B I O S T A T I S T I C S 4th Year Rates, Ratios & Proportions

MEASURES OF DISEASE FREQUENCY

SECTION IV

16/01/2012Fawad - Biostats - Rates, ratios &

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Rate

• Rate is the basic measure of disease occurrence because it is the measure that most clearly expresses probability or risk of disease in a defined population over a specific period of time

• A rate measures the occurrence of some particular event in a population during a given time period

• Categories:• Crude Rates• Specific Rates• Standardized Rates


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Rate….

• In a rate Numerator is part of Denominator

• Rate has 5 components

– Numerator (Number of people, episodes…)

– Denominator (Population at risk, Mid-year population, Person-Time or total events…)

– Time specification.

– Place specification (at a given place..)

– Constant or multiplier…


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Crude Rates

• Actual observed rates– Birth rates

– Death rates

• Also known as unstandardised sates

• Portrays information in a single figure


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Crude Death Rate

• Simplest measure of mortality

• Summarizes the effects of two factors

– Population composition

– Age specific death rates

• Limitation

– No comparability16/01/2012 Fawad - Biostats - Rates, ratios & proportions 5

CDR=

Number of deaths in a specified period

Average total population during that

period (mid year population)

X10n

Specific Rates• Actual observed rates due to

– specific causes

e.g tuberculosis

– Specific groups

• Age

• Gender

– During Specific time periods

• Annual

• Monthly

• Weekly

• Specific Death rates– Most useful single measure of mortality

– Helps us in identifying risk groups

– Permit comparisons between different causes within the same population


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Standardized Rates

• Obtained by direct or indirect methods of standardization eg age and sex standardisedrates

• Standard population

– The population for which the numbers in each age and sex are known


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Direct standardisation

• Combining the two populations in both the age groups to create a standard population

• Then applying the observed age specific rates to the standard population.


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Indirect Standardisation

• Standardised mortality ratio (SMR)– Occupational groups

• Compares the mortality in a study group eg occupationalgroup with the mortality that the occupational group wouldhave had if they had experienced the national mortality rates

• If ratio > 100– Occupation would appear to carry a greater mortality risk than that of

the whole population

• If ratio < 100– Occupation risks is less than the for the whole population


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Ratio

• It expresses a relation in size between two random quantities

• Numerator is not a part of the denominator

• Ratio is the result of dividing one quantity by another

– X : Y or x/ y

• Vital index

• Doctor population ratio

• Child woman ratio16/01/2012

Fawad - Biostats - Rates, ratios & proportions

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Proportion

• Is a ratio which indicates the relation in magnitude of a part to the whole.

• The numerator is always a part of the denominator

• Usually expressed as ……Males %

Female + Male


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Proportion…..

• Proportional Mortality From Specific Causes


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Total deaths from all causes in that year

100Number of deaths from the specific disease in a year

Numerator & Denominator

• Numerator

– Refers to the number of times an event egsickness, birth, death, episodes of sickness hasoccurred in a population, during a specific timeperiod


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Numerator & Denominator….• Denominator

– Related to the population

• Mid year population…….

• Population at risk

– Is restricted solely to those who are capable of having or acquiring the disease or condition in question

– General Fertility Rate (15 – 49 years of age )

• Person Time

– Person Years

– Person weeks

• Person Distance

– Person Miles

• Subgroups of the population– Age, occupation

– Related to total events• IMR

• Case fatality ratio


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Measures of Morbidity

• Incidence

• Prevalence


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Incidence

• It is defined as the number of NEW cases occurring in a defined population during a specific period of time.

• I R=Number of new cases of a specific disease in a given time period

X 1000

• Attack Rate (At risk for only a limited time)

• Secondary attack Rate (Incidence after the primary case)


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Population at risk during that period

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Incidence Rate ….(Incidence calculated for populations that are at risk for only a limited time.Weekly, monthly or further duration of epidemic lasting less than one year.

• Attack Rate

Number of new cases of a specified disease during a specified time interval

Total population at risk during the same interval

3. Secondary Attack RateNumber of new cases after the primary cases during a specified time interval

Total population (minus primary cases) at risk during the same interval

The attack rate reflects the extent of the epidemic &

Secondary Attack rate reflects the infectivity of the cases.

X 100

X 100


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Uses of Incidence Rate

1. It is helpful for research into aetiology, pathogenesis and distribution of the diseases.

2. It is helpful to control the diseases.

3. It is helpful in evaluating the efficacy of preventive and therapeutic measures.


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Prevalence Rate

It is calculated as

Data on the population at risk are not always

available and in many studies total population in the

study area is used as an approximation.

Examples:

1. Point Prevalence

2. Period prevalence

No of people with the disease (old & new) or condition

at a specified time

No of people in the population at risk at that specified time

X 10n

=


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TYPES OF PREVALENCE RATES

• Point prevalenceNumber of all current cases (old and new) of a specified disease

existing at a given point in time

Estimated population at the same point in time

• Period Prevalence

Number of existing cases (old and new) of a specified disease during a given period of time interval

Estimated mid-interval population at risk

X 100

X 100


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Relationship between prevalence and incidence

• P = I x D= incidence x mean duration

• Example (for a stable condition)• Incidence = 10 cases per 1000 population per year• Mean duration of disease = 5 years• Prevalence = 10 x 5 = 50 per 1000 population • Conversely, it is possible to derive incidence and

duration


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Prevalence is increased by following factors

Longer Duration of illness

Prolongation of life of the patient without cure

Increase in new cases

In-migration of cases

In-migration of susceptible people

Out-migration of healthy people

Improved diagnostic facilities

Prevalence Rate


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Prevalence Rate (Contd)

Prevalence will be decreased by the following factors.

