Compute the Area Under the ROC Curve (AUC) of a predictor and possibly its 95% confidence interval.

```
AUC(pred, target, digits = NULL)
AUCBoot(pred, target, nboot = 10000, seed = NA, digits = NULL)
```

- pred
Vector of predictions.

- target
Vector of true labels (must have exactly two levels, no missing values).

- digits
See round. Default doesn't use rounding.

- nboot
Number of bootstrap samples used to evaluate the 95% CI. Default is

`1e4`

.- seed
See set.seed. Use it for reproducibility. Default doesn't set any seed.

The AUC, a probability, and possibly its 2.5% and 97.5% quantiles (95% CI).

Other packages provide ways to compute the AUC (see this answer). I chose to compute the AUC through its statistical definition as a probability: $$P(score(x_{case}) > score(x_{control})).$$ Note that I consider equality between scores as a 50%-probability of one being greater than the other.

```
set.seed(1)
AUC(c(0, 0), 0:1) # Equality of scores
#> [1] 0.5
AUC(c(0.2, 0.1, 1), c(0, 0, 1)) # Perfect AUC
#> [1] 1
x <- rnorm(100)
z <- rnorm(length(x), x, abs(x))
y <- as.numeric(z > 0)
print(AUC(x, y))
#> [1] 0.7926731
print(AUCBoot(x, y))
#> Mean 2.5% 97.5% Sd
#> 0.79333279 0.69267707 0.88535292 0.04971805
# Partial AUC
pAUC <- function(pred, target, p = 0.1) {
val.min <- min(target)
q <- quantile(pred[target == val.min], probs = 1 - p)
ind <- (target != val.min) | (pred > q)
bigstatsr::AUC(pred[ind], target[ind]) * p
}
pAUC(x, y)
#> [1] 0.008148148
pAUC(x, y, 0.2)
#> [1] 0.05473251
```