Description Usage Arguments Details Value References See Also Examples
intELtest
gives a class of integrated EL statistics:
∑_{i=1}^{m}w_i\cdot \{-2\log R(t_i)\},
where R(t) is the EL ratio that compares the survival functions at each given time t, w_i is the weight at each t_i, and 0<t_1<…<t_m<∞ are the (ordered) observed uncensored times at which the Kaplan–Meier estimate is positive and less than 1 for each sample.
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formula |
a formula object with a |
data |
an optional data frame containing the variables in the |
group_order |
a k-vector containing the values of the grouping variable, with the j-th element being the group hypothesized to have the j-th highest survival rates, j=1,…,k. The default is the vector of sorted grouping variables. |
t1 |
the first endpoint of a prespecified time interval, if any, to which the comparison of the survival functions is restricted. The default value is 0. |
t2 |
the second endpoint of a prespecified time interval, if any, to which the comparison of the survival functions is restricted. The default value is ∞. |
sided |
2 if two-sided test, and 1 if one-sided test. The default value is 2. |
nboot |
the number of bootstrap replications in calculating critical values for the tests. The default value is 1000. |
wt |
the name of the weight for the integrated EL statistics:
|
alpha |
the pre-specified significance level of the tests. The default value is 0.05. |
seed |
the seed for the random number generator in |
nlimit |
a number used to calculate |
There are three options for the weight w_i:
(wt = "p.event"
)
This default option is an objective weight,
w_i=\frac{d_i}{n},
which assigns weight proportional to the number of events d_i at each observed uncensored time t_i. Here n is the total sample size.
(wt = "dF"
)
Inspired by the integral-type statistics considered in Barmi and McKeague (2013),
another weigth function is
w_i= \hat{F}(t_i)-\hat{F}(t_{i-1}),
for i=1,…,m, where \hat{F}(t)=1-\hat{S}(t), \hat{S}(t) is the pooled KM estimator, and t_0 \equiv 0. This reduces to the objective weight when there is no censoring. The resulting I_n can be seen as an empirical version of the expected negative two times log EL ratio under H_0.
(wt = "dt"
)
Inspired by the integral-type statistics considered in Pepe and Fleming (1989), another weight function is
w_i= t_{i+1}-t_i,
for i=1,…,m, where t_{m+1} \equiv t_{m}. This gives more weight to the time intervals where there are fewer observed uncensored times, but can be affected by extreme observations.
intELtest
returns a intELtest
object, a list with 15 elements:
call
the function call
teststat
the resulting integrated EL statistics
critval
the critical value based on bootstrap
pvalue
the p-value of the test
formula
the value of the input argument of intELtest
data
the value of the input argument of intELtest
group_order
the value of the input argument of intELtest
t1
the value of the input argument of intELtest
t2
the value of the input argument of intELtest
sided
the value of the input argument of intELtest
nboot
the value of the input argument of intELtest
wt
the value of the input argument of intELtest
alpha
the value of the input argument of intELtest
seed
the value of the input argument of intELtest
nlimit
the value of the input argument of intELtest
Methods defined for intELtest
objects are provided for print
and summary
.
H. Chang, I.W. McKeague, "Nonparametric testing for multiple survival functions with non-inferiority margins," Annals of Statistics, Vol. 47, No. 1, pp. 205-232, (2019).
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. 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
hepatitis
, supELtest
, ptwiseELtest
, nocrossings
, print.intELtest
, summary.intELtest
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