Lecture 3:Measuring the Occurrence of

Disease

Reading:Gordis – Chapter 3 Lilienfeld and Stolley – Chapter 4 Chapter 6, pp. 101-105, 109-117

Counting cases

• One’s knowledge of science begins when he can measure what he is speaking about and express it in numbers Lord Kelvin (1824-1907)

• To examine the transmission of disease in human populations, we need to be able to measure the frequency of disease occurrence and of deaths from the disease.

Measures

• How do we express the extent of morbidity and mortality resulting from disease?– Counts– Ratio

• a fraction with no specified relationship– Proportions

• what fraction of the population is affected

– Rates• how fast things are occurring

Measures

• Measures of morbidity– Prevalence: a proportion– Cumulative incidence: a rate– Incidence density: a rate

• Measures of mortality– Mortality rate: a rate– Standardized mortality (SMR)

Defining case

Natural course of disease

Exposure onset symptoms dx outcome

Incubationperiod

SubclinicalStage

ClinicalStage

RecoveryDeath

Chronic disease

Counts

• Prerequisite for epidemiologic investigation• Simplest measure of disease frequency

– Frequency of affected individuals• Useful for planning adequacy of health care

allocation at a particular level • For example:

– Number of West Nile virus cases

Ratio

• A fraction with no specified relationship between numerator and denominator

• Range: 0 to • A/B• Examples

– sex ratio (M:F)

Ratio

• Number of men with syphilis, 19912,412

• Number of women with syphilis. 19912,314

• Ratio of male to females2,412/2,314 = 1.04

(The numerator is not included in the denominator)

Proportion

• Type of ratio• Numerator included in denominator• May be expressed as percentage

Percentage = proportion x 100 %• Range: 0 to 1• A/(A+B)• Example

– Prevalence

Prevalence

• All individuals with a disease at a given point in time

• Dimensionless - should not be described as a rate - may be described as a percent

number of cases (A) todayP =

total population (A+B) today

Prevalence

• Proportion of individuals in a population who have the disease or condition of interest at a specific time period

• Utility– Describe health burden of a population– Status of disease in a population– Estimate the frequency of exposure– Project health care needs of affected

individuals

Types of prevalence

• Point prevalence – proportion of all cases at a specific point in time

• Period prevalence – proportion of all cases during a period of time

Point and period prevalence• Point prevalence

– Do you currently have asthma?• Period prevalence

– Have you had asthma during the last five years?• Every person in the numerator had the

disease at some time during the period specified.

• Period prevalence consists of the point prevalence at the beginning of a specified period of time plus all new cases that occur during that period.

Rate

• A special type of proportion• Unit of time in denominator• A/(A+B) per time interval• Always two components:

– New cases and time

Incidence• Incidence is an important rate…

– It is the proportion of people (at risk) who develop diseased during a specific time period.

• Three key elements:– Only new cases included in numerator– Total population at risk in the denominator– Time element – period over which new

cases developed

• Two main types of Incidence:

– Cumulative Incidence

– Incidence Rate (a.k.a. incidence density)

Cumulative Incidence

• One of the most widely used measures of disease risk.

• Estimate of probability (risk) that an individual will develop disease during a specified period of time

• Cumulative Incidence =

No. of new cases in a given period of time

No. of people at risk during that time

Incidence rate (incidence density)

• Cumulative Incidence gives each individual equal weight, but different people stay in the study for different length- having different contribution.

• Measure of the true rate of disease development

• Incidence rate =No. of new cases in a given period of time

total person-time of observation

Person-time

ID 1/95 1/96 1/97 1/98 1/99 1/00 Total

A 3

B 3

C 5

D 1

E 4

Total years at risk

• = enter the study, X = having disease,

loss to follow-up

16

x

x

5-year (1/95-1/00) Incidence rate = 2/16 = 12.5/100 person-years of observation

x

x

Prevalence vs. incidenceID 1/95 1/96 1/97 1/98 1/99 1/00

A

B

C

D

E

• = enter the study, X = having disease,

loss to follow-up, disease developing

x

x

x

x

1/97-1/00 cumulative incidence cases: A, E1/97-1/00 period prevalence cases: A, D, E1/98 point prevalence: A, D

Relationship between prevalence and incidence

• Incidence is a proxy for “risk”, whereas prevalence is best for assessing disease burden or case load in a geographic area.

• There is a well known relationship between them, namely –

Prevalence = Incidence x Duration of disease

P = I x D

Prevalent cases

+ Incident cases

Whole population at time t

Prevalent cases

Prevalent cases

Prevalent cases

Minus

cures or deaths due to disease

Whole population at time t +1

Examples of P = I x D • If the incidence of diabetes mellitus is 1% per

year and its approximate duration is 5 years, then what is its expected point prevalence?

