mdir.onesided {mdir.logrank}

Two-sample multiple-direction log rank test for stochastic ordered alternatives

Description

The mdir.onesided function calculates the multiple-direction logrank statistic for (one-sided) stochastic ordered alternatives and its p-value based on a wild bootstrap approach

Usage

mdir.onesided(data, group1, rg = list(c(0, 0), c(0, 4), c(4, 0)),
  w.user = NA, wild = "rade", iter = 10000, dig_p = 3,
  dig_stat = 3)

Arguments

data

A data.frame, list or environment containing the variables time, event (with values 0 for censored and 1 for uncensored) and group.

group1

The name or the coding for the first group in the data set (neceassary for a one-sided testing problem).

rg

A list containing the exponents c(r, g) of the directions w(x) = x^r (1-x)^g or NA. Both exponents r,g need to be natural numbers including 0. Default is list(c(0, 0), c(0, 4), c(4, 0)) corresponding to the choice of the proportional, early and late direction/weight.

w.user

A list containing the user specified functions or NA (default).

wild

The wild bootstrap approach used for estimating the p-value. The Rademacher (rade, default), the normal distribution (norm) or the centred Poisson distribution (pois) approach can be selected.

iter

The number of iteration used for calculating the wild bootstrap p-value. The default option is 10000.

dig_p

The p-values are rounded to dig_p digits, the default is 3.

dig_stat

The test statistic is rounded to dig_stat digits, the default is 3.

Details

The function provides the multiple-direction logrank statistic for the two sample one-sided testing problem of stochastic ordering within right-censored survival data. The null hypothesis H:F_1=F_2 is tested against the one-sided alternative K:F_1 \ge F_2, F_1 \neq F_2. The first group corresponding to F_1 can be specified by the argument group1. An arbitrary amount of directions/weights of the form w(x) = x^r (1-x)^g for natural numbers r,g (including 0) can be chosen in the list rg. The multiple-direction onesided logrank test needs linearly independent directions. A check for this is implemented. If the directions chosen by the user are linearly dependent then a subset consisting of linearly independent directions is selected automatically. The user can also specify weights of a different shape in the list w.user. But if the user specified own weights in w.user then there is no automatic check for linear independence.

The mdir.onesided function returns the test statistic and the p-value based on a wild bootstrap procedure wild.

Value

An mdirone object containing the following components:

Descriptive

The directions used and whether the directions specified by the user were linearly independent.

p.value

The p-value of the one-sided multiple-direction logrank test using the the using the permutation approach (Perm.).

wild

The wild bootstrap approach which was used

stat

Value of the one-sided multiple-direction logrank statistic.

rg

The argument rg.

w.user

The argument w.user.

group1

The name of the first group.

indep

logical or NA. indep=TRUE/FALSE when the directions specified by rg were linearly independent. indep=NA when rg=NA.

iter

The number of iterations used for calculating the wild bootstrap p-value.

References

Ditzhaus, M., Pauly, M. (2018). Wild bootstrap logrank tests with broader power functions for testing superiority. arXiv preprint arXiv:arXiv:1808.05627.

See Also

mdir.onesided

Examples

library(coin)
data(GTSG)
out <- mdir.onesided(data = GTSG, group1 = "Chemotherapy+Radiation", iter = 1000)

## Detailed information:
summary(out)