casanova {GFDsurv}

CASANOVA: Cumulative Aalen survival analyis-of-variance

Description

The function casanova calculates the Wald-type statistic based on the combination of differently weighted Nelson-Aalen-type integrals. Respective p-values are obtained by a \chi^2-approximation and a permutation approach, respectively.

Usage

casanova(
  formula,
  event = "event",
  data = NULL,
  nperm = 1999,
  cross = TRUE,
  nested.levels.unique = FALSE,
  rg = list(c(0, 0))
)

Arguments

formula

A model formula object. The left hand side contains the time variable and the right hand side contains the factor variables of interest. An interaction term must be specified.

event

The name of censoring status indicator with values 0=censored and 1=uncensored. The default choice is "event"

data

A data.frame, list or environment containing the variables in formula and the censoring status indicator. Default option is NULL.

nperm

The number of permutations used for calculating the permuted p-value. The default option is 1999.

cross

logical. Should the crossing weight w(x) = 1 - 2x be included? The default is TRUE.

nested.levels.unique

A logical specifying whether the levels of the nested factor(s) are labeled uniquely or not. Default is FALSE, i.e., the levels of the nested factor are the same for each level of the main factor.

rg

A list containing the exponents c(r, g) of the weights w(x) = x^r (1-x)^g. Both exponents need to be natural numbers including 0. Default is list( c(0, 0) ) corresponding to the log-rank weight.

Details

The casanova function calculates the Wald-type statistic of weighted Nelson-Aalen type integrals for general factorial survival designs. Crossed as well as hierachically nested designs are implemented. Moreover, the approach allows the combination of different weights into a joint statistic. The user can choose between weights of the following form: w(x) = 1 - 2x (cross = TRUE) and w(x) = x^r * (1-x)^g for natural numbers r,g (including 0). The function automatically check whether the specified weights fulfill the linear independence assumption and choose a subset of linearly independent weights if the original weights violate the aforemention assumption.

The casanova function returns the test statistic as well as two corresponding p-values: the first is based on a \chi^2 approximation and the second one is based on a permutation procedure.

Value

A casanova object containing the following components:

pvalues_stat

The p-values obtained by \chi^2-approximation

pvalues_per

The p-values of the permutation approach

statistics

The value of the casanova along with degrees of freedom of the central chi-square distribution and p-value, as well as the p-value of the permutation procedure.

rg

A list containing the exponents of the direction considered in the statistical analysis

cross

logical. Was the crossing direction considered in the statistical analysis

indep

logical. Were the directions specified by the user linearly independent?

nperm

The number of permutations used for calculating the permuted p-value.

References

Ditzhaus, M., Janssen, A. and Pauly, M. (2020). Permutation inference in factorial survival designs with the CASANOVA. ArXiv preprint (arXiv:2004.10818v2).

Examples

library("survival")
data(veteran)
out <- casanova(formula ="time ~ trt*celltype",event = "status",
 data = veteran)

## Detailed informations:
summary(out)