ipcw.dcor {dcortools}

Calculates an inverse-probability-of-censoring weighted (IPCW) distance correlation based on IPCW U-statistics (Datta et al. 2010).

Description

Calculates an inverse-probability-of-censoring weighted (IPCW) distance correlation based on IPCW U-statistics (Datta et al. 2010).

Usage

ipcw.dcor(
  Y,
  X,
  affine = FALSE,
  standardize = FALSE,
  timetrafo = "none",
  type.X = "sample",
  metr.X = "euclidean",
  use = "all",
  cutoff = NULL
)

Arguments

Y

A matrix with two columns, where the first column contains the survival times and the second column the status indicators (a survival object will work).

X

A vector or matrix containing the covariate information.

affine

logical; specifies if X should be transformed such that the result is invariant under affine transformations of X

standardize

logical; should X be standardized using the standard deviations of single observations?. No effect when affine = TRUE.

timetrafo

specifies a transformation applied on the follow-up times. Can be "none", "log" or a user-specified function.

type.X

For "distance", X is interpreted as a distance matrix. For "sample", X is interpreted as a sample.

metr.X

specifies the metric which should be used to compute the distance matrix for X (ignored when type.X = "distance").

Options are "euclidean", "discrete", "alpha", "minkowski", "gaussian", "gaussauto", "boundsq" or user-specified metrics (see examples).

For "alpha", "minkowski", "gaussian", "gaussauto" and "boundsq", the corresponding parameters are specified via "c(metric,parameter)", c("gaussian",3) for example uses a Gaussian metric with bandwidth parameter 3; the default parameter is 2 for "minkowski" and "1" for all other metrics.

use

specifies how to treat missing values. "complete.obs" excludes observations containing NAs, "all" uses all observations.

cutoff

If provided, all survival times larger than cutoff are set to the cutoff and all corresponding status indicators are set to one. Under most circumstances, choosing a cutoff is highly recommended.

Value

An inverse-probability of censoring weighted estimate for the distance correlation between X and the survival times.

References

Bottcher B, Keller-Ressel M, Schilling RL (2018). “Detecting independence of random vectors: generalized distance covariance and Gaussian covariance.” Modern Stochastics: Theory and Applications, 3, 353–383.

Datta S, Bandyopadhyay D, Satten GA (2010). “Inverse Probability of Censoring Weighted U-statistics for Right-Censored Data with an Application to Testing Hypotheses.” Scandinavian Journal of Statistics, 37(4), 680–700.

Dueck J, Edelmann D, Gneiting T, Richards D (2014). “The affinely invariant distance correlation.” Bernoulli, 20, 2305–2330.

Huo X, Szekely GJ (2016). “Fast computing for distance covariance.” Technometrics, 58(4), 435–447.

Lyons R (2013). “Distance covariance in metric spaces.” The Annals of Probability, 41, 3284–3305.

Sejdinovic D, Sriperumbudur B, Gretton A, Fukumizu K (2013). “Equivalence of distance-based and RKHS-based statistics in hypothesis testing.” The Annals of Statistics, 41, 2263–2291.

Szekely GJ, Rizzo ML, Bakirov NK (2007). “Measuring and testing dependence by correlation of distances.” The Annals of Statistics, 35, 2769–2794.

Szekely GJ, Rizzo ML (2009). “Brownian distance covariance.” The Annals of Applied Statistics, 3, 1236–1265.

Examples

X <- rnorm(100)
survtime <- rgamma(100, abs(X))
cens <- rexp(100)
status <- as.numeric(survtime < cens)
time <- sapply(1:100, function(u) min(survtime[u], cens[u]))
surv <- cbind(time, status)
ipcw.dcor(surv, X)