nocrossings {survELtest}

The test that excludes the possibility of crossings or alternative orderings among the survival functions

Description

The test nocrossings should be used before one-sided testing via intELtest or supELtest to exclude the possibility of crossings or alternative orderings among the survival functions.

Usage

nocrossings(
  formula,
  data = NULL,
  group_order = NULL,
  t1 = 0,
  t2 = Inf,
  sided = 2,
  nboot = 1000,
  alpha = 0.05,
  seed = 1011,
  nlimit = 200
)

Arguments

formula

a formula object with a Surv object as the response on the left of the ~ operator and the grouping variable as the term on the right. The Surv object involves two variables: the observed survival and censoring times, and the censoring indicator, which takes a value of 1 if the observed time is uncensored and 0 otherwise. The grouping variable takes different values for different groups.

data

an optional data frame containing the variables in the formula: the observed survival and censoring times, the censoring indicator, and the grouping variable. If not found in data, the variables in the formula should be already defined by the user or in attached R objects. The default is the data frame with three columns of variables taken from the formula: column 1 contains the observed survival and censoring times, column 2 the censoring indicator, and column 3 the grouping variable.

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,\ldots,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 \infty.

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.

alpha

the pre-specified significance level of the tests. The default value is 0.05.

seed

the seed for the random number generator in R, for generating bootstrap samples needed to calculate the critical values for the tests. The default value is 1011.

nlimit

a number used to calculate nsplit= m/nlimit, the number of parts into which the calculation of the nboot bootstrap replications is split. The use of this variable can make computation faster when the number of time points m is large. The default value for nlimit is 200.

Value

nocrossings returns a nocrossings object, a list with 12 elements:

• call the function call

• decision 1 for rejection of the null hypothesis that there are crossings or alternative orderings among the survival functions, and 0 otherwise

• formula the value of the input argument of nocrossings

• data the value of the input argument of nocrossings

• group_order the value of the input argument of nocrossings

• t1 the value of the input argument of nocrossings

• t2 the value of the input argument of nocrossings

• sided the value of the input argument of nocrossings

• nboot the value of the input argument of nocrossings

• alpha the value of the input argument of nocrossings

• seed the value of the input argument of nocrossings

• nlimit the value of the input argument of nocrossings

Methods defined for nocrossings objects are provided for print and summary.

References

• H. Chang, 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).

• 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).

See Also

hepatitis, intELtest, supELtest, ptwiseELtest, print.nocrossings, summary.nocrossings

Examples

library(survELtest)
nocrossings(survival::Surv(hepatitis$time, hepatitis$censor)~
    hepatitis$group, sided = 1)

## OUTPUT:
## Call:
## nocrossings(formula = survival::Surv(hepatitis$time, hepatitis$censor) ~ 
##     hepatitis$group, sided = 1)
## 
## Decision = 1