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Table 4 Third 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
4% use A 40% use A (Sum over unadventurous and risk takers)
A Not A A Not A A Not A
200 4800 2000 3000 2200 7800
5% use B 3% use B 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
10 190 144 4656 1000 1000 900 2100 1010 1190 1044 6756
OR (within unadventurous) = (10/190)/(144/4656) = 1.70 OR (within risk takers) = (1000/1000)/(900/2100) = 2.33 OR (overall, unadjusted) = (1010/1196)/(1044/6756) = 5.49
OR (overall, adjusted for risk taking) = ((10 × 4656)/5000 + (1000 × 2100)/5000)/((190 × 144)/5000 + (1000 × 900)/5000) = 2.31  
  1. In this example, unlike in Tables 2 and 3, there is some use of A and B in the “unadventurous”, though much less than in the “risk takers”. It is also assumed that the use of A and B is correlated in both subgroups. It is demonstrated that the unadjusted OR substantially overestimates the adjusted OR.