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Epidemiology

What is Epidemiology?

Epidemiology is the study of how a disease is distributed in a population and of the factors that influence or determine this

distribution.

http://www.usuhs.mil/2005/Epid_Notes_1.htm

Epidemiology, literally translated from Greek, means "the study of [a] people".http://www.aea.asn.au/home_whatisepidemiology.htm

Objectives of Epidemiology

- determine the extent of disease in a population- study the natural history and prognosis of a

disease - characterise the aetiology of a disease- identify risk factors or protective factors

- evaluate preventive and therapeutic measures - provide the foundation for developing public

policy and regulatory decisions

Historical Examples

- smallpox survivors were immune to the disease- variolation, the administration of material from infected people, was common (dangerous) practice

- cowpox (mild form of smallpox) was found inmilkmaids, who never contracted smallpox

- pus from cowpox-infected patient was used toperform the first successful smallpox vaccination

Edward Jenner(1749-1823)

- miasmatic theory of cholera: cloud of disease close to earth, with lower altitudes more susceptible than higher ones

- house to house survey of where cholera deaths obtained their water

- proof of contagious nature and transmission pathwaysJohn Snow

(1813-1858)

Morbidity MeasuresPrevalence (π)

Point Prevalence

proportion of affected individuals present in a population at a specific time pointmathematically: probability πt that an individual randomly drawn at a specific time point is affected

Period Prevalence

proportion of affected individuals present in a population during a specific time periodmathematically: probability πd that a randomly drawn individual is, or has been, affected during a specific time period

period prevalence point prevalence

time

30 years

Period and Point Prevalence

43.07

3ˆt ==π57.0

7

4ˆd ==π

Confidence Interval

The number X of diseased individuals in a sample of size n follows a Bin(n,π) distribution.

n

)ˆ1(ˆtˆ:KI 1n,2/1

π−⋅π⋅±π −α−

yields a confidence interval for the estimate of π.

57.035

20ˆd ==π

17.057.035

43.057.004.257.0 ±=⋅⋅±95%KI:

Example: 20 diseased among 35 probands

Morbidity MeasuresIncidence Proportion (γ), "Risk"

A: number of new cases in a population at risk that occur during a specified time period

N: number of individuals at risk during a specified time period

mathematically: probability (or risk) that an unaffected, randomly chosen individual gets affected during the time period of interest

N

A=γ

time

T: 30 years

Incidence Proportion

333.09

3ˆ ==γ

Morbidity MeasuresIncidence Rate (γ), "Risk"

N: number of individuals at risk during time periodA: number of new cases arising during time periodTi: time units spent under risk by the ith individual

mathematically: (time) rate at which unaffected, randomly chosen individuals get affected

∑ =

=γN

1i iT

A

time

T: 30 years

321

309

224

1730

027

Incidence Rate

incidents per person-year018.0163

3ˆ ==γ

Prevalence and IncidenceD: disease duration

expected prevalence pool inflow

expected prevalence pool outflow

t)1( ∆⋅π−⋅γ t)D(E

1 ∆⋅π⋅

1-ππ

)D(E1

prevalence pool

γγγγ

Prevalence and Incidence

Through causing longer disease duration, improved medical care may increase the disease burden

to society in the form of an increased prevalence.

In a stable, closed population(i.e. without migration into, or out of, the population)

)D(E1

⋅γ=π−

π

t)D(E

1t)1( ∆⋅π⋅=∆⋅π−⋅γ

so that

Typhus

Pediculus humanus Rickettsia prowazekii

In the German population, the incidence rate of typhus is 2×10-6 per year. The average disease duration is approximately one month.

76 1067.112

1102)D(E

1−− ×=⋅×=⋅γ=

π−π

In the German population, approximately 81.5×106⋅1.67×10-7=14 cases of typhus are to be expected at any point in time.

- ambiguous or incorrect diagnoses, latency- identification of highly selected cases from

hospital admissions (severity, policy)- bad recording of cases (incomplete, missing)- variable diagnostic standards (temporal,

regional)- ambiguous definition of population base

(medical, ethnic, social)- temporal changes of disease patterns (spatial,

phenotypical)

Prevalence and IncidenceProblems

Effect Measures

Let a population be stratified into two strata (e.g. "exposed", "not exposed") with corresponding

incidence rates or proportions ("risks") γe and γn during the observational period.

Relative Risk (ρ)

is called the 'relative risk' under exposure.

