= Logistic interaction as a ratio of odds ratios
{title2=$e^\delta=\operatorname{OR}_{A\mid B=1}/\operatorname{OR}_{A\mid B=0}$}
For binary predictors $A,B$, a <logistic regression> with <linear predictor> $a+bA+cB+\delta AB$ has conditional <odds ratios> $e^b$ at $B=0$ and $e^{b+\delta}$ at $B=1$. Their ratio is $e^\delta$. The same interaction can be computed from the four cell <logit link> values as $\delta=\eta_{11}-\eta_{10}-\eta_{01}+\eta_{00}$. Independent positive event and nonevent counts in each cell give an estimated <variance> for this contrast equal to the sum of all eight reciprocal counts. An interaction on the <odds ratio> scale is not an interaction on the absolute-risk scale.
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