Table 1 Abbreviations

RR

Relative Risk

OR

Odds Ratio

S

Susceptibility factor

E

Environmental exposure

ICR_c/nc

The interaction contrast ratio (ICR) in a study with cases and non-cases

\({\mathrm{ICR}}_{\mathrm{c}/\mathrm{nc}}=\frac{{\mathrm{RR}}_{\mathrm{s}\mathrm{e}}}{{\mathrm{RR}}_{\mathrm{s}}{\mathrm{RR}}_{\mathrm{e}}}=\left(\frac{\mathrm{ag}}{\mathrm{c}\mathrm{e}}\right)\left(\frac{\left(\mathrm{c}+\mathrm{D}\right)\left(\mathrm{e}+\mathrm{F}\right)}{\left(\mathrm{a}+\mathrm{B}\right)\left(\mathrm{g}+\mathrm{H}\right)}\right)\)

ICR_cc

The ICR in a case-control study

\({\mathrm{ICR}}_{\mathrm{cc}}=\frac{{\mathrm{OR}}_{\mathrm{s}\mathrm{e}}}{{\mathrm{OR}}_{\mathrm{s}}{\mathrm{OR}}_{\mathrm{e}}}=\left(\frac{\mathrm{ag}}{\mathrm{ce}}\right)\left(\frac{\mathrm{DF}}{\mathrm{BH}}\right)\)

ICR_co

The ICR in a case-only study

\({\mathrm{ICR}}_{\mathrm{co}}=\left(\frac{\mathrm{ag}}{\mathrm{ce}}\right)\)

S-E OR_c/nc

Susceptibility factor-Environmental exposure odds ratio in a study with cases and non-cases

S-E OR_c/nc = \(\left(\frac{\left(\mathrm{c}+\mathrm{D}\right)\left(\mathrm{e}+\mathrm{F}\right)}{\left(\mathrm{a}+\mathrm{B}\right)\left(\mathrm{g}+\mathrm{H}\right)}\right)\)

S-E OR_control

Susceptibility factor-Environmental exposure odds ratio in the control population

S-E OR_control\(=\left(\frac{\mathrm{DF}}{\mathrm{BH}}\right)=\frac{\mathrm{df}}{\mathrm{bh}}\)