# condKendall: Conditional Kendall's tau In stc04003/tranSurv: Estimating a Survival Distribution in the Presence of Dependent Left Truncation and Right Censoring

## Description

Computes the Conditional Kendall's Tau and Inference

## Usage

 1 2 condKendall(trun, obs, delta = NULL, method = "MB", weights = NULL, a = 0, trans = "linear", ...) 

## Arguments

 trun left truncation time satisfying trun <= obs. obs observed failure time, must be the same length as trun, might be right-censored. delta an optional 0-1 vector of censoring indicator (0 = censored, 1 = event) for obs. If this vector is not specified, condKendall assumes no censoring and all observed failure time denote events. method a character string specifying the different version of conditional Kendall's tau to be computed. The following are permitted: MBconditional Kendall's tau proposed in Martin and Betensky (2005) as \hat{τ_c} , IPW1inverse probability weighted estimator proposed in Austin and Betensky (2014) as \hat{τ_{c2}} , IPW2restricted inverse probability weighted estimator proposed in Austin and Betensky (2014) as \hat{τ_{c3}} . weights an optional vector of sampling weights used when method = IPW1 or method = IPW2. Inverse probability censored weighting (IPCW) is the default. a a numeric transformation parameter. The default value is 0, which applies no transformation. This parameter must be greater than -1. See ?tranSurvfit for the transformation model structure. trans a character string specifying the transformation structure. The following are permitted: linearlinear transformation structure, loglog-linear transformation structure, expexponential transformation structure. ... for future methods.

## Details

This function performs statistical test for quasi-independence between truncation time and failure time. The hypothesis test is based on the conditional Kendall's tau of Martin and Betensky (2005) and the two versions of the inverse probability weighted Kendall's tau of Austin and Betensky (2014).

The output contains the following components:

PE

consistent point estimate of the conditional Kendall's tau.

SE

asymptotic standard error of the conditional Kendall's tau estimator.

STAT

the value of the normal test statistic.

p.value

the (Wald) p-value of the test.

trans

the transformation model (if applied).

a

the estimated transformation parameter.

## References

Martin E. and Betensky R. A. (2005), Testing quasi-independence of failure and truncation times via conditional Kendall's tau, Journal of the American Statistical Association, 100 (470): 484-492.

Austin, M. D. and Betensky R. A. (2014), Eliminating bias due to censoring in Kendall's tau estimators for quasi-independence of truncation and failure, Computational Statistics & Data Analysis, 73: 16-26.

trSurvfit

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ## Generate simulated data from transformation model datgen <- function(n) { a <- -0.3 X <- rweibull(n, 2, 4) ## failure times U <- rweibull(n, 2, 1) ## latent truncation time T <- (1 + a) * U - a * X ## apply transformation C <- 10 ## censoring dat <- data.frame(trun = T, obs = pmin(X, C), delta = 1 * (X <= C)) return(subset(dat, trun <= obs)) } set.seed(123) dat <- datgen(300) with(dat, condKendall(trun, obs, delta)) with(dat, condKendall(trun, obs, delta, method = "IPW1")) with(dat, condKendall(trun, obs, delta, method = "IPW2")) 

stc04003/tranSurv documentation built on Oct. 22, 2018, 7:26 p.m.