# Causation seminar 20 November 2014 Paradoxes - solved

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Causation seminar 20 November 2014 Paradoxes - solved

Obesity paradox – A survival advantage of being obese – in a population diagnosed with a medical condition (Epidemiology 2014; 25: ) Better survival for obese has been demonstrated for diabetes, CVD, hypertension, LC, MI, and more.

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.

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.

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to smoking mothers have lower infant mortality rates than low birth weight children of non smokers (Judea Pearl, unpublished manuscript 2014 – in Lord´s Paradox Revisited.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.

Smoking LBW Death U

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?

Simpsons paradox more white than black hats Next day
All hats fell down on the floor now more black than white hats

Simpsons´s paradox E = treatment, R = recovery, G = gender Str E
Recovery rate A11 + 20 40 50% - 16 24 40% M 18 12 30 60% 7 3 10 70% F 2 8 20% 9 21 30% E = treatment, R = recovery, G = gender

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.

E G R E has a direct effect on R But the E – R association is confounded by G. G has a direct effect on R and E.

’paradoxes’ in routine epidemiologic decision making – what should we adjust for??

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 Now adjustment for CW – but cause comes before the effect.

More likely CW U BW BP Now adjustment for CW. U1 U2 No adjustments needed.

CW U1 U2 BW U3 BP BW has no effect but will be associated with BP (confounder, U3). U BW BP BW BP ass is biased – bias BW – CW – BP + BW – CW – U – BP Causal ass. BW – BP + BW – CW – BP but CW – U – BP should be closed.