Untitled

cls <- c('P', 'P', 'N', 'P', 'P', 'P', 'N', 'N', 'P', 'N', 'P',
        'N', 'P', 'N', 'N', 'N', 'P', 'N', 'P', 'N')
score <- c(0.9, 0.8, 0.7, 0.6, 0.55, 0.51, 0.49, 0.43, 0.42, 0.39, 0.33, 
          0.31, 0.23, 0.22, 0.19, 0.15, 0.12, 0.11, 0.04, 0.01)

pos <-  score[cls == 'P']
neg <- score[cls == 'N']

n <- 50000

out <- logical()

for (i in 1:n) {
  
  p_samp <- sample(pos,1)
  
  n_samp <- sample(neg,1)
  
  out[i] <- p_samp > n_samp
  
}

mean(out)

## [1] 0.67692

pROC::auc(cls, score)

## Setting levels: control = N, case = P

## Setting direction: controls < cases

## Area under the curve: 0.68