glrt (version 2.0)

gLRT4: Conduct a generalized logrank test for interval-censored data

Description

Function gLRT4 conducts a $k$(=2)-sample test for interval-censored survival data. The test is based on Zhao, Duan, Zhao, and Sun (2013). The null hypothesis is that the two survival functions of the failure time are the same, and the alternative hypothesis is that the two functions are not the same.

Usage

gLRT4(A, k = 2, rho = 0, gamma = 0, EMstep = TRUE, ICMstep = TRUE, 
tol = 1e-06, maxiter = 1000, inf = Inf)

Arguments

A

an $n$ by 3 data matrix with the censoring interval of the format $(L, R]$ in columns 1 & 2 and treatmentment indicator ranging from 0 to $k-1$ in column 3. No exact observations (i.e., $L = R$) are allowed.

k

number of treatments. Only $k = 2$ is allowed.

rho

non-negative parameter in [0, 1] of the link function used for calculating the test statistics. It is the same as $b$ in Zhao, Duan, Zhao, and Sun (2013). The default is 0.

gamma

non-negative parameter in [0, 1] of the link function used for calculating the test statistics. It is the same as $c$ in Zhao, Duan, Zhao, and Sun (2013). The default is 0.

EMstep

a boolean variable indicating whether to take an EM step in the iteration when estimating the common distribution function. The default is TRUE.

ICMstep

a boolean variable indicating whether to take an ICM step in the iteration when estimating the common distribution function. The default is TRUE.

tol

the maximal $L_1$ distance between successive estimates before stopping iteration when estimating the common distribution function. The default is 1.0e-6.

maxiter

the maximal number of iterations to perform before stopping when estimating the common distribution function. The default is 1000.

inf

value used in data for infinity. The default is Inf.

Value

The function returns an object containing the following components:

method

test procedure used

u

the test statistic

v

NA is returned

fstat

the f-test statistic

df

the numerator and denominator degrees of freedom of the f-test, i.e., (1, 1)

p

p-value of the f-test

Details

The NPMLE of the distribution function for each treatment group is computed by function ModifiedEMICM.

The f-test in gLRT4 is based on an F distribution with degrees of freedom 1 and 1.

The link function used in gLRT4 is $\xi(x) = x log(x) x^\rho (1 - x)^\gamma = x log(x) x^b (1 - x)^c. $

References

X. Zhao, R. Duan, Q. Zhao, and J. Sun (2013), "A New Class of Generalized Log Rank Tests for Interval-censored Failure Time Data", Computational Statistics and Data Analysis. 60: 123-131.

See Also

gLRT, gLRT1, gLRT2, gLRT3, ScoreTest

Examples

data(cmv)
cmvBlood = cmv[,c(2,3,6)]
cmvUrine = cmv[, 4:6]
gLRT4(cmvBlood)
gLRT4(cmvUrine, rho=1, gamma=1)