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Analytical epidemiology
Disease frequency
Study design: cohorts & case control
Choice of a reference group
Biases
Impact
Causal inference
Stratification
- Effect modification
- Confounding
Matching
Significance testing
Multivariable analysis
Alain Moren, 2006
Exposure
Outcome
Third variable
Two main complications
(1) Effect modifier
- useful information
(2) Confounding factor
- bias
To analyse effect modification
To eliminate confounding
Solution =
stratification
stratified analysis
Create strata
according to categories
inside the range of values
taken by third variable
Effect modifier
Variation in the magnitude
of measure of effect
across levels of a third variable.
Effect modification is not a bias but
useful information
Happens when RR or OR
is different between strata
(subgroups of population)
Effect modifier
To identify a subgroup
with a lower or higher risk
To target public health action
To study interaction
between risk factors
Vaccine efficacy
AR NV - AR V
VE = ----------------------------AR NV
VE =
1 - RR
Vaccine efficacy
Pop.
Cases
Cases
per 1000
RR
V
301 545
150
0.49
0.28
NV
298 655
515
1.72
Ref.
Total
600 200
665
1.11
Status
VE
= 1 - RR
VE
=
72%
= 1 - 0.28
Vaccine efficacy by age group
Age
Status
Pop.
Cases
Cases
/1000
RR
VE
<1y
V
NV
35 625
24 375
38
30
1.07
1.23
0.87
13%
1-4y
V
NV
44 220
46780
34
86
0.77
1.84
0.42
58%
5-9y
V
NV
78 200
75 000
50
250
0.64
3.33
0.19
81%
10-24y
V
NV
83 400
82 600
18
120
0.22
1.45
0.15
85%
> 24y
V
NV
60 100
69 900
10
29
0.17
0.41
0.40
60%
Effect modification
Different effects (RR) in different strata
(age groups)
VE is modified by age
Test for homogeneity among strata
(Woolf test)
Oral contraceptives (OC) and
myocardial infarction (MI)
Case-control study, unstratified data
OC
MI
Controls
Yes
No
693
307
320
680
Total
1000
1000
OR
4.8
Ref.
Smokers
OC
MI
Yes
No
Total
Controls
517
183
160
340
1000
1000
MI
Controls
OR
6.0
Ref.
Nonsmokers
OC
OR
Yes
176
160
3.0
No
124
340
Ref.
1000
1000
Total
Physical activity and MI
Physical activity
MI
Controls
OR, 95%CI
 2500 kcal/d
190
266
0.67, 0.6-0.9
< 2500 kcal/d
176
157
Ref.
Men
Physical activity
MI
Controls
OR, 95%CI
2500 kcal/d
141
208
0.53, 0.4-0.7
< 2500 kcal/d
144
112
Ref.
Physical activity
MI
Controls
OR, 95%CI
2500 kcal/d
49
56
1.2, 0.7-2.2
< 2500 kcal/d
32
45
Ref.
Women
Effect function
Effect (OR or RR) is a function of the effect modifier
Relative risk (RR) of dying from coronary heart disease
for smoking physicians, by age groups, England & Wales,
RR
6
*
5
4
3
*
2
*
1
10
20
30
40
50
60
*
70
*
80
Age
Doll et Hill, 1966
Any statistical test to help us?
Breslow-Day
Woolf test
Test for trends: Chi square
Confounding
Distortion of measure of effect
because of a third factor
Should be prevented
Needs to be controlled for
Simpson’s paradox
Hats
Fit
Do not fit
% fit
Red
17
3
85%
Blue
9
1
90%
Second table
Hats
Fit
Do not fit
% fit
Red
1
9
10%
Blue
3
17
15%
Day 2, one table only
Hats
Fit
Do not fit
% fit
Red
18
12
60%
Blue
12
18
40%
Cases of Down syndroms by birth order
Cases per 100 000
live births
180
160
140
120
100
80
60
40
20
0
1
2
3
Birth order
4
5
Cases of Down Syndrom by age groups
Cases per 1000
900
100000 live 800
births
700
600
500
400
300
200
100
0
< 20
20-24
25-29
30-34
Age groups
35-39
40+
Birth
order
Down
syndrom
Age or
mother
Cases of Down syndrom
by birth order and mother's age
Cases per 100000
1000
900
800
700
600
500
400
300
200
100
0
1
2
3
Birth order
4
5
<2
0
30
-34
25
29
20
-24
40
+
35
-39
e
Ag
ps
u
o
gr
Confounding
To be a confounding factor, 2 conditions must be met:
Exposure
Outcome
Third variable
Be associated with exposure
- without being the consequence of exposure
Be associated with outcome
- independently of exposure
To identify confounding
Compare crude measure of effect
(RR or OR)
to
adjusted (weighted) measure of effect
(Mantel Haenszel RR or OR)
Are Mercedes more dangerous than Porsches?
