Log odds ratio ($\log \mathrm{OR}$)

The log odds ratio is the natural logarithm of an odds ratio. For two independent binomial groups with positive event and non-event counts $(a,b)$ and $(c,d)$, its estimate is $\log (ad/(bc))$, with first-order variance $1/a+1/b+1/c+1/d$ by the delta method. Zero cells need a method that handles boundary data; the displayed normal approximation is not valid there.