ROCnp {emplik} | R Documentation |
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)] .
ROCnp(t1, d1, t2, d2, b0, t0)
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. |
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.
A list with the following components:
"-2LLR" |
the -2 loglikelihood ratio; have approximate chisq distribution under H_o. |
cstar |
the estimated common quantile. |
Mai Zhou.
Zhou, M. and Liang, H (2008). Empirical Likelihood for Hybrid Two Sample Problem with Censored Data. Tech. Report.
#### 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)