eltest4aucONE {emplikAUC} | R Documentation |
Testing one AUC value by Empirical likelihood.
Description
This function computes the two sample Log Empirical Likelihood ratio
for testing : 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 |
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 |
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
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 <maizhou@gmail.com>.
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