Chapter 2 Epidemiologic Measurements Rates,Ratios,and Proportions Incidence Rates Prevalence Rates Mortality Rates Fatality Rates Infection Rates

Rates,Ratios,and Proportions Ratios A ratio express the relationship

between two numbers in the form x:y or x/y.

For example, the ratio of male to female births in the United States in 1979 was 1,791,000 : 1,703,000 or 1.052:1.

Proportions

A proportion is a specific type of ratio in which the numerator is included in the denominator, and the result value is expressed as a percentage.

For example,the proportion of all births that were male is :

Male births 179×104

= Male+female births (179+170)×104

=51.3%

Rates

A rate is a special form of proportion

that includes specification of time. The rate is the measure that most

clearly expresses probability or risk of disease in a defined population over a specified period of time.

Rates are defined as follows:

Number of events in a specified period ×KPopulation at risk of these events in a specified period

K=100%, 1000‰ …

For example, the death rate from cancer in the United States in 1980 was 186.3 per 100,000 population, the formula:

Deaths from cancer among U.S residents in 1980 100,000 × U.S. population in 1980 100,000

Incidence Rates

Incidence rates measure theprobability that health people will develop a disease during a specified period time. It is the number of new cases of adisease in a population over a period of time.

Formula:

Number of new cases of a disease over a period of time × K Population at risk

Some considerations:1. Time of onset2. Specification of numerator3. Specification of denominator4. Period of observation

1 Time of Onset When we want to know whether a

case is a new case, firstly,we must determine the time of onset. If this case suffered from a disease actually during the defined time, so, he is a new case. On the contrary, he is not a new case,he is just a old case.

But ,how to determine the time of onset?

That means when did he begin to suffer from a disease?

For some diseases, this determination is relatively simple. Such as influenza,

diarrhea….

However, for other conditions,it maybe indefinite,especially for chronic diseases. How can we do for these diseases? We can take the earliest , objectivelyverifiable event as the time of onset.

For example, in cancer, the date of onset is defined by the date of definitivediagnosis, rather than the date when symptoms were first noted. For different illness, we should according to the particular conditions todetermine the time of onset.

2. Specification of Numerator Firstly, we must distinguish patients

and cases. In certain conditions, more than one

event can occur to the same person within a stated time period.

For example, a person may have more than one cold in a year. That’s meanone patient may be more than one cases. If one person has 3 colds in a year, he

is 1 patient, but 3 cases.

So , we can get two rates:Number of people who developed a cold in one-year period people at risk

Number of colds in one-year periodPeople at risk

The meaning of these two rates are different.

The first refer to the probability that any people will develop a cold in one year. It emphasizes the risk for one person to get cold.

The second rate tell us the number of colds to be expected among the group of people in that year.

It emphasizes the number of cold one person may get in a year in a population.

For this kind disease, before calculating the incidence rate,we must determine the aim,then to get the numerator.

3.Specification of DenominatorDenominator is population at risk. Average PopulationWe can get this number through two

ways. (population in 12.31 of last year+this year)/2

midyear population: 7.31 24:00

Population at RiskPopulation at risk refer to people who

have probability of risk to suffer from certain disease.

So, we should get rid of those who have no probability of risk in this population,including those who have the disease now or those who are not susceptible because they have already had it or have previously been immunized.

They are not at risk, they can not become new cases. So we must eliminate them from denominator.

For example,to test the effectiveness of measles vaccine in a group of six-year-old children,incidence rate of measles in this population should be calculated.

The denominator should include only those who are still susceptible.

We should exclude those who have suffered from measles or have immunized at the beginning of the study, because they were not at risk of developing measles.

For large populations,such as a city or state,it is not customary to correct the denominator by removing those not at risk.

For example,tuberculosis cases rates for a county or state are calculated by using midyear population,no need to correct who already have tuberculosis.

4.Period of ObservationIt is usually one year but can be any

length of time.For diseases of low frequency, period

can be several years.It should be marked in the incidence

rate. If no marking ,it usually refer to one year.

Attack Rate

The concept and formula of attack rate are similar to incidence rate.

But ,there are 3 points of attack rate different from incidence rate.

1.Period of time is shorter

This term is usually used to describe infectious disease outbreak,and the study period spans the entire epidemic. So,period of time is usually very short,may be several days,1 week,2 weeks ,no more than 1 month.

2.Population is smallSuch as a family,school,or industrial

group.

3.Denominator must be population at risk

Because the population is small,we must correct who have no possibility to get a disease at the start of the interval.

It can not be replaced by total population.

Prevalence Rates

Definition:Prevalence rate measures the number

of people in a population who have disease at a given time.

Formula:

number of existing cases of a disease at a point in time ×K total population

5 points to be paid attention:

1.Numerator Different from incidence rate.It refers to existing cases,including

new and old cases.No matter when he began ill,if only he

has disease at the study time,he is one of numerator.

