# Measures of Disease Frequency

**Objectives**

1.Differentiate rates, proportions and ratios

2.Compute prevalence and incidence rates

3.Define the different mortality rates and

years of potential life lost

4.Compute and differentiate crude, specific

and adjusted rates

5.Determine the uses for adjusted rates

6.Name the two methods of rate

adjustment

**Introduction**

• The most common form of organizing

epidemiologic information is through collecting

information about cases and non non-cases.

• The numbers are usually translated into rates.

• Rates indicate the risk of disease for a population.

• This helps to identify high

•high-risk groups and causal

•factors.

• Data elements collected from cases and non-

cases are called variables (age, sex, race,

weight, height, temperature, blood pressure,

disease, death etc)

**Rates, Ratios and Proportions**

• Variables or data elements are summarized to

provide number of cases, proportions, rates and

ratios = frequency

• In epidemiology many variables have only two

possible categories

• these are called dichotomous variables

• (e.g. disease or no disease; alive or dead).

• The frequency measures we use with

dichotomous variables are ratios, proportions

and rates.

• Ratio= the values of x and y may be completely

independent, or x may be included in y. For

example, the sex of children attending well baby

clinic (male to female).

• Proportion= x is included in y (female/all *10^{n})

i.e. Percent of females

• Rate= is a proportion with time dimension. It measures

the occurrence of an event in a population over time.

• Rate= number of cases or events occurring during a

given time period/ population at risk during the same

time period*10^{n}

• Rate

is the measure of risk for disease with a time

components

• The persons in the denominator must reflect the

population from which the cases in the numerator

arose

• The counts in the numerator and denominator should

cover the same time period

• The person in the denominator must be at risk for the

event

• Once numerator is divided by denominator– the

quotient is multiplied by a factor to make it easier to

understand

**Incidence Rate**

• Incidence rate is the most common way of

measuring and comparing the frequency of

disease in populations.

•
Definition: incidence refers to the occurrence of

new cases in a population over a period of time.

• It estimates the risk of developing a disease in a

specified population during a specified period of

time.

**Cumulative Incidence**

There are two types of Incidence
rates:

1.Cumulative Incidence (CI):

is the proportion of people who become diseased during a specified

period of time.

• CI provides an estimate of the probability, or risk that

an individual will develop a disease during a specified

period of time.

• The time period must be clearly specified when

reporting the C

• The CI assumes

• That the entire population is at risk at

the beginning of the study period

• That the populations has been followed

for the specified time interval

• In 2000:

• 733,151 new cases of gonorrhea were

reported among the United States civilian

population.

• The mid

mid-year civilian population was

estimated to be 246,552,000.

CI=[733,151/246,552,000] x 1,000=2.97 per

1000 population.

Incidence Density

2. Incidence density (ID)= measure of risk in a changing

population where people are free of disease at start and

observed for onset of disease for different time periods

• Shows how rapidly cases develop

• In presenting an incidence density, it is essential to

specify the relevant time units – i.e. number of cases

per person person-day, person person-month, person person-year, etc.

•
Person-time is the number of persons at risk for disease

multiplied by the length of time they are observed for

onset of disease

Person years = # of person * # of years followed up

Example: In a cohort study, 600 contraceptive users were

followed over the course of three years as follows:

• 100 women for 1year

• 200 women for 2 years

• 300 women for 3 years

The number of person person-years of observation in this study is:

• 100 women x 1 = 100
person-years

• 200 women x 2 = 400
person-years

• 300 women x 3 = 900
person-years

Total= 1400 person person-years

• Of these 600 people

• 10 developed thromboembolism .

• The incidence rate of thromboembolism is

calculated as:

• 10/1400 = 7.1 per 1000 person years of follow

up.

**Prevalence Rate
**

• Is the proportion of persons in a population who

have a particular disease or attribute at a

specified point in time or over a specified period

of time

• Gives an indication of the “burden burden” of disease in

a population - numerator is existing cases

• Usually expressed as a percentage i.e.,

multiplier = 100 and if the disease is rare it is

expressed as 10

^{n}

There are two types of prevalence:

1.Point prevalence: is the presence of a disease at a

single point in time (snap shot).

2. Period Prevalence:

the presence of a disease at a

particular time interval.

