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# Table 4 Third example of confounding

 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.
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