sampled.kendall.tau {bayesSurv}  R Documentation 
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 Gspline 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
Gsplines if more Gsplines were used in one simulation (with
doublycensored data) According to which

K 
a~vector of length 2 specifying the number of knots at each side of the middle knot for each dimension of the Gspline. 
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 
nwrite 
frequency with which is the user informed about the
progress of computation (every 
Value
A vector with sampled values of the Kendall's tau.
Author(s)
Arnošt Komárek arnost.komarek@mff.cuni.cz
References
Komárek, A. (2006). Accelerated Failure Time Models for Multivariate IntervalCensored Data with Flexible Distributional Assumptions. PhD. Thesis, Katholieke Universiteit Leuven, Faculteit Wetenschappen.
Komárek, A. and Lesaffre, E. (2006). Bayesian semiparametric accelerated failurew time model for paired doubly intervalcensored 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 extandmobPA.R and
## https://www2.karlin.mff.cuni.cz/~komarek/software/bayesSurv/extandmobPA.pdf
##