2.DenominatorTotal population.Not population at

risk.No matter whether he has suffered

from certain disease, or he is ill now, or he has immunized.

3.A point in timeIn the survey of prevalence rate,time

should be very short,at best no more than 1 day.

But, in fact, surveying a population need a length of time.

So,generally,time should be no more than 1 month,such as 1 week or 2 weeks.(point prevalence)

If more than 1 month,be called period prevalence.

When the term “prevalence”is used without farther specification,it generally refers to “point prevalence”.

4.Influence factorThere are two factors can influence

prevalence:incidence rate(I) and duration(D) of disease.

For chronic disease,incidence rate is usually low.Even if only a few people in a group become ill each year, but the number will mount,so prevalence rate will be large.

For acute disease,incidence rate is usually high, but the duration is short because of their recovery or death,then prevalence will be relatively low.

So, we can use a formula to express the relation of P to both I and D.

P = I×DIf we know two parts of this equation,

we can calculate the third.

5.Difference between P and I I PNumerator new cases new and old casesDenominator population at risk total populationTime of onset a period of time a point in time (1 year) (<1 month)

Example :

··

···

·

· ·

·

1

23

4

5 6

7

8

t1 t2 (Jan 1) (Dec 31)

Incident cases: No 3, 4, 5, 7 (4)Point prevalence: point at t1: No 1, 2, 6, 8 (4) point at t2: No 1, 3, 5 (3) Period prevalence: =point P at t1 + I between t1 and t2 =4+4=8

Mortality Rate

Number of deaths (defined place and time period) ×K Average population (same place and time period)

Crude Death Rate

the rate of deaths ( who died from all cause) from the total population in a period of time.

Numerator: No matter what reason a person died

from, if only he died, he is one of numerator.

Denominator:Average population.

Crude death rate can measure the risk of death of a population, and reflect resident health condition and the level of hygiene in certain place at different period of time.

Crude death rate can not be used to compare between different city.

Why?

Because , the composition of population in different city is different, especially age and sex.

For example, age is a major influencing risk of death.

There are two cities,in one city,elder people are more than younger people.In the other one,younger people are more than elder. And the crude death rates of two cities are similar.

Do you think the risk of death of these two cities are also similar?

No, in fact, the risk of death in the later city is higher than the former.

Because the composition of age are different, we can not compare directly.

Now , how can we do?

We must adjust the composition of age.

Therefore, in evaluating crude death rate,it is necessary to examine age composition to determine whether adjustment is necessary.

Fatality Rate

Fatality rate measures the rate of deaths who died from a disease among the cases suffered from this disease in a period of time.

Formula:

Number of deaths who died from the certain disease

Number of cases with the same disease who are determined

Defined place and time period

It indicates the serious degree of disease, also reflects the level of medical treatment and ability of diagnosis in some place.

It is usually used to acute infectious diseases.

Infection Rate

Formula:

Number of people who are infectious in survey ×KNumber of people who are examined in survey

Infection rate is usually used to covert infectious diseases, such as Hepatitis B, tuberculosis.

Important contents:The formula of every rate.

Exercise 1.in one city,there were 200 new cases

diagnosed as diabetes in 1998.The number of population at the beginning of 1998 is 9500,and there are 10500 at the end of this year.there are 800 patients with diabetes at the beginning of this year and 40 patients died from diabetes during this year.

Please calculate the indexes as below:(1)incidence rate of diabetes in 1998(2)death rate of diabetes in 1998(3)fatality rate of diabetes in 1998(4)prevalence rate of diabetes in January 1st

,1998(5)period prevalence rate in 1998

(1)incidence rate of diabetes in 1998 200/((9500+10500)/2-800)(2)death rate of diabetes in 1998 40 /(9500+10500)/2(3)fatality rate of diabetes in 1998 40/(200+800)(4)prevalence rate of diabetes in January 1st ,1998 800/9500(5)period prevalence rate in 1998 (800+200)/(9500+10500)/2

There are 300 students in a primary school. One year,from January to May,20 students suffered from measles.The other earliest two cases occurred in September of last year. Looking at the figure:

Jau Feb Mar Apr May

Calculate:(1)attack rate of measles during the

epidemic period(2)period prevalence rate of measles during

Jan to May(3)attack rate of every month from Jan to

May

(1)attack rate of measles during the epidemic period 20/(300-2)(2)period prevalence rate of measles during Jan to May Jan: 7/300 Feb: 9/300 March: 8/300 Apr: 5/300 May: 4/300

(3)attack rate of every month from Jan to May Jan: 5/(300-2) Feb: 6/(300-2-5) March: 5/(300-2-5-6) Apr: 2/(300-2-5-6-5) May: 2/(300-2-5-6-2)