The harmonic mean between precision and recall (F1 score) is a common metric to evaluate binary classification. It is useful because it strikes a balance between precision (FP) and recall (FN).
For some problems, specificity more relevant than precision to measure the FP. In these cases, which metric should be used to balance sensitivity and specificity? Is there an equivalent of the F1 score?
The $F_{\beta}$ score is defined as:
$$ (1+\beta^2)\left(\dfrac{ P\times R }{ R +\left( \beta^2P \right) }\right) $$
($P$ is precision. $R$ is recall.)
When $\beta=1$, this is the $F_1$ score and weights precision and recall equally. When $\beta\in(0,1)$, precision is weighted higher than recall. When $\beta>1$, recall is weighted higher than precision.
$F_{\beta}$ is available through the Python package sklearn, the documentation of which gives some references.
Note, however, the issues with $F_1$ and related calculations like $F_{\beta}$ (sensitivity/recall, specificity, accuracy).
