How can I get The optimal cutoff point of the ROC in logistic regression as a number

Question

I would like to get the optimal cut off point of the ROC in logistic regression as a number and not as two crossing curves. Using the code below I can get the plot that will

Answer 1

As per documentation the optimal cut-off point is defined as the point where Sensitivity + Specificity is maximal (see MX argument in ?ROC). You can get the according values as follows (see example in ?ROC):

x <- rnorm(100)
z <- rnorm(100)
w <- rnorm(100)
tigol <- function(x) 1 - (1 + exp(x))^(-1)
y <- rbinom(100, 1, tigol(0.3 + 3*x + 5*z + 7*w))
rc <- ROC(form = y ~ x + z, plot="sp") 
## optimal combination
opt <- which.max(rowSums(rc$res[, c("sens", "spec")]))
## optimal cut-off point 
rc$res$lr.eta[opt]

This is the point that will be shown when you run

ROC(form = y ~ x + z, plot = "ROC", MX = TRUE)