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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”.