ROCnp {emplik}R Documentation

Test the ROC curve by Empirical Likelihood

Description

Use the empirical likelihood ratio to test the hypothesis Ho: (1-b0)th quantile of sample 1 = (1-t0)th quantile of sample 2. This is the same as testing Ho: R(t0)= b0, where R(.) is the ROC curve.

The log empirical likelihood been maximized is

sum_{d1=1} log Delta F_1(t1_i) + sum_{d1=0} log [1-F_1(t1_i)] + sum_{d2=1} log Delta F_2(t2_j) + sum_{d2=0} log [1-F_2(t2_j)] .

Usage

ROCnp(t1, d1, t2, d2, b0, t0)

Arguments

t1 a vector of length n. Observed times, may be right censored.
d1 a vector of length n, censoring status. d=1 means t is uncensored; d=0 means t is right censored.
t2 a vector of length m. Observed times, may be right censored.
d2 a vector of length m, censoring status.
b0 a scalar between 0 and 1.
t0 a scalar, betwenn 0 and 1.

Details

Basically, we first obtain two log likelihood ratios from two samples, in testing a common quantile c. And then we minimize the sum of the two test statistic over c.

See the tech report below.

Value

A list with the following components:

"-2LLR" the -2 loglikelihood ratio; have approximate chisq distribution under H_o.
cstar the estimated common quantile.

Author(s)

Mai Zhou.

References

Zhou, M. and Liang, H (2008). Empirical Likelihood for Hybrid Two Sample Problem with Censored Data. Tech. Report.

Examples

#### An example of testing the equality of two medians. No censoring.
ROCnp(t1=rexp(100), d1=rep(1,100), t2=rexp(120), 
                                d2=rep(1,120), b0=0.5, t0=0.5)

[Package emplik version 0.9-4 Index]