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

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((mu[1,i] - mu[1,k])/(sqrt(2)*sigma[1])) * Phi((mu[2,j] - mu[2,l])/(sqrt(2)*sigma[2])) - 1,

where mu[1,-K[1]],...,mu[1,K[1]] are knots in the first margin, mu[2,-K[2]],...,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],...,K[1], j=-K[2],...,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 `nwrite`th iteration count of iterations change).

### Value

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

### Author(s)

Arnost Komarek arnost.komarek@med.kuleuven.be

### References

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

Komarek, A. and Lesaffre, E. (2006b). Bayesian semiparametric accelerated failurew time model for paired doubly-interval-censored data. Submitted.
See `Komarek_Lesaffre_2006b.pdf`.

### Examples

    ## See the description of R commands for
    ## the models described in
    ## Komarek (2006),
    ## Komarek and Lesaffre (2006b),
    ##
    ## R commands available
    ## in the documentation
    ## directory of this package
    ##    tandmobPA.pdf, tandmobPA.R.
    ##

[Package bayesSurv version 0.4 Index]