Do one of the four generalized logrank tests or a score test for interval-censored data

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Description

The gLRT function conducts four k(>=2)-sample tests for interval-censored survival data. Four of them are different nonparametric generalized logrank tests, and the other is a score test under a proportional hazards model. They are two-sided tests. The null hypothesis is that all k survival functions of the failure time are identical, and the alternative hypothesis hypothesis is that not all survival functions are the same. This function calls one of functions (gLRT1, gLRT2, gLRT3, gLRT4, ScoreTest) based on the method specified. However, each of these tests can be called individually to perform a test. Note that gLRT2 and gLRT4 do not allow exact observations. gLRT4 only allows k = 2 and is no longer called ScoreTest as in Zhao (2012).

Usage

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gLRT(A, k = 2, method = c("glrt1", "glrt2", "glrt3", "glrt4", "score"), 
M = 50, 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.

method

a character string specifying the test to be performed: "glrt1", "glrt2", "glrt3", "glrt4", and "score".

M

number of multiple imputations used in estimating the covariance in function gLRT1. The default is 50.

rho

non-negative parameter in [0, 1] of the link function used for calculating the test statistics in gLRT2, gLRT3, and gLRT4. 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 in gLRT2, gLRT3, and gLRT4. 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 a distribution function. The default is 1000.

inf

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

Details

For all tests, it is assumed that the censoring interval for each observation takes the form (L_i, R_i]. For exact observations, L_i = R_i; for left-censored observations, L_i = 0; and for right-censored observations, R_i = inf, infinity or a large number representing infinity.

Exact observations are not allowed in gLRT2. If no exactly observations exist, gLRT3 reduces to gLRT2 in terms of chi-square statistic and p-value.

When method="glrt1" is selected, gLRT1 is called to perform the test proposed by Zhao and Sun (2004). When method="glrt2" is selected, gLRT2 is called to perform the test proposed by Sun, Zhao, and Zhao (2005). When method="glrt3" is selected, gLRT3 is called to perform the test proposed by Zhao, Zhao, Sun, and Kim (2008). When method="score" is selected, ScoreTest is called to perform a score test under a proportional hazards model proposed by Finkelstein (1986). For the above methods, the NPMLE of the common distribution function under the null hypothesis is computed by function ModifiedEMICM. When method="glrt4" is selected, gLRT4 is called to perform the test proposed by Zhao, Duan, Zhao, and Sun (2013) where ModifiedEMICM is applied to each of the two groups.

The link function used in gLRT2, gLRT3, and gLRT4 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 u (NA for gLRT4)

chisq/fstat

the chi-square or f (for gLRT4) statistic

df

the degrees of freedom of the chis-square test or f-test

p

p-value of the test

Author(s)

Qiang Zhao and Jianguo Sun

References

Q. Zhao and J. Sun (2004), "Generalized Log-rank Test for Mixed-Censored Failure Time Data", Statistics in Medicine, 23: 1621-1629.

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

X. Zhao, Q. Zhao, J. Sun, Q. and J. S. Kim (2008), "Generalized Log-rank Tests for Partly Interval-Censored Failure Time Data", Biometrical Journal, 50 (3): 375-385.

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.

Finkelstein, DM (1986), "A Proportional Hazards Model for Interval-censored Failure Time Data", Biometrics, 42: 845-854.

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

gLRT1, gLRT2, gLRT3, gLRT4, ScoreTest

Examples

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data(cosmesis)
gLRT(cosmesis, method="glrt1", M=20, inf=100)
gLRT(cosmesis, method="glrt2", rho=1, inf=100)

data(diabetes)
gLRT(diabetes, method="glrt3", gamma=1)
gLRT(diabetes, method="score")

data(cmv)
cmvBlood = cmv[,c(2,3,6)]
cmvUrine = cmv[, 4:6]
gLRT(cmvBlood, method="glrt4")
gLRT(cmvUrine, method="glrt4", rho=1, gamma=1)

# 3-sample test
data(cosmesis)
cosmesis[80:94, 3] = 2
gLRT(cosmesis, k=3, method="glrt3", rho=0, gamma=0, inf=100)

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