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

Table 2 First example of confounding

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

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.