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The accumulated number of previous successes may enter the conditional mean in a history-dependent logistic regression. Its coefficient exponentiates to the conditional success odds ratio per previous success. For a specified future path, update this cumulative predictor after each outcome before multiplying the conditional probabilities.

A forest plot shows each study's effect estimate and confidence interval, together with a pooled estimate when appropriate. A vertical null-effect line allows comparison on a common scale. For an odds ratio the null is one and a logarithmic axis treats reciprocal ratios symmetrically; marker areas commonly encode study weights.

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.

For two independent binomial distributions with event and nonevent counts $a,b$ and $c,d$, the odds ratio is $ad/(bc)$. The delta method applied to $\log (p/(1-p))$, whose derivative is $1/[p(1-p)]$, gives a group variance $1/[Np(1-p)]$. Substitution of the fitted proportion gives $1/a+1/b$ in the first group and $1/c+1/d$ in the second. Their independence gives the displayed sum. A normal approximation then gives a confidence interval on the log odds ratio scale; exponentiation produces an odds-ratio interval. Zero cells require another approximation or model.

For independent two-by-two tables with counts $a_i,b_i,c_i,d_i$ and total $n_i$, the Mantel–Haenszel pooled odds ratio is the displayed ratio of sums. When all $b_i{c}_i>0$, it is also the weighted arithmetic mean of study odds ratios with weights $b_i{c}_i/n_i$. These differ from inverse estimated variance weights for log odds ratios. Both constructions can represent a fixed-effect meta-analysis, but they should not be silently interchanged when interpreting a supplied plot.