– Shorter duration of disease

– High case-fatality rate from the disease

– Decrease in new cases (decrease in the incidence)

– In-migration of healthy people

– Out migration of cases

– Improved cure rate of cases.


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USES OF PREVALENCE

1. Prevalence help to estimate the magnitude of health or disease problems in the community and identified the population at risk. (Burden of Disease)

2. Prevalence rates are helpful for administrative and planning purposes for Example:

a. Human Resource

b. Hospital Beds

c. Rehabilitation facility 16/01/2012

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EXERCISE

Q#1. Of the 75 persons who attended the picnic, 46 subsequently developed gastroenteritis.

a. What is the Attack Rate?b. Is this primary or secondary attack rate?

Q#2. 7 cases of hepatitis A occurred among 70 childrenattending a child day care centre. Each infected childcame from a different family. The total number ofpersons in the 7 affected families was 32. oneincubation period later, 5 family members of the 7infected children also developed hepatitis

a. Calculate the secondary attack rate.


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Answers

1.a Attack Rate = (46/75) X 100 =61.33%

1.b It is a primary attack rate

2. Secondary attack rate = (5/25) X 100= 20%

At risk population = 32 - 7 = 25

Cases= 12- 7 = 5


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Q#1. In a bulk of hundred children out of whom 28 are immunized 2 of them get measles simultaneously. Subsequently 14 get measles. Assume the efficacy of the vaccine to be 100%. What is the secondary attack rate?

1. 5%

2. 10%

3. 20%

4. 21.5%

5. 19.4%


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Answer is

Total children=100

No. of immunized=28

No. of un-immunized=100-28=72

No. of primary cases=2

Secondary attack rate=14/(72-2)=14/70 X100 =20%


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Q#2. A village has total of 100 under-five children. The coverage with measles vaccine in this age group is 60%. Following the occurrence of a measles case in a child after a visit outside, twenty- six children developed measles. The secondary attack rate of measles is:

1. 25%

2. 40%

3. 50%

4. 65%

5. 66%


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Total No. of children=100

No. of immunized =60

No. of un-immunized=40

Primary case=1

Secondary attack rate=26/(40-1)=26/39 X100= 66%

Answer is


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Q#3. In a population of 1000, measles coverage is 60%, one child goes out of station and comes back with measles from whom 20 more children get measles. Secondary attack rate of measles is:

1. 0.65%

2. 5%

3. 6%

4. 6.5%

5. 7%


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Total No. of children=1000

No. of immunized =600

No. of un-immunized=400

Primary case=1

Secondary attack rate=20/(400-1)=20/399 X100= 5%

Answer is


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1. BLACK LINE INDICATES CASES

2. BROKEN LINE INDICATES MIGRATED PEOPLE

3. CONTINUOUS LINE INDICATES HEALTHY PEOPLE

4. + SIGN INDICATES DEATH

Q#1 Calculate the average duration of the disease.

Q#2 Calculate the prevalence rate at the start of year 4.16/01/2012Fawad - Biostats - Rates, ratios &

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Answers

1. The average duration of disease is the total number of years ofdisease divided by the number of cases, i.e. (10/3) = (3.3) years.

2. a. The prevalence rate depends on the point in time at which thestudy takes place; at the start of year (4), for example, it is theratio of the number of people with the disease (2) to the numberof people in the population observed at that time (6), i.e. (33)cases per (100)persons.

b. P=I X D

incidence rate=9.1 cases/100 person years

Duration = 3.3 years

Prevalence = 9.1X 3.3 = 30 cases/ 100 population


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ExerciseQ#1. In a population of 5000 incidence of disease is 100

in 1 year duration of disease studied for 2 years calculate prevalence:

1. 10/1000

2. 40/1000

3. 80/1000

4. 400/1000


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Answer is

2. 40/1000


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Q#2. In a stable situation:

1. Incidence = Prevalence + Duration

2. Prevalence = Incidence X Duration

3. Incidence = Prevalence X Duration

4. Prevalence = Incidence + Duration

5. Prevalence = Duration - Incidence


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Answer is

2. Prevalence = Incidence X Duration


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Q#3. Which of the following measures is used frequently as a denominator to calculate the incidence rate of disease?

1. Number of cases observed

2. Number of new cases observed

3. Number of asymptomatic cases

4. Person-years of observation

5. Persons lost to follow-up


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Answer is

4. Person-years of observation


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Questions# 4-5The results of a study of the incidence of pulmonary tuberculosis in a village in India are given in the table below. All persons in the village are examined during two surveys made 2 years apart, and the number of new cases was used to determine the incidence rate.

Category of Household at First survey

Number of Persons

Number of new cases

With culture positive case 500 10

Without culture positive

case

10,000 10


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Q#4 what is the incidence of new cases per 1000 persons years in households that had a culture positive case during the first survey?

1. 0.02

2. 0.01

3. 1.0

4. 10

5. 20


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Answer is

10 new cases =10 cases/1000 persons years

500 persons x 2 years


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Q#5 what is the incidence of new cases per 1000 persons years in households that did not have a culture positive case during the first survey?

1. 0.001

2. 0.1

3. 0.5

4. 1.0

5. 5.0


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Answer is

10 new cases =0.5 cases/1000 persons years

10,000 persons x 2 years


proportions


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B I O S T A T I S T I C S 4th Year Rates, Ratios & Proportions

Documents

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