• Prevalence usually refers to point prevalence

**RELATIONSHIP BETWEEN PREVALENCE AND**

INCIDENCE

INCIDENCE

• Incidence– new cases

• Prevalence– all cases (existing and new)

• Prevalence and Incidence are related by average

duration (D) of disease in a stable population

• If a disease lasts a long time, there will be higher

prevalence in the population

• If incidence is low but those affected have the condition

for long = the prevalence will be high relative to the

incidence

• If disease is short short-lived, there will

be low prevalence in the population

• If incidence is high but the disease duration is short then

the prevalence will be low relative to the incidence

• Example: a follow up study of the Framingham

data showed males and females had same IR

for heart disease but females had a higher

prevalence of disease – WHY?

• PR = What proportion of the population has this

condition?

• IR = At what rate do new cases arise over time

in the population?

• Example: in Richmond City, 2006, there were a

total of 5,000 hepatitis B cases of which 1,000

were newly diagnosed.

• The total population of Richmond City is

200,000.

• Prevalence in 2006: 5,000/200,000*1000=25

per 1,000 population

• Incidence in 2006: 1,000/200,000* 1000=5

per 1,000 population

**Uses of Prevalence and Incidence
Measures**

• Prevalence is mostly used for planning,

evaluating

• Incidence is used to identify causal

relationships

**Attack Rate**

1)Attack Rate: Is a variant of an incidence rate,

applied to a narrowly defined population

observed for a limited time, such as during an

epidemic or outbreak of a disease. It is usually

expressed in %.

A measure of probability of risk.

Attack Rates and Picnics |

Example: Of 75 persons who attended a church picnic, 46

subsequently developed gastroenteritis. The attack rate

of gastroenteritis is:

• The risk of developing gastroenteritis in this population

was 61%.

Secondary Attack Rate

2) Secondary attack rate: is a measure of

the frequency of new cases of a disease

among the contacts of known cases.

• Example:

• Seven
cases of hepatitis A occurred among 70 elderly

patients in an adult day care center.

• The total number of persons in the 7 affected families

were 32 .

• In several weeks,5 family members of the 7 infected

patients also developed hepatitis A.

• Calculate the attack rate and the secondary

attack rate among family contacts of those

cases.

• Cases of hepatitis A among the elderly = 7

• Number of elderly in the adult care center = 70

Attack rate = 7/70 x 100 = 10%

• Cases of hepatitis A among family contacts = 5

Number of persons at risk in the families (total number of

family member with elderly already infected) = 32-7 = 25

• Secondary attack rate = 5/25 x 100 = 20%

**Mortality Measures
**

• Crude Mortality Rate: is a measure of the frequency of

occurrence of death in a defined population during a

specified interval i.e. for a defined population over a

specified period of time

Crude x10n

Example: In 2001, there were 12,000 deaths from all

causes among 2 million population of Atlanta, Georgia.

Crude deaths per 1000 population per year

•Case Fatality Rate: is the proportion of persons with a

particular condition (cases) that die from the condition. It

is usually expressed in percent.

• Case Fatality Rate:

Example: in Richmond city, there were 500 cases of colon

cancer, of whom five died within a year after their initial

diagnosis. The case fatality rate for colon cancer in

Richmond city was:

5/500 x 100 = 1%

• Age-specific MR = is a mortality rate

limited to a particular age group.

• Infant Mortality
Rate: is one of the most commonly

used measures for comparing health service among

nations.

I

Example: Denver, Colorado, with a population of 2.37

million, reported a total of 270 infant deaths and 30,000

live births in 1981.

• IMR = 270/30,000 x 1000 = 9 infant deaths per 1000 live

births per year.

• Neonatal Mortality Rate: is defined as the

period from birth up to 28 days.

E.g. Memphis, Tennessee, with a population of 1.37

million, reported a total number of 150 neonatal deaths

and 30,000 live births in 1982.

NMR = 150/30,000 x 1000 = 5

Five neonatal deaths per 1000 live births per year.

• Post neonatal mortality rate: The post neonatal period

is defined as the period from 28 days of age up to but

not including 1 year of age.

• Example: In Oakland California there were 2 million

births in 1995, of which 10,000 died before they reach

their first birth day. 7,500 of the infant died within the

first 28 days. Calculate the IMR, NMR and PNMR

• Live births | 2,000,000 |

• Infant deaths | 10,000 |

• Neonates | 7,500 |

• Post Post-neonates |
2,500 = 10,000 10,000-7,500 |

IMR = 10,000/2,000,000 x 1,000 = 5 per 1,000 live births

NMR = 7,500/2,000,000 x 1000 = 4 per 1,000 live births

PNMR = 2,500/2,000,000 x 1000 = 1 per 1,000 live births

• Years of Potential Life Lost (YPLL)= measure of

premature death

• Premature death = when a death occurs earlier than

expected if disease were not present.