ρ>1: "risk factor", ρ<1: "protective"

n

e

γγ=ρ

time

exp

ose

dnot

exp

ose

d

30 years

Relative Risk (ρ)

50.22.0

5.0

10/2

10/5ˆ ===ρ

Experimental (Interventional)

Types of Epidemiological Studies

Clinical Trials

- evaluation of therapeutic measures (e.g. drugs)

Field Trials

- performed on single diseased individuals in a clinical setting

- evaluation of preventive measures (e.g. vaccination)- performed on single non-diseased individuals in the field

Community Interventions

- evaluation of preventive measures (e.g. water treatment)- performed on groups of non-diseased individuals

Assignment of Exposure by Investigator

time

exp

ose

dnot

exp

ose

d

Archetypal Experimental Study

Types of Epidemiological Studies

Cohort Studies

Case-Control Studies

- performed prospectively on non-diseased individuals of known exposure status, disease incidences are recorded

Cross-Sectional (Prevalence) Studies

- performed retrospectively on individuals of known diseasestatus, exposure status is recorded

- performed retrospectively on the whole population or on a representative sample, disease and exposure is recorded

Non-Experimental (Observational)

Assignment of Exposure by Nature

time

Archetypal Observational Study

To identify the common factors or characteristics that contribute to cardiovascular disease (CVD) by following its development over a long period of time in a large group of participants who had not yet developed overt symptoms of CVD or suffered a heart attack or stroke.

In 1948, 5209 men and women between the ages of 30 and 62 were recruited from Framingham, Massachusetts (representing 2/3 of the adult population). In 1971, another sample of 5135 men and women was established, comprising the offspring of the original cohort and their spouses.

Objective

Design

The Framingham Study

Careful monitoring of the Framingham Study population has led to the identification of the major CVD risk factors- high blood pressure- high blood cholesterol- smoking- obesity- diabetes- physical inactivity and critical information upon related factors such as age, gender, and psychosocial issues.

The Framingham study has produced approximately 3500 articles in leading medical journals.

The Framingham Study

Results

Risk and Odds

"The risk of catching a viral flue this winter is 0.20."one affected among five at risk

"The odds of catching a viral flue this winter is 0.25."one affected for every four non-affected

Risk1

RiskOdds

−=

Horse Race Betting

"Old Mule"

payoffodds

1:5 1:10 1:50 1:200

5-110-150-1

200-1

fair poor poor poorgood fair poor poorgood good fair poorgood good good fair

Effect Measures

If risks γe and γn are "sufficiently small" for the chosen time unit, i.e. of the order a few percent, then

Odds Ratio (OR)

)1/(

)1/(OR

nn

ee

γ−γγ−γ=

ρ=γγ≈

γ−γγ−γ=

n

e

nn

ee

)1/(

)1/(OR

time

exp

ose

dnot

exp

ose

d

Odds Ratio (OR)

time unit: 10 years

00.210/1

10/2ˆ ==ρ25.2

9/18/2

OR ==

10 years

Odds Ratio (OR)

time

exp

ose

dnot

exp

ose

d

time unit: 30 years

00.48/2

5/5OR == 50.2

10/2

10/5ˆ ==ρ

30 years

Which Effect Measure ?

exposed

affectednot

affected

a b

not exposed c d

total a+c b+d

total

a+b

c+d

n

Cohort Studies (Relative Risk)

ρ=γγ=

++

ˆˆ

ˆ

)dc/(c

)ba/(a

n

e

e

e

N

A

ba

a ≈+ n

n

N

A

dc

c ≈+

and

Which Effect Measure ?Case-Control Studies (Odds Ratio)

exposed

affectednot

affected

a b

not exposed c d

total a+c b+d

total

a+b

c+d

n

n

e

A

A

c

a ≈nn

ee

AN

AN

d

b

−−≈and

OR)ˆ1/(ˆ

)ˆ1/(ˆ...

)AN/()AN(

A/A

d/b

c/a

nn

ee

nnee

ne =γ−γγ−γ==

−−≈

Effect MeasuresConfidence Intervals

)dc/(c

)ba/(aˆ

++=ρ

d/b

c/aOR =

dc

1

c

1

ba

1

a

1ˆ )ln( +

−++

−=σ ρd

1

c

1

b

1

a

1ˆ )ORln( +++=σ

confidence intervals for the natural logarithms

)ln(2/1 ˆz)ˆln( ρα− σ⋅±ρ )ORln(2/1 ˆz)ORln( σ⋅± α−

Cohort Study

exposed

affectednot

affected

10 140

not exposed 5 145

total 15 285

total

150

150

300

00.2150/5

150/10

)dc/(c

)ba/(aˆ ==

++=ρ 07.2

145/140

5/10

d/b

c/aOR ===

95% CI: 0.69 - 6.2195% CI: 0.70 - 5.71

exposed

affectednot

affected

100 140

not exposed 50 145

total 150 285

total

240

195

435

Case-Control Study

07.2145/140

50/100

d/b

c/aOR ===

95% CI: 1.37 - 3.19

63.1195/50

240/100

)dc/(c

)ba/(aˆ ==

++=ρ

An odds ratio provides a good approximation of the relative risk for a disease if the incidence rate (over the chosen time unit) is small.

