Tests \(H_0\colon \mathrm{AUC} = A_0\) vs the specified alternative, using an exact finite-sample unbiased variance estimator with the mid-rank kernel.
Usage
wmwAUC_pvalue_EU(
x,
y,
alternative = "two.sided",
A0 = 0.5,
max_exact = 10000,
n_perm = 2000
)Arguments
- x
Numeric vector of cases (group 1) values.
- y
Numeric vector of reference/control (group 2) values.
- alternative
Character:
"two.sided","greater", or"less".- A0
Numeric null value of \(\mathrm{AUC} = P(X < Y)\). Defaults to 0.5. Only supported when
length(x) + length(y) >= 20(see Details); an error is raised otherwise.- max_exact
Integer; the permutation branch (used when
length(x) + length(y) < 20) enumerates all permutations exactly when their count is at mostmax_exact, and falls back to Monte Carlo sampling above that. Default 10000.- n_perm
Integer; number of Monte Carlo permutation replicates used when exact enumeration is not feasible. Default 2000.
Details
Uses two-tier approach: studentized permutation
for length(x) + length(y) < 20 and the exact finite-sample unbiased
estimator for length(x) + length(y) >= 20.
For length(x) + length(y) < 20, a studentized permutation test is
used: the same t-statistic is recomputed on each permuted split of
the pooled data, and the p-value is the proportion of permuted statistics
at least as extreme as the observed one. This permutation scheme relies on
group-relabeling exchangeability, which preserves \(H_0\) only when
\(A_0 = 0.5\); general A0 is therefore not currently
supported in this small-sample regime and will raise an error.
For length(x) + length(y) >= 20, EU estimates
\(\mathrm{Var}(\hat A)\) by the exact finite-sample unbiased
combination derived from the Hoeffding decomposition of the mid-rank
kernel, with Welch–Satterthwaite degrees of freedom.
x is taken to represent cases and y the reference/control
group, matching the convention of wilcox.test(). Internally, the
test statistic and variance components are computed in the
\(P(X<Y)\) framework.