el2testPaucT {emplikAUC}

Testing one pAUC(0, p) value and one quantile: F(tau) = 1-p together by Empirical Likelihood.

Description

This function computes the two sample Log Empirical Likelihood ratio for testing H_0: pAUC(0, p) = theta and F(tau) = 1-p. (F is the CDF of X). The two samples data are in the x-vector and y-vector inputs. It uses EM.

Usage

el2testPaucT(tau, pauc, ind, partial, x, y, epsxy, epsT)

Arguments

tau

The "true" value of the (1-p)-th quantile of X-distribution F, to be tested.

pauc

The H_0 value of pAUC(0, p) to be tested.

ind

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

partial

The probability p in pAUC(0, p); also the p in F(tau) = 1-p.

x

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

y

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

epsxy

The smoothing parameter when compare x-y.

epsT

The smoothing parameter when compare x to Tau, for quantile estimation.

Details

This function is called by el2testPauc( ). It is listed here stand alone because users may find it useful elsewhere.

It make use of function smooth3( ) and the function el2.cen.EMm( ) from the emplik2 package.

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

It returns one value that is the "-2LLR". It should have chi square df=2 under H_0.

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)