Differences in AUC calculation in R between pROC and AUC

Question

I was comparing the performance of pROC and AUC libraries when performing auc() calculations on random data:

library("pROC");
library("AUC")

predictor <- rnorm(10000, 5);
outcome <- rnorm(10000) > 0;

print ("pROC:::auc() time & output")
system.time(x <- pROC:::auc(outcome, predictor))
print(x);

print ("AUC:::auc() time & output")
system.time(x <- AUC:::auc(AUC:::roc(predictor, factor(outcome))))
print(x);

AUC:::auc seemed to perform substantially faster, but what I found strange is that the compute different auc values for the same dataset:

> system.time(x <- pROC:::auc(outcome, predictor))
   user  system elapsed 
   1.00    0.01    1.31 

> print(x);
Area under the curve: 0.5058

> print ("AUC:::auc() time & output")
[1] "AUC:::auc() time & output"

> system.time(x <- AUC:::auc(AUC:::roc(predictor, factor(outcome))))
   user  system elapsed 
   0.19    0.00    0.18 

> print(x);
    [1] 0.4942452

I thought the Auc() function was deterministic so they should produce the same number.

Yet pROC produces 0.5058 and AUC produces 0.4942452 .

Am I misusing either function?

EDIT: FYI I tried making the number semi random and the functions now give identical results (bar rounding errors):

predictor <- runif(10000);
outcome <- as.integer((predictor + runif(10000)) > 0.5);

Answer 1

First, notice that $1 - 0.4942452 = 0.5057548 ≈ 0.5058$.

Second, notice that ?AUC::roc accepts only labels as {0,1}, with predictions being the probability of the positive event.

predictions: A numeric vector of classification probabilities
      (confidences, scores) of the positive event.

labels: A factor of observed class labels (responses) with the only
      allowed values {0,1}.

pROC::roc makes no such assumptions on the input data. It has some heuristics to detect which level is the positive and negative case, and more importantly if value of the predictions score are higher in the positive or negative cases. They don't have to be probabilities, any numeric values or even ordered factors will do. This can be controlled by the levels and direction arguments:

levels: the value of the response for controls and cases
      respectively. By default, the first two values of
      ‘levels(as.factor(response))’ are taken, and the remaining

direction: in which direction to make the comparison?  “auto”
      (default): automatically define in which group the median is
      higher and take the direction accordingly.  “>”: if the
      predictor values for the control group are higher than the
      values of the case group (controls > t >= cases).  “<”: if
      the predictor values for the control group are lower or equal
      than the values of the case group (controls < t <= cases).

pROC auto-detects the direction, based on the median values in the two groups that are being compared.

Please note that when you sample curves with AUC close to 0.5, this will result in a bias towards a higher AUC; therefore you should keep the direction fixed. To get results identical to AUC::roc you should use the following:

x <- pROC::auc(outcome, predictor, levels = c(0, 1), direction = "<")