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Bis vivit qui bene vivit
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