Description Usage Arguments Details Value Author(s) References See Also Examples
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).
1 2 3 |
A |
an n by 3 data matrix with the censoring interval of the format ( |
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 |
rho |
non-negative parameter in [0, 1] of the link function used for calculating the test statistics in |
gamma |
non-negative parameter in [0, 1] of the link function used for calculating the test statistics in |
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. |
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.
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/fstat |
the chi-square or f (for |
df |
the degrees of freedom of the chis-square test or f-test |
p |
p-value of the test |
Qiang Zhao and Jianguo Sun
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.
gLRT1
, gLRT2
, gLRT3
, gLRT4
, ScoreTest
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | 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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