• Assuming equal incidence of disease, which is more prevalent: pancreatic cancer or brain cancer?

Average duration of pancreatic cancer = 3 months

Average duration of brain cancer = 1.5 years

Measures of mortality

• Annual mortality rate from all causes =

Total no. of death from all causes in 1 year

No.of people in the population at midyear• Case-fatality rate =

No. of individuals dying during a specified period of time after disease onset

No. of individuals with the specified disease

Three common forms of rates

• Crude rates

e.g. crude birth rate, crude death rate

• Specific rates

e.g. sex-specific, age-specific, race-specific

• Adjusted rates

e.g. age-adjusted

Crude rate: exampleSuppose County B recorded 4000 births and 1500 deaths in 1999. Using U.S. Census data, we find that the population size is 200,000.

Crude birth rate =

No. of live births in time interval T

Total population

= 4,000/200,000 = 20 births per 1,000

Crude death rate =

No. of deaths in time interval T

Total population

= 1,500/200,000 = 7.5 deaths per 1,000

Specific Rates for Mortality in Older Adults

Rates for selected leading causes of death among older adults, by sex, and race -- United States, 1996*

Sex Race Cause of death† Total Male Female White BlackHeart disease 1,808 1,983 1,686 1,820 1,937(612,199)Malignant neoplasms 1,131 1,442 915 1,125 1,338(382,988) Cerebrovascular diseases 415 374 443 412 479(140,448)

* MMWR Dec 17, 1999 / 48(SS08);7-25

How do we compare rates across populations?

Crude rates are not helpful because …

Populations differ in their age distributions

Populations differ in their racial distributions

Populations differ in their SES distributions

How do we compare rates across populations?

We compare rates across populations by putting them on an even playing field -

that is, we either standardize one population on another or

we use an outside standard and adjust our populations to that standard.

For our purposes, the most important is age-adjustment

Two types of age-adjustment

Direct Method

Indirect Method (SMR = standard mortality ratio)

Direct method: example

Population A Population B

AGE N Risk Cases N Risk Cases

<20 100 .1 10 500 .1 5021-50 200 .2 40 200 .2 40>50 500 .4 200 100 .4 40 800 250 800 130

CRUDE RISK = 250/800 = 31% 130/800 = 16%

• Crude risk indicates different risks of disease between populations.

• But age-specific rates indicate similar risks.

Direct method: example

Using the total of the two populations as the standard population

Population A Population B

AGE Std. Risk Cases Std. Risk Casespop. pop.

<20 600 .1 60 600 .1 6021-50 400 .2 80 400 .2 80>50 600 .4 240 600 .4 240

1600 380 1600 380

AGE-ADJUSTED RISK = 24% 250/800 = 24%

Direct method: exampleApply risks in population B to population A (using population A as the standard population.

Population A Population B

AGE Std. Risk Cases Std. Risk Casespop. pop.

<20 100 .1 10 100 .1 1021-50 200 .2 40 200 .2 40>50 500 .4 200 500 .4 200

800 250 800 250

AGE-ADJUSTED RISK = 31% 250/800 = 31%

Direct method• What information is needed to calculate age-

adjusted death rate, using the direct method?– Standard population distributed by age– Age-specific death rates in study

populations• The actual value of an age-adjusted rate is

meaningless because it depends on the choice of the standard population.

• It is only meaningful in comparison to other rates which have been adjusted by the same method and the same standard population.

Indirect method

• Apply rates from a standard population

to each age stratum in the study population

to obtain expected number.• This adjusted rate interpreted as:

the rate that would have been experienced by the study population if their rates had been similar to the standard population.

Standardized mortality ratio (SMR)• SMR =

Observed number of cases per timeExpected number of cases per time

• SMR = 0 – indicates observed is not unusual

• SMR > 1.0 – indicates morbidity (or mortality) exceeds

expected• SMR = 2.0 indicates two-fold increase

• SMR < 1.0– indicates morbidity (or mortality) is less

than expected

SMR: example- death in white miners

Est. pop. of white miners

Death rate in general pop.

Expected death

Observed death

Age (1) (2) (3)=(1)X(2) (4)

20-24 74598 12.26 9.14 10

25-29 85077 16.12 13.71 20

30-34 80845 21.54 17.41 22

35-44 148870 33.96 50.55 98

45-54 102649 56.82 58.32 174

55-59 42494 75.23 31.96 112

Total 534533 181.09 436

SMR = 436/181.09 = 2.41

SMR disadvantage

• SMR produces a ratio instead of a rate. It gives relative information but does not describe the mortality in the population.

• SMR depends on the choice of the standard population.