eltest4aucONE {emplikAUC}

Testing one AUC value by Empirical likelihood.

Description

This function computes the two sample Log Empirical Likelihood ratio for testing H_0: AUC = theta. The two samples are in the x-vector and y-vector.

Usage

eltest4aucONE(theta, x, y, ind, tol.u, tol.v, tol.H0)

Arguments

theta

The "true" value of the AUC under H_0, to be tested.

x

a vector of observations, length m, for the first sample. The test-results of healthy subjects

y

a vector of observations, length n, for the second sample. The test-results of desease subjects.

ind

A smoothed indicator function, to generate a Matrix of (smoothed) indicator values: I[x[i] < y[j]].

tol.u

Error tol for final u probability vector. Must > 0.

tol.v

Error tol for final v probability vector. Must > 0.

tol.H0

The error bound for the constrained NPMLE to satisfy H_0, must >0.

Details

This function is similar to el2test4auc, but using our own algorithm (not EM). It may be slightly different to the above in terms of speed and convergence property. We listed 3 kind of tol to control convergence.

The empirical likelihood we used here is defined as

EL = \prod_{i=1}^m v_i \prod_{j=1}^n \nu_j ~;~~~~~~ \sum v_i =1 ~,~~ \sum \nu_j =1 ~.

Value

A list containing

lambda

The final tilting parameter.

u

the new u vector.

v

The new v vector.

"-2LLR"

The -2 log empirical likelihood ratio.

Pval

The p-value.

iterNum

The iteration number used in computing.

Author(s)

Mai Zhou <[e-mail]>.

References

Zhao, Y., Ding, X. and Zhou (2021). Confidence Intervals of AUC and pAUC by Empirical Likelihood. Tech Report. https://www.ms.uky.edu/~mai/research/eAUC1.pdf

Examples

 
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)
#### We know the AUC estimator here is 0.75.
#### We may test a hypothesis about the AUC value: H0: AUC= 0.7
eltest4aucONE(theta=0.7, x=x, y=y, ind=smooth3, tol.u=1e-6, tol.v=1e-6, tol.H0=1e-6)
#### Two of the outputs should be '-2LLR'=0.1379561 and Pval=0.7103214