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Table 3 Second 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 2200 8000
No B users No B users 50% use B 30% 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 1000 1000 900 2100 1000 1000 900 7100
  OR (within risk takers) = (1000/1000)/(900/2100) = 2.33 OR (overall, unadjusted) = (1000/1000)/(900/7100) = 7.89
  1. As in Table 2, it is assumed that there is no use of A or B among the “unadventurous”. Here, however, the use of A and B is assumed to be correlated among the “risk takers”. It is demonstrated that the unadjusted odds ratio is substantially higher than the OR in the “risk takers”.