CAUSATION SEMINAR
20 NOVEMBER 2014
PARADOXES - SOLVED
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
PARADOXES:
A paradox is a statement that apparently contradicts itself and
yet may be true.
•
•
•
•
3 will be addressed
The obesity paradox
The smoking paradox
Simpsons paradox
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014

Obesity paradox – A survival advantage of being obese – in a
population diagnosed with a medical condition (Epidemiology 2014; 25:
454-61)

Better survival for obese has been demonstrated for diabetes, CVD,
hypertension, LC, MI, and more.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
COLLIDER STRATIFICATION BIAS
Obesity
[Diabetes]
Mortality
U
Obesity is a less ‘dangerous’ cause of death in patients with diabetes than other causes of diabetes.
It is better to have obesity as a cause of diabetes than pancreatic cancer!
if you did not have diabetes because of a causal field including obesity, you had another causal
filed leading to diabetes and mortality in the group may be higher. Diseases have causes.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
This paradox – and the next and many others - is the result of collider stratification
bias.
By conditioning on the collider you link the causes of the collider. You then compare
obese with those having a different cause of diabetes like pancreatic cancer.
A Berksonian bias model
Dis A
Dis B
[Hospitalization]
When studying hospital patients disease A and B will be associated even if they
occur independently in the population.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
THE BIRTH WEIGHT PARADOX
The Paradox:

Low birth weight children to smoking mothers have lower infant mortality rates than low
birth weight children of non smokers (Judea Pearl, unpublished manuscript 2014 – in
Lord´s Paradox Revisited.

LBW children have a MRR of 100 and smoking causes LBW.

Smoking is not beneficial but again we see collider stratification bias.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
Smoking
LBW
Death
U
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
In counterfactual language:

How would the mortality rate of babies of smoking mothers compare
with that of non smokers had there been no pre-existing uncontrolled
difference in birth weight?
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
SIMPSONS PARADOX
more white than black hats
more white than black hats
Next day
All hats fell down on the floor
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
now more black than white hats
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
SIMPSONS´S PARADOX
Str
E
A11
+
20
20
40
Recovery
rate
50%
-
16
24
40
40%
+
18
12
30
60%
-
7
3
10
70%
+
2
8
10
20%
-
9
21
30
30%
M
F
Recovery
N
E = treatment, R = recovery, G = gender
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014

If you think data speak for themselves, call a shrink not a statistician.

Data are passive vehicles of information that needs to be understood in the context driven
by logical reasoning.

It is not surprising that we see a change in association between 2 variables when a third
variable is controlled for
– we see this all the time
– we call this effect measure modification
– and even the direction of association can change.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
E
E has a direct effect on R
G
R
But the E – R association is
confounded by G.
G has a direct effect on R and E.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
’PARADOXES’ IN ROUTINE
EPIDEMIOLOGIC DECISION
MAKING – WHAT SHOULD WE
ADJUST FOR??
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
An example of analytical thinking guided by DAGs (after O. ARAH)
Analyses of BW and adult BP.
How to deal with current weight (CW).
CW
BW
BP
Look at BW – BP association no adjustment.
If like this
CW
BW
BP
Now adjustment for CW – but cause comes before the effect.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
More likely
CW
U
BW
BP
Now adjustment for CW.
CW
U1
U2
BW
BP
No adjustments needed.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
CW
U1
BW
U2
U3
BP
BW has no effect but will be associated with BP (confounder, U3).
CW
U
BW
BW
BP
BP ass is biased – bias BW – CW – BP + BW – CW – U – BP
CW
U
BW
BP
Causal ass. BW – BP + BW – CW – BP but CW – U – BP should be closed.
AU
AARHUS
UNIVERSITY
DEPARTMENT OF PUBLIC HEALTH
JØRN OLSEN
M.D., PHD
CAUSATION SEMINAR.
20 NOVEMBER 2014
AU
AARHUS
UNIVERSITY