el2testPauc {emplikAUC} | R Documentation |
Testing one pAUC(0, p) value by Empirical likelihood.
Description
This function computes the two sample Log Empirical Likelihood ratio
for testing : pAUC(0, p) = theta.
The two samples are in the x-vector and y-vector inputs.
Usage
el2testPauc(theta, x, y, ind, nuilow, nuiup, partial, epsxy, epsT)
Arguments
theta |
The "true" value of the pAUC(0, p) under |
x |
a vector of observations, length m, for the first sample, test-results with the healthy subjects. |
y |
a vector of observations, length n, for the second sample, test-results with the desease subjects. |
ind |
The (smoothed) indicator function for compare x-y. |
nuilow |
Lower bound for the nuisamce parameter (1-p)-th quantile of X) search. |
nuiup |
Upper bound for nuisance parameter search. |
partial |
The probability p in pAUC(0, p). |
epsxy |
The smoothing parameter when compare x-y. |
epsT |
The smoothing parameter when calculating quantile. |
Details
This function will call another function: el2testPaucT( )
.
We then use optimize( )
to profile out the nuisance
parameter tau: the (1-p)-th quantile of X distribution.
Can be used by findUnew( )
etc.
The empirical likelihood we used here is defined as
Value
A list containing
"-2LLR" |
The -2 log empirical likelihood ratio. |
Nupar |
The nuisance parameter value that achieved the minimum. |
Pval |
The p-value, by using chi square distribution with 1 df. |
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)