Table 1 Equivalence of the crude RR computed from a cohort of N subjects and the crude OR computed from the expanded cohort with N+N.1 records, where \(N_{.1} = N_{e1} + N_{\bar {e}1}\) is the total number of cases in the original cohort
From: Estimating risk ratio from any standard epidemiological design by doubling the cases
A) Cohort | Y=1 | Y=0 | Total | Prevalence | Crude RR |
X=e | Ne1 | Ne0 | Ne.=Ne1+Ne0 | pe=Ne1/Ne. | \(RR = p_{e} / p_{\bar {e}}\) |
\(X = \bar {e}\) | \(N_{\bar {e}1}\) | \(N_{\bar {e}0}\) | \(N_{\bar {e}.} = N_{\bar {e}1} + N_{\bar {e}0}\) | \(p_{\bar {e}} = N_{\bar {e}1} / N_{\bar {e}.}\) | |
B) Expanded cohort | Y∗=1 | Y∗=0 | Odds | Crude OR | |
X=e | Ne1 | Ne. | \(odds^{*}_{e} = N_{e1} / N_{e.}\) | \(OR^{*} = p_{e} / p_{\bar {e}}\) | |
\(X = \bar {e}\) | \(N_{\bar {e}1}\) | \(N_{\bar {e}.}\) | \(odds^{*}_{\bar {e}}= N_{\bar {e}1} / N_{\bar {e}.}\) |