year Number alive at start of year Expected Deaths Cumulative Deaths 1 1,000 12 12 2 988 12 24 3 976 12 36 4 964 12 47 5 953 11 59 6 941 11 70 7 930 11 81 8 919 11 92 9 908 11 103 10 897 11 114 11 886 11 124 12 876 11 135 13 865 10 145 14 855 10 156 15 844 10 166 16 834 10 176 17 824 10 186 18 814 10 195 19 805 10 205 20 795 10 215

Number of expected deaths over 20 years among 1000 people experiencing a mortality rate of 12 deaths per 1000 person-year

(Rothman 2002)

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BASIC CONCEPTS OF MEASUREMENT

• Ratio: a ratio expresses the relationship

between two numbers in the form x : y

• Proportion: a proportion is a fraction in

which all elements of the numerator are included in the denominator

• Rate: a rate is an instantaneous change

in one quantity per unit of time

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Number of deaths in a year of children less than 1 year of age = Number of live births in the same year

• Perinatal mortality: 28 wks gestation 1 wk of life
• Neonatal mortality: 1st month of life
• Post neonatal mortality: 1 month 1 year

INFANT MORTALITY RATIO (IMR)

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MORTALITY MEASURES

• As with incidence, the frequency of death can

be expressed as a risk (probability) in individuals or as a rate (hazard) in populations

• 3 types of mortality frequency measures:

– case fatality: death from a specific disease among cases with that disease – total mortality: all deaths in the total population – disease-specific mortality: death from a specific disease in the total population

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CASE FATALITY

• Case fatality risk (CFR) is defined as:

The probability of a case dying from the disease during a given period

• CFR is calculated by:

Number of deaths from a disease during a specified period after disease occurrence CFR = Number of incident cases of the disease during that period

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TOTAL MORTALITY

• Total mortality risk, also called crude

mortality risk (CMR), is calculated by:

Total number of deaths during a specified period CMR = Total number of population at baseline

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SPECIFIC MORTALITY

• Disease-specific mortality risk is calculated

by: Number of deaths from a disease during a specific period = Total number of population at baseline

• Other specific mortality--e.g., age-specific

mortality, sex-specific mortality

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AGE SPECIFIC MORTALITY

• Age-specific mortality rate per year is

calculated by:

Number of deaths among people in a specified age-group during a given year = Average number of population in that age-group of the same year

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EXAMPLE

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• 1

2 3 4 5 6 7

Individuals Total time under

• bservation and

in health (years) 1 2 3 4 5 6 7

7 3 6 1 7 3

Years of follow-up

• healthy period
• disease period

death

7-yr risk of disease (simple estimation) = 3/6 = 0.5 = 50%

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• 1

2 3 4 5 6 7

Individuals Total time under

• bservation and

in health (years) 1 2 3 4 5 6 7

7 3 6 1 7 3

Years of follow-up

• PT = 7+3+6+1+7+3 = 27 person-years

Average incidence rate for 7-year follow-up period =

healthy period

• disease period

death

incident cases/PT = 3/27 = 0.11 / person year

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• 1

2 3 4 5 6 7

Individuals Total time under

• bservation and

in health (years) 1 2 3 4 5 6 7

7 3 6 1 7 3

Years of follow-up

• healthy period
• disease period

death

Case fatality risk in 1 year after disease occurrence = death cases/incident cases = 1/3 = 0.33 = 33%

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• 1

2 3 4 5 6 7

Individuals Total time under

• bservation and

in health (years) 1 2 3 4 5 6 7

7 3 6 1 7 3

Years of follow-up

• healthy period
• disease period

death

7-year total mortality risk = death cases/total pop. = 3/7 = 0.43 = 43%

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Error! Error!

Cumulative Number of Reported Probable Cases Of SARS

From: 1 Nov 20021 To: 2 June 2003, 18:00 GMT+2

• SARS Travel Recommendations Summary Table - 2 June

Country Cumulati ve number

• f case(s)2

Number of new cases since last WHO update2,3 Num ber

• f

death s Num ber recov ered4 Date last probable case reported Date for which cumulative number of cases is current Total 8384 27 770 5402 Notes: Cumulative number of cases includes number of deaths. As SARS is a diagnosis of exclusion, the status of a reported case may change over time. This means that previously reported cases may be discarded after further investigation and follow-up.

Exercise: Compute case fatality ratio, case fatality risk, case fatality rate

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The study of situation and mobilization of human resources for dental health, 2006

• Objective: To study mobilization of

human resources for dental health

• Design: Survey by mailed

questionnaires

• Source population: Registered dentists

graduated in 1975, 1980, 1985, 1990

• Sampling: 50% of source population
• Results: 31% responded (450/1448)

Source: Komet Wichawut, Division of Dental Health Department of Health, 2006

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Proportion of dentists employed in government workforce by work year in service, 2006

40 30 20 10 1.1 1.0 .9 .8 .7 .6 .5

1975 1980 1985 1990 Graduation Year Work Year in Service

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All PIX from Royal Flora Expo 2006