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 H0H_0: 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 H0H_0, to be tested.

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

EL=i=1mvij=1nνj ;    s.t.   vi=1 ,  νj=1 . EL = \prod_{i=1}^m v_i \prod_{j=1}^n \nu_j ~; ~~~~s.t. ~~~ \sum v_i =1 ~,~~ \sum \nu_j =1 ~.

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)

[Package emplikAUC version 0.4 Index]