Summary of
Measures and Design
Hein Stigum
Presentation, data and programs at:
http://folk.uio.no/heins/
May-16
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Epidemiological measures
• Frequency
– prevalence
– incidence
How much disease?
• Association
– Risk difference
– Risk ratio
– Odds ratio
More disease
among exposed?
• Potential impact
– Attributable fraction
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Important cause?
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2
Time
E,D
E → D
E ← D
No time
prospective
retrospective
Present time
May-16
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3
Cohorts
Closed cohort
start
Open cohort
end
start
Count persons
end
Count person-time
Closed cohort with time varying covariates
start
end
Count person-time
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Mathematical concepts
• Proportion (risk)
a
p
N
• Rate
a
r
t
• Odds
p
Disease
o

1  p notDisease
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Frequency measures
Name
Prevalence
Incidence Proportion
(Cumulative Incidence)
Incidence Rate
Odds
P
Type
Unit
Existing Cases
Population
risk
cases/person
New Cases
Healthy
risk
cases/person
New Cases
Healthy  Time
rate
cases/person-time
odds
cases/person
IP 
IR 
odds 
May-16
Equation
p
Disease

1 - p NotDisease
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!
Disease frequency depicted
100
Existing
Cases
t
a New
Healthy
Healthy*time
0
50
Cases
time
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ASSOCIATION MEASURES
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Association measures
• More disease among exposed?
– Compare frequency among exposed1 and unexposed0
– Difference:
– Ratio:
RD=IP1-IP0
RR=IP1/IP0
Frequency
0=no effect
1=no effect
Association or Effect
Difference
Ratio
Risk
Risk Difference, RD
Risk Ratio, RR
Rate
-
Rate Ratio, RR, IRR, (HRR)
Odds
-
Odds Ratio, OR
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Adjusted measures
Remove the effect of confounders in regression models
Frequency
Association or Effect
Difference
Ratio
Linear-binomial
Risk
RD:
RR:
Rate
-
IRR:
Odds
-
OR:
Log-binomial
Cox, Poisson
Logistic
RD
glm y x1 x2 x3, family(binnomial) link(identity)
RR
glm y x1 x2 x3, family(binomial) link(log)
OR
glm y x1 x2 x3, family(binomial) link(logit)
Cox regression
glm y x1 x2 x3, family(poisson) link(log)
IRR
Linear-binomial
Log-binomial
Logistic
Cox
Poisson
glm=generalized linear models
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Being bullied, 3 models
glm bullied Island Norway Finland Denmark sex age, family(binomial) link(logit)
glm bullied Island Norway Finland Denmark sex age, family(binomial) link(log)
glm bullied Island Norway Finland Denmark sex age, family(binomial) link(identity)
Bullied=17%
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Designs
• Aims
– Disease occurrence
– Exposure-Disease association
• Designs
– Cross-sectional studies
– Cohort studies
– Case-control studies
• Case-Cohort
• Nested Case Control
• Traditional Case Control
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THE 2 BY 2 TABLE
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The 2 by 2 table
Exposure
+
-
Disease
+
100
100
10
100
OR=
1 1 1 1
se(ln( OR )) 
  
a b c d
.01+.01+.1 +.01 =.13
10.0
The lowest number sets the precision
To increase power:
Cohort: balance exposure
Case-Control: balance disease
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COHORT
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Disease frequency depicted
100
Existing
Cases
t
a New
50
Cases
Healthy
Healthy*time
0
=
Risk time
time
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Cohort: Risk, Odds and Rate
Full Cohort, 3 year Risk:
CHD
Exercise
Inactive
+
100
800
1900
7200
2000
8000
10000
Frequency
Risk
Odds
0.05
0.05
0.10
0.11
Association
RD
RR
OR
-0.05 0.50 0.47
0
1
1
Balance?
Full Cohort, Rate:
CHD
Exercise
Inactive
May-16
+
100
800
1900
7200
3 years follow up time
Risk time
Frequency
Rate
0.017
0.035
5 850
22 800
28 650
H.S.
Association
IRR
0.49
1
17
Case-Control studies:
1) Case-Cohort
Inside an existing cohort
2) Nested Case-Control
At the end of an imaginary cohort
3) Traditional Case-Control
1) CASE-COHORT
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Case-Cohort
Existing
cases
t
.
.
.
.
New
cases
a+b
controls
Healthy
N1+N0
Healthy*time
py
start
c+d
end
time
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Case-Cohort, Risk
Full Cohort, Risk:
CHD
Exercise
Inactive
N
+
100 1 900
800 7 200
2 000
8 000
10 000
Frequency
Risk
0.05
0.10
Association
RR
0.50
1
Case-Cohort, Risk:
CHD
Exercise
Inactive
N
+
100 1 900
800 7 200
2 000
8 000
10 000
Controls
f=0.1
200
800
Sample controls from
healthy at start
May-16
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Frequency
Pseudo Risk
0.50
1.00
Association
RR
0.50
1
In practice:
Count: person time
Analyze: Cox model
20
2) NESTED CASE-CONTROL
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Nested Case-Control
Existing
cases
.
case
.
case
controls
Healthy
N1+N0
.
.
t
New
cases
a+b
controls
Healthy*time
py
.
risk set
c+d
.
risk set
start
end
time
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Nested Case-Control, Rate
Full Cohort, Rate:
CHD
Exercise
Inactive
Risk time
+
100 1900
800 7200
5 850
22 800
28 650
Frequency
Rate
0.017
0.035
Association
IRR
0.49
1
Nested Case-Control:
CHD
Exercise
Inactive
+
100
800
Risk time
1900
7200
5 850
22 800
28 650
Controls
f=0.1
585
2 280
Sample controls from
risk time
May-16
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Frequency
Association
Pseudo Rate
IRR
0.171
0.49
0.351
1
Analyze:
Conditional logistic model
23
3) TRADITIONAL CASE CONTROL
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Traditional Case-Control
Existing
cases
Healthy
N1+N0
t
Healthy*time
py
start
.
.
.
.
New
cases
a+b
controls
c+d
end
time
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Traditional Case-Control
Full Cohort, Odds:
CHD
Exercise
Inactive
N
+
100 1 900
800 7 200
2 000
8 000
10 000
Frequency
Odds
0.05
0.11
Association
OR
0.47
1
Trad. Case-Control, Odds:
CHD
Exercise
Inactive
+
100 1 900
800 7 200
Controls
f=0.1
190
720
Frequency
Pseudo Odds
0.53
1.11
Sample controls from
non-disease at end
May-16
Association
OR
0.47
1
Analyze: Logistic model
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Case-Control studies
• Cohort studies
– Measure the exposure experience of the entire
population
• Case-Control studies
– Measure the exposure experience of a sample
of the source population of cases
– Key assumption
• Sample controls independent of exposure
( same sampling fraction)
– Prospective or retrospective
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Summing up
• Measures
Frequency
Association or Effect
Difference Ratio
Risk
Rate
!
Odds
RD
RR
-
IRR
-
OR
• Designs
– Cohort
– Case-Control
full cohort
all cases + sample of healthy
• Case-Cohort
• Nested Case-Control
• Trad. Case-Control
May-16
sample at start
sample during
sample at end
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of follow up
28