I fitted a Logistic regression with a number of variables, and was asked about the absolute risk (AR) and number needed to treat (NNT) for one of the variable with the outcome. I understand how to calculate them in a 2x2 table, but I am wondering if it can be calculated from the logistic regression?
From my understanding, in a Logistic regression we have (say I'm interested in $X_1$):
$$\newcommand{\exposed}{{\rm exposed}}\newcommand{\unexposed}{{\rm unexposed}}
\ln\bigg[\frac{\pi(\exposed_1)}{\pi(\unexposed_1)}\bigg] = \ln\bigg[\frac{(\beta_0 + \beta_1X_1 + \beta_2X_2 + ...)}{(\beta_0 + \beta_2X_2 + ...)}\bigg]
$$
and since $AR=\pi(\unexposed1)-\pi(\exposed1)$, can we calculate AR like this?
\begin{align}
\pi(\unexposed) &= \frac{\exp(\beta_0+\beta_2X_2+...)}{(1+\exp(\beta_0+\beta_2X_2+...)} \\[5pt]
&\qquad{\rm and} \\[5pt]
\pi(\exposed) &= \frac{\exp(\beta_0+\beta_1X_1+\beta_2X_2+...)}{(1+\exp(\beta_0+\beta_1X_1+\beta_2X_2+...)}
\end{align}
And the NNT is:
$$
\frac 1 {\pi(\unexposed)-\pi(\exposed))}
$$
But since it varies with different $X_2$, $X_3$, etc., is it possible to get a single number for AR and NNT? Would it be appropriate to calculate the $\pi$'s for all possible $X_n$, and then just take the average?
