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Table 2 An example of a study with cases and non-cases

From: Case-only approach applied in environmental epidemiology: 2 examples of interaction effect using the US National Health and Nutrition Examination Survey (NHANES) datasets

Environment (E)

Susceptibility (S)

Disease

No disease

Total

Relative Risk (RR)

Odds Ratio (OR)

–

–

a

B

a + B

1.0 (ref)

1.0 (reference)

–

+

c

D

c + D

RRs=\(\frac{\mathrm{c}\left(\mathrm{a}+\mathrm{B}\right)}{\mathrm{a}\left(\mathrm{c}+\mathrm{D}\right)}\)

ORs=\(\frac{\mathrm{cB}}{\mathrm{aD}}\)

+

–

e

F

e + F

RRe=\(\frac{\mathrm{e}\left(\mathrm{a}+\mathrm{B}\right)}{\mathrm{a}\left(\mathrm{e}+\mathrm{F}\right)}\)

ORe=\(\frac{\mathrm{eB}}{\mathrm{aF}}\)

+

+

g

H

g + H

RRse=\(\frac{\mathrm{g}\left(\mathrm{a}+\mathrm{B}\right)}{\mathrm{a}\left(\mathrm{g}+\mathrm{H}\right)}\)

ORse=\(\frac{\mathrm{gB}}{\mathrm{aH}}\)

  1. Under additive scale: ICRc/nc = RRse-(RRs + RRe-1), ICRc/nc = ORse-(ORs + ORe-1)
  2. Under multiplicative scale: ICRc/nc = RRse/(RRs × RRe), ICRc/nc = ORse/(ORs × ORe)