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Table 2 First example of confounding

From: Appropriate and inappropriate methods for investigating the “gateway” hypothesis, with a review of the evidence linking prior snus use to later cigarette smoking

Unadventurous Risk takers Overall
5000 5000 10000
No A users 40% use A (Sum over unadventurous and risk takers)
A Not A A Not A A Not A
0 5000 2000 3000 2000 8000
No B users No B users 40% use B 40% use B (sum) (sum)
B Not B B Not B B Not B B Not B B Not B B Not B
0 0 0 5000 800 1200 1200 1800 800 1200 1200 6800
  OR (within risk takers) = (800/1200)/(1200/1800) =1.00 OR (overall, unadjusted) = (1000/1200)/(1200/6800) = 3.78
  1. It is assumed that there is no use of A or B among the “unadventurous”, and that use of A and B is independent among the ‘risk takers’. The table shows the joint distribution of use of A and B, separately for the “unadventurous” and the “risk takers” and overall, and demonstrates that the unadjusted OR shows a markedly spurious relationship.