Conduct a generalized logrank test for interval-censored data

Description

The gLRT2 function conducts a k(>=2)-sample test for interval-censored survival data. The test is based on Sun, Zhao, and Zhao (2005). The null hypothesis is that all k survival functions of the failure time are the same, and the alternative hypothesis is that not all functions are the same.

Usage

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gLRT2(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.

k

number of treatments. The default is 2.

rho

non-negative parameter of the link function used for calculating the test statistics. The default is 0.

gamma

non-negative parameter of the link function used for calculating the test statistics. 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 commondistribution 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.

Details

Under the null hypothesis, the NPMLE of the common distribution function is computed by function ModifiedEMICM.

Censoring interval for each observation take the form (L_i, R_i]. No exact observations are allowed, i.e., L_i < R_i.

The chi-square test used in gLRT2 has k-1 degrees of freedom.

The link function used in gLRT2 is ξ(x) = x log(x) x^ρ (1 - x)^γ.

Value

The function returns an object containing the following components:

method

test procedure used

u

the test statistic

v

the estimated covariance of the test statistic

chisq

the chisquare test statistic

df

the degrees of freedom of the test

p

p-value of the test

Author(s)

Qiang Zhao and Jianguo Sun

References

J. Sun, Q. Zhao, and X. Zhao (2005), "Generalized Log-rank Test for Interval-Censored Data", Scandinavian Journal of Statistics, 32: 45-57.

Q. Zhao (2012), "gLRT - A New R Package for Analyzing Interval-censored Survival Data", Interval-Censored Time-to-Event Data: Methods and Applications, CRC Press, 377-396.

See Also

gLRT, gLRT1, gLRT3, gLRT4, ScoreTest

Examples

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data(cosmesis)
gLRT2(cosmesis, rho=0, gamma=1, inf=100)

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