Type
Total
Accidents
AR %
RR
Porsche
1 000
300
30
1.5
Mercedes
1 000
200
20
Ref.
Total
2 000
500
25
95% CI = 1.3 - 1.8
< 25 years
Type
Total
Accidents
AR %
Porsche
550
250
45.5
Mercedes
300
120
40.0
RR, 95%
CI
1.14
(0.9-1.3)
25 years
Type
Total
Accidents
AR %
Porsche
450
50
11.1
Mercedes
700
90
11.4
Crude RR = 1.5
Adjusted RR = 1.1 (0.94 - 1.27)
RR, 95%
CI
0.97
(0.7-1.4)
Car type
Accidents
Confounding factor:
Age of driver
Age
Porsches
Mercedes
< 25 years
550
300 (30%)
>= 25 years
450
(55%)
700
Chi2 = 127.9
Age
< 25 years
Accidents
370 (44%)
No accidents
480
>= 25 years
130 (11%)
1020
Chi2 = 270.7
Exposure
Outcome
Hypercholesterolaemia
Myocardial infarction
Third factor
Atheroma
Any factor which is a necessary step in
the causal chain is not a confounder
Salt
Myocardial
infarction
Hypertension
Any statistical test to help us?
When is ORMH different from crude OR ?
10 - 20 %
How to prevent/control confounding?
Prevention
– Restriction to one stratum
– Matching
Control
– Stratified analysis
– Multivariable analysis
Mantel-Haenszel summary measure
Adjusted or weighted RR or OR
Advantages of MH
• Zeroes allowed
k
SUM (ai di / ni)
i=1
OR MH = ------------------k
SUM (bi cci / ni)
i=1
k
SUM (ai di / ni)
i=1
OR MH = ------------------k
SUM (bi cci / ni)
i=1
Strata
Exposure
Cases
Controls
OR
1
Yes
No
a1
c1
b1
d1
OR1
Ref.
2
Yes
No
a2
c2
b2
d2
OR2
Ref.
3
Yes
No
a3
c3
b3
d3
OR3
Ref.
Examples of stratified analysis
Examples
1
2
3
4
5
Stratum 1
Stratum 2
Crude RR
4.00
1.01
3.05
1.02
1.07
4.00
1.03
5.20
1.86
9.40
4.00
4.00
4.00
4.00
4.00
Effect modifier
Belongs to nature
Different effects in different strata
Simple
Useful
Increases knowledge of biological mechanism
Allows targeting of PH action
Confounding factor
Belongs to study
Weighted RR different from crude RR
Distortion of effect
Creates confusion in data
Prevent (protocol)
Control (analysis)
How to conduct a stratified analysis
Perform crude analysis
Measure the strength of association
List potential effect modifiers and confounders
Stratify data according to
potential modifiers or confounders
Check for effect modification
If effect modification present, show the data by stratum
If no effect modification present, check for confounding
If confounding, show adjusted data
If no confounding, show crude data
How to define strata
In each stratum, third variable
is no longer a confounder
Stratum of public health interest
If 2 risk factors, we stratify
on the different levels of one of them
to study the second
Residual confounding ?
Logical order of data analysis
How to deal with multiple risk factors:
Crude analysis
Multivariate analysis
1. stratified analysis
2. modelling
linear regression
logistic regression
A train can mask a second train
A variable can mask another variable
What happened?
Hat
Colour
Blue and red hats
not evenly distributed
between the 2 tables
- table I, 33 % blue
- table II, 66 % blue
% Fitting
Tables
Hat fitting
higher in Table I (83%)
vs table II (13%)