Which Effect Measure ?

Case-control studies do not normally allow the estimation of relative risks.

Attributable Risk

Q: Which incidences are due to the exposure?

A: This question cannot be answered on the basis of epidemiological data alone.

E.g. many smokers will get lung cancer from causes other than tobacco smoke

(e.g. asbestos, radiation, chance).

Aetiological Fraction

Attributable Risk

Q: What proportion of the risk under exposure is due to the exposure?

Rate Fraction

assesses the excess risk in an individual.

ρ−ρ=

γγ−γ= 1

ARe

ne

γe,males = 0.50γn,males = 0.20

γe,females = 0.08γn,females = 0.02

Attributable Risk (AR)

Although the disease risk of exposed males is much higher than the disease risk of exposed females, the AR is higher in females because their relative risk is higher.

60.05.2

0.15.2ARmales =−= 75.0

0.4

0.10.4AR females =−=

5.220.0/50.0males ==ρ 0.402.0/08.0females ==ρ

Population Attributable Risk

Q: What proportion of the incidences in the population is attributable to the exposure?

γ: general incidence, fe: exposure frequency

assesses the excess morbidity in a population.

Excess Fraction

1)1(f

)1(fPAR

e

en

+−ρ⋅−ρ⋅=

γγ−γ=

Population Attributable Risk (PAR)

γe,males = 0.50γn,males = 0.20

γe,females = 0.08γn,females = 0.02

23.00.15.12.0

5.12.0PARmales =

+⋅⋅= 23.0

0.10.31.0

0.31.0PAR females =

+⋅⋅=

Although the AR is higher in females than in males, the PAR's are the same because males are exposed more

frequently than females.

5.220.0/50.0males ==ρ 0.402.0/08.0females ==ρ

fe,males = 0.20 fe,females = 0.10

Summary

- Epidemiology is the science that studies the distribution ofdiseases and of their causal factors in populations.

- The major morbidity measures used in epidemiology are the prevalence, i.e. the disease frequency, and the incidence, i.e. the occurrence rate of new cases.

- Epidemiological studies can be either interventional or observational. In terms of their timing, studies can be of prospective or retrospective design.

- The effect of an exposure upon disease risk can be measured by the relative risk or the odds ratio.

- (Observational, retrospective) case-control studies do not allow the estimation of relative risks, only of odds ratios.

Let a population be stratified into k strata (e.g. age, gender) with incidence rates γ1,...,γk.

Let s1,...,sk be "standard" person-times, e.g. in a reference population.

is called the 'standardised incidence rate'.

∑

∑

=

= γ⋅=γ

k

1i i

i

k

1i iS

s

s

Standardisation

Appendix

Appendix: Sex-Specific Incidence Rates

population

100 y21

femalesa Σti

0.02 200 y8

malesa Σti

0.04

fγ̂ mγ̂

500 y52 0.01 100 y6 0.06

033.0300/101̂ ==γ

018.0600/11ˆ2 ==γ

y-1

y-1

Appendix: Sex-Specific Incidence Rates

population

100 y21

femalesa Σti

0.02 200 y8

malesa Σti

0.04

sfemale=150 smale=100

fγ̂ mγ̂

500 y52 0.01 100 y6 0.06

033.0300/10ˆ1 ==γ 018.0600/11ˆ2 ==γ

028.0250/)04.010002.0150(ˆ S,1 =⋅+⋅=γ030.0250/)06.010001.0150(ˆ S,2 =⋅+⋅=γ

y-1

y-1

y-1y-1

proportion of males

0.0 0.2 0.4 0.6 0.8 1.0

rela

tive

ris

k

2.0

2.5

3.0

3.5

4.0

4.5

5.0

γe,males = 0.50

γn,males = 0.20

γe,females = 0.08

γn,females = 0.02

females

males

Appendix: Collapsing of Relative Risks

overall

proportion of males

0.0 0.2 0.4 0.6 0.8 1.0

odds

ratio

2.0

2.5

3.0

3.5

4.0

4.5

5.0

females

males

Appendix: Collapsing of Odds Ratios

γe,males = 0.50

γn,males = 0.20

γe,females = 0.08

γn,females = 0.02

overall