# mdir.onesided: Two-sample multiple-direction log rank test for stochastic... In mdir.logrank: Multiple-Direction Logrank Test

## 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

 ```1 2 3``` ```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 ≥ 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.

`mdir.onesided`
 ```1 2 3 4 5 6``` ```library(coin) data(GTSG) out <- mdir.onesided(data = GTSG, group1 = "Chemotherapy+Radiation", iter = 1000) ## Detailed information: summary(out) ```