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1 + 1 + 1 3
ORMH = ————— = —— = 1.5
1 + 1 2
So the formula becomes simply OR=B/C, where B is the number of discordant pairs in which
the case is exposed and C is the number of pairs in which the control is exposed. Note that the
concordant pairs (types A and D) have no effect on the OR.
Mathematical models
Earlier in this chapter we showed that when the RR is the same in all strata of a stratified analysis, then
data conform to a multiplicative model, and vice-versa. We also stated that for difference measures,
equality of the stratum-specific difference measures is equivalent to having the data conform to an
additive model. In fact, these simple models can serve as a jumping off point for understanding
mathematical models used to control confounding.
Returning to the topic of breast cancer in relation to obesity and/or reserpine use, suppose that the
following table shows data from a cohort study. (Note that this is hypothetical - reserpine was at one
time suspected of being related to breast cancer risk, but that evidence has since been discounted.)
Thus:
Ten-year risk of breast cancer, by obesity and use of reserpine
(hypothetical data)
Risk factors Numeric (illustrative) Algebraic
None (background risk) .01 R00
Obesity only .03 R10
Reserpine only .02 R01
Both reserpine and obesity .04 R11
R00 indicates background risk (no reserpine, non-obese)
R10 indicates risk for obesity (without reserpine)
R01 indicates risk for reserpine (without obesity)
R11 indicates risk both reserpine and obesity
In this example, the joint risk conforms to an additive model:
RD11 = RD10 + RD01 (Risk differences are additive)
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www.sph.unc.edu/courses/EPID 168, © Victor J. Schoenbach 13. Multicausality ― analysis approaches ― 441
rev. 10/28/1999, 11/16/2000, 4/2/2001