• YPLL == Years lost before age 75 years or set age

• Difference between age 75 years and the age of

death is calculated for each decedent in population

and summed

**Adjusted Rates
**

• A statistically manipulated rate controlling for the factor

of interest (age, race, etc)

• Specific rates give more valuable information when

comparing rates between sub sub-groups

However, specific rates do not provide accurate comparison

with other population.

• Adjusted rates provide a summary statistic that

corrects for differences in age or other factors in

populations – making comparisons possible between

different populations

• The computational process for adjusted rate is called

“standardization standardization” or “adjustment adjustment”

• Advantages

• Provides summary statement

• Differences in groups removed to permit unbiased

comparisons

• Disadvantages

• Statistically manipulated rates (fictional)

• Absolute magnitude dependent on choice of reference

population

• Two methods of adjustment:

• 1) Direct

• 2) Indirect

• Direct Method is commonly utilized in

practice

• But is this necessarily the most accurate?

**Adjusted Mortality Rates
**

Example:

– You are a primary care practitioner in a suburb of a

medium medium-sized city.

– Some of your patients lately have been older men

with cardiac chest pain, and after appropriate testing

you have decided that several of them should

undergo coronary artery bypass surgery.

– There are 2 groups of surgeons and you want to send

your patients to the group with lowest mortality rate.

**Direct Comparison of Mortality Rate**

Age Group | Clinic A | Clinic B | ||||||

Surgeries | Operative Deaths | Operative Mortality | Surgeries | Operative Deaths | Operative Mortality | |||

45-54 | 500 | 6 | 1.2% | 300 | 3 | 1% | ||

55-64 | 300 | 15 | 5% | 300 | 12 | 4% | ||

65-74 | 200 | 20 | 10% | 400 | 36 | 9% | ||

Total 45-74 | 1000 | 41 | 4.1% | 1000 | 51 | 5.1% |

• Step 1:Calculate age age-specific rates in the populations

you want to compare

Age Group | Clinic A | Clinic B | ||||||

Surgeries | Operative Deaths | Operative Mortality | Surgeries | Operative Deaths | Operative Mortality | |||

45-54 | 500 | 6 | 1.2% | 300 | 3 | 1% | ||

55-64 | 300 | 15 | 5% | 300 | 12 | 4% | ||

65-74 | 200 | 20 | 10% | 400 | 36 | 9% | ||

Total 45-74 | 1000 | 41 | 4.1% | 1000 | 51 | 5.1% |

• Step 2: Choose a reference population whose

: age composition is known.

• US 2000 standard population

• 45-54 years 134,834

• 55-64 years 87,247

• 65-74 years 66,037

• Step 3:Calculate Expected deaths in

reference population if the Clinic A A- or

Clinic B B-specific rates were the true rates

Age Group | No. in ref pop (1) | Operative Mortality | Expected # of deaths in ref pop using rates from |
||||

Clinic A (2) |
Clinic B (3) |
Clinic A (1)x(2) |
Clinic B (1)x(3) |
||||

45-54 | 134,834 | 1.20% | 1.00% | 1618.0 | 1348.3 | ||

55-64 | 87,247 | 5.00% | 4.00% | ||||

65-74 | 66,037 | 10.00% | 9.00% | ||||

Total | 288,118 | 12,584.1 |

• Step 4. Add up the total number of deaths expected in

. the reference population under each clinic's set of rates.

Age Group | No. in ref pop (1) | Operative Mortality | Expected # of deaths in ref pop using rates from |
||||

Clinic A (2) |
Clinic B (3) |
Clinic A (1)x(2) |
Clinic B (1)x(3) |
||||

45-54 | 134,834 | 1.20% | 1.00% | 1618.0 | 1348.3 | ||

55-64 | 87,247 | 5.00% | 4.00% | 4362.35 | 3489.88 | ||

65-74 | 66,037 | 10.00% | 9.00% | 6603.70 | 5943.33 | ||

Total | 288,118 | 12,584.1 | 10,781.5 |

• Step 5. Calculate the age . age-adjusted operative

mortality rate for each study group by dividing

the sum of expected deaths by the total size of

the reference population:

• Clinic A:12,584.1 / 288,118 * 100 =

• 4.37 / 100 surgeries

• Clinic B:10,781.5 / 288,118 * 100 =

• 3.74 / 100 surgeries

• Which clinic would you recommend

now?