intELtest {EL2Surv} | R Documentation |
The integrated likelihood ratio test
Description
intELtest
gives a class of the weighted likelihood ratio statistics:
where is an objective weight function, and
is an empirical likelihood
(EL) ratio that compares two survival functions at each time point
in the set of
observed uncensored lifetimes,
.
Usage
intELtest(data, g1 = 1, t1 = 0, t2 = Inf, sided = 2,
nboot = 1000, wt = "p.event", alpha = 0.05, compo = FALSE,
seed = 1011, nlimit = 200)
Arguments
data |
a data frame/matrix with 3 columns. The first column is
the survival time. The second is the censoring indicator. The last is
the grouping variable. An example as the input to |
g1 |
the group with longer survival in one-sided testing with the default value of |
t1 |
pre-specified |
t2 |
pre-specified |
sided |
2 if two-sided test, and 1 if one-sided test.
It assumes the default value of |
nboot |
number of bootstrap replications in calculating critical values
with the defualt value of |
wt |
a string for the integral statistic with a specific weight function.
There are four types of integral statistics provided: |
alpha |
pre-specified significance level of the test with the default value of |
compo |
FALSE if taking the standardized square of the difference as the local statisic
for two-sided testing, and TRUE if constructing for one-sided testing, but only the positive
part of the difference included. It assumes the default value of |
seed |
the parameter with the default value of |
nlimit |
the splitting unit with the default value of |
Details
intELtest
calculates the weighted likelihood ratio statistics:
where are the values of the weight function evaluated at
the distinct ordered uncensored times
in
.
There are four types of weight functions considered.
(
wt = "p.event"
)
This default option is an objective weight,In other words, this
assigns weight proportional to the number of events at each observed uncensored time
.
(
wt = "dF"
)
Based on the integral statistic built by Barmi and McKeague (2013), another weigth function isfor
,where
,
is the pooled KM estimator, and
. This reduces to the objective weight when there is no censoring.The resulting
can be seen as an empirical version of
, where
denotes the lifetime random variable of interest distributed as the common distribution under
.
(
wt = "dt"
)
By means of an extension of the integral statistic derived by Pepe and Fleming (1989), another weight function isfor
, where
. This gives more weight to the time intervals where there are fewer observed uncensored times, but may be affected by extreme observations.
(
wt = "db"
)
According to a weigthing method mentioned in Chang and McKeague (2016), the other weight function iswhere
, and
is given. The
is chosen so that the limiting distribution is the same as the asymptotic null distribution in EL Barmi and McKeague (2013).
Value
intELtest
returns a list with three elements:
-
teststat
the resulting integrated test statistic -
critval
the critical value -
pvalue
the p-value based on the integrated statistic
References
H.-w. Chang and I. W. McKeague, "Empirical likelihood based tests for stochastic ordering under right censorship," Electronic Journal of Statistics, Vol. 10, No. 2, pp. 2511-2536 (2016).
M. S. Pepe and T. R. Fleming, "Weighted Kaplan-Meier Statistics: A Class of Distance Tests for Censored Survival Data," Biometrics, Vol. 45, No. 2, pp. 497-507 (1989). https://www.jstor.org/stable/2531492?seq=1#page_scan_tab_contents
H. Uno, L. Tian, B. Claggett, and L. J. Wei, "A versatile test for equality of two survival functions based on weighted differences of Kaplan-Meier curves," Statistics in Medicine, Vol. 34, No. 28, pp. 3680-3695 (2015). http://onlinelibrary.wiley.com/doi/10.1002/sim.6591/abstract
H. E. Barmi and I. W. McKeague, "Empirical likelihood-based tests for stochastic ordering," Bernoulli, Vol. 19, No. 1, pp. 295-307 (2013). https://projecteuclid.org/euclid.bj/1358531751
See Also
hepatitis
, supELtest
, ptwiseELtest
Examples
library(EL2Surv)
intELtest(hepatitis)
## OUTPUT:
## $teststat
## [1] 1.406016
##
## $critval
## [1] 0.8993514
##
## $pvalue
## [1] 0.012