Symmetry of Odds Ratio

Unlike the case with normally distributed continuous variable, the Confidence Interval (CIs) of Odds Ratio (OR), the often-used measure of association in medical literature, is said NOT to be symmetrical about the point estimates. The inference is based on the conventional additive construct, which is why it is shown that the CIs of natural logarithm (ln) of OR is symmetrical about the ln(OR), and NOT the OR itself. There is consensus that the log-scale is not quite intuitive, and hence the CI of ln(OR) is later expressed (taking anti-log) in natural scale. However, after the transformation from ln(OR) to OR, the CI of OR is blamed not to have symmetry about the point estimate, and hence the construct of CI of OR remains unintuitive. However, we show mathematically that CI of OR is also symmetrical about the point estimate of OR, only that it is on multiplicative construct. The same is applicable for Risk Ratios (RR) too.