sampled.kendall.tau {bayesSurv}

Estimate of the Kendall's tau from the bivariate model

Description

This function computes an estimate of the residual (after adjustment for covariates) Kendall's tau for the bivariate survival model fitted using the functions bayesHistogram or bayesBisurvreg.

For both these function their argument prior$specification must be equal to 2!

When G is a bivariate distribution function, the population version of the Kendall's tau is defined as

\tau = 4\int G dG - 1

.

For the model estimated using one of the above mentioned functions the value of Kendall's tau at each iteration of MCMC is equal to

\tau = 4\sum_{i=-K_1}^{K_1}\sum_{j=-K_2}^{K_2}\sum_{k=-K_1}^{K_1}\sum_{l=-K_2}^{K_2}w_{i,j} w_{k,l} \Phi\left(\frac{\mu_{1,i} - \mu_{1,k}}{\sqrt{2}\sigma_1}\right) \Phi\left(\frac{\mu_{2,j} - \mu_{2,l}}{\sqrt{2}\sigma_2}\right) - 1,

where \mu_{1,-K_1},\dots,\mu_{1,K_1} are knots in the first margin, \mu_{2,-K_2},\dots,\mu_{2,K_2} are knots in the second margin, \sigma_1 is the basis standard deviation in the first margin, \sigma_2 is the basis standard deviation in the second margin, and w_{i,j},\;i=-K_1,\dots,K_1,\;j=-K_2,\dots,K_2 are the G-spline weights.

Usage

sampled.kendall.tau(dir = getwd(), extens = "", K,
  skip = 0, by = 1, last.iter, nwrite)

Arguments

dir

directory where to search for files (‘mixmoment.sim’, ‘mweight.sim’, ‘mmean.sim’, ‘gspline.sim’) with the MCMC sample.

extens

an extension used to distinguish different sampled G-splines if more G-splines were used in one simulation (with doubly-censored data) According to which bayes*survreg* function was used, specify the argument extens in the following way.

bayesHistogram:

always extens = ""

bayesBisurvreg:

\quad

• to compute the bivariate distribution of the error term for the onset time: extens = "";

• to compute the bivariate distribution of the error term for the event time if there was doubly-censoring: extens = "_2";

K

a~vector of length 2 specifying the number of knots at each side of the middle knot for each dimension of the G-spline.

skip

number of rows that should be skipped at the beginning of each *.sim file with the stored sample.

by

additional thinning of the sample.

last.iter

index of the last row from *.sim files that should be used. If not specified than it is set to the maximum available determined according to the file mixmoment.sim.

nwrite

frequency with which is the user informed about the progress of computation (every nwriteth iteration count of iterations change).

Value

A vector with sampled values of the Kendall's tau.

Author(s)

Arnošt Komárek [e-mail]

References

Komárek, A. (2006). Accelerated Failure Time Models for Multivariate Interval-Censored Data with Flexible Distributional Assumptions. PhD. Thesis, Katholieke Universiteit Leuven, Faculteit Wetenschappen.

Komárek, A. and Lesaffre, E. (2006). Bayesian semi-parametric accelerated failurew time model for paired doubly interval-censored data. Statistical Modelling, 6, 3 - 22.

Examples

## See the description of R commands for
## the models described in
## Komarek (2006),
## Komarek and Lesaffre (2006),
## 
## R commands available
## in the documentation
## directory of this package
## - see ex-tandmobPA.R and
##   https://www2.karlin.mff.cuni.cz/~komarek/software/bayesSurv/ex-tandmobPA.pdf
##