ptwiseELtest {survELtest}

The pointwise EL testing

Description

ptwiseELtest gives pointwise EL testing to compare the survival curves at each time point.

Usage

ptwiseELtest(
  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

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

• call the function call

• result_dataframe a dataframe with time_pts in the first column, decision in the second column, stat_ptwise in the third column and critval_ptwise in the fourth column.

  • time_pts a vector containing the observed uncensored time points at which the Kaplan—Meier estimate is positive and less than 1 for each sample.

  • decision a vector containing the decisions of the pointwise EL tests at time_pts. The decision at each of time_pts is 1 for rejection of the null hypothesis that the survival functions are the same at the specific time point, and 0 otherwise.

  • stat_ptwise a vector containing the pointwise EL statistics at time_pts.

  • critval_ptwise a vector containing the critical values for pointwise EL testing at time_pts.

• formula the value of the input argument of ptwiseELtest

• data the value of the input argument of ptwiseELtest

• group_order the value of the input argument of ptwiseELtest

• t1 the value of the input argument of ptwiseELtest

• t2 the value of the input argument of ptwiseELtest

• sided the value of the input argument of ptwiseELtest

• nboot the value of the input argument of ptwiseELtest

• alpha the value of the input argument of ptwiseELtest

• seed the value of the input argument of ptwiseELtest

• nlimit the value of the input argument of ptwiseELtest

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

See Also

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

Examples

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

## OUTPUT:
## Call:
## ptwiseELtest(formula = survival::Surv(hepatitis$time, hepatitis$censor) ~ 
##     hepatitis$group, sided = 1)
## 
## Range of time_pts is from 5.2 to 153.1
## 30 out of 45 decisions are 1, the other 15 decisions are 0
## -----
## Summary of stat_ptwise:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  
##   0.000   2.293   3.694   4.263   6.288  10.360 
## -----
## Summary of critval_ptwise:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  
##   2.117   2.346   2.483   2.509   2.669   2.951