Obtaining threshold values from a ROC curve

Question

I have some models, using ROCR package on a vector of the predicted class percentages, I have a performance object. Plotting the performance object with the spe

Answer 1

2 solutions based on the ROCR and pROC packages:

threshold1 <- function(predict, response) {
    perf <- ROCR::performance(ROCR::prediction(predict, response), "sens", "spec")
    df <- data.frame(cut = perf@alpha.values[[1]], sens = perf@x.values[[1]], spec = perf@y.values[[1]])
    df[which.max(df$sens + df$spec), "cut"]
}
threshold2 <- function(predict, response) {
    r <- pROC::roc(response, predict)
    r$thresholds[which.max(r$sensitivities + r$specificities)]
}
data(ROCR.simple, package = "ROCR")
threshold1(ROCR.simple$predictions, ROCR.simple$labels)
#> [1] 0.5014893
threshold2(ROCR.simple$predictions, ROCR.simple$labels)
#> [1] 0.5006387

See also OptimalCutpoints package which provides many algorithms to find an optimal thresholds.

Answer 2

This is why str is my favorite R function:

library(ROCR)
data(ROCR.simple)
pred <- prediction( ROCR.simple$predictions, ROCR.simple$labels)
perf <- performance(pred,"tpr","fpr")
plot(perf)
> str(perf)
Formal class 'performance' [package "ROCR"] with 6 slots
  ..@ x.name      : chr "False positive rate"
  ..@ y.name      : chr "True positive rate"
  ..@ alpha.name  : chr "Cutoff"
  ..@ x.values    :List of 1
  .. ..$ : num [1:201] 0 0 0 0 0.00935 ...
      ..@ y.values    :List of 1
      .. ..$ : num [1:201] 0 0.0108 0.0215 0.0323 0.0323 ...
  ..@ alpha.values:List of 1
  .. ..$ : num [1:201] Inf 0.991 0.985 0.985 0.983 ...

Ahah! It's an S4 class, so we can use @ to access the slots. Here's how you make a data.frame:

cutoffs <- data.frame(cut=perf@alpha.values[[1]], fpr=perf@x.values[[1]], 
                      tpr=perf@y.values[[1]])
> head(cutoffs)
        cut         fpr        tpr
1       Inf 0.000000000 0.00000000
2 0.9910964 0.000000000 0.01075269
3 0.9846673 0.000000000 0.02150538
4 0.9845992 0.000000000 0.03225806
5 0.9834944 0.009345794 0.03225806
6 0.9706413 0.009345794 0.04301075

If you have an fpr threshold you want to hit, you can subset this data.frame to find maximum tpr below this fpr threshold:

cutoffs <- cutoffs[order(cutoffs$tpr, decreasing=TRUE),]
> head(subset(cutoffs, fpr < 0.2))
          cut       fpr       tpr
96  0.5014893 0.1495327 0.8494624
97  0.4997881 0.1588785 0.8494624
98  0.4965132 0.1682243 0.8494624
99  0.4925969 0.1775701 0.8494624
100 0.4917356 0.1869159 0.8494624
101 0.4901199 0.1962617 0.8494624

Answer 3

Package pROC includes function coords for calculating best threshold:

library(pROC)
my_roc <- roc(my_response, my_predictor)
coords(my_roc, "best", ret = "threshold")