Odds Ratio

Risk Ratio

Risk Difference

Geometric Comparison of the Three Operators

• Odds Ratio (Non-Collapsible): The isocline p1 = c*p0 / (1 + (c-1)*p0) is a strictly curved hyperbola . The straight chord (dashed orange) cuts across the hypograph below the curve. Jensen's inequality guarantees OR_marginal < OR_conditional .
• Risk Ratio (Collapsible): The isocline p1 = c * p0 is a straight ray passing through the origin (0, 0) . The secant chord lies directly on the ray. The marginal mixture point never departs from the line, so RR_marginal == RR_conditional .
• Risk Difference (Collapsible): The isocline p1 = p0 + c is an affine straight line with slope 1 . The chord coincides with the line, so RD_marginal == RD_conditional .