bayesGspline {bayesSurv}

Summary for the density estimate based on the model with Bayesian G-splines.

Description

Compute the estimate of the density function based on the values sampled using the MCMC (MCMC average evaluated in a grid of values) in a model where density is specified as a Bayesian G-spline.

This function serves to summarize the MCMC chains related to the distributional parts of the considered models obtained using the functions: bayesHistogram, bayesBisurvreg, bayessurvreg2, bayessurvreg3.

If asked, this function returns also the values of the G-spline evaluated in a grid at each iteration of MCMC.

Usage

bayesGspline(dir, extens="", extens.adjust="_b",
   grid1, grid2, skip = 0, by = 1, last.iter, nwrite,
   only.aver = TRUE, standard = FALSE, version = 0)

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 (e.g. with doubly-censored data or in the model where both the error term and the random intercept were defined as the G-splines). According to which bayes*survreg* function was used, specify the argument extens in the following way.

bayesHistogram:

always extens = ""

bayesBisurvreg:

• 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";

bayessurvreg2:

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

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

bayessurvreg3:

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

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

• to compute the distribution of the random intercept for the onset time: extens = "_b";

• to compute the distribution of the random intercept term for the event time if there was doubly-censoring: extens = "_b2";

extens.adjust

this argument is applicable for the situation when the MCMC chains were created using the function bayessurvreg3, and when both the distribution of the error term and the random intercept was specified as the G-spline.

In that case the location of the error term and the random intercept are separately not identifiable. Only the location of the sum \varepsilon + b can be estimated. For this reason, the function bayesGspline always centers the distribution of the random intercept to have a zero mean and adds its original mean to the mean of the distribution of the error term.

Argument extens.adjust is used to match correctly the files containing the G-spline of the random intercept corresponding to the particular error term.

The following values of extens.adjust should be used in the following situations:

• if there are no doubly-censored data or if we are computing the distribution of the error term/random intercept from the model for the onset time then

  extens.adjust = "_b"

• if there are doubly-censored data and we are computing the distribution of the error term/random intercept from the model for the event time then

  extens.adjust = "_b2"

grid1

grid of values from the first dimension at which the sampled densities are to be evaluated.

grid2

grid of values from the second dimension (if the G-spline was bivariate) at which the sampled densities are to be evaluated. This item is missing if the G-spline is univariate.

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).

only.aver

TRUE/FALSE, if TRUE only MCMC average is returned otherwise also values of the G-spline at each iteration are returned (which might ask for quite lots of memory).

standard

TRUE/FALSE, if TRUE, each G-spline is standardized to have zero mean and unit variance. Only applicable if version = 30 or 31, otherwise standard is always set to FALSE.

version

this argument indicates by which bayes*survreg* function the chains used by bayesGspline were created. Use the following:

bayesHistogram:

version = 0;

bayesBisurvreg:

version = 0;

bayessurvreg2:

version = 0;

bayessurvreg3:

version = 30 or 31.

Use version = 30 if you want to compute the density of the error term.

Use version = 31 if you want to compute the density of the random intercept.

Use version = 32 if you want to compute the density of the error term in the model with doubly-interval-censored data and bivariate normal distribution for random intercepts in the onset and time-to-event parts of the model OR if you have just interval-censored data and a simple AFT model without random effects and you want to compute the density of the error term of the model.

Value

An object of class bayesGspline is returned. This object is a list with components grid, average for the univariate G-spline and components grid1, grid2, average for the bivariate G-spline.

grid

this is a grid of values (vector) at which the McMC average of the G-spline was computed.

average

these are McMC averages of the G-spline (vector) evaluated in grid.

grid1

this is a grid of values (vector) for the first dimension at which the McMC average of the G-spline was computed.

grid2

this is a grid of values (vector) for the second dimension at which the McMC average of the G-spline was computed.

average

this is a matrix length(grid1) times length(grid2) with McMC averages of the G-spline evaluated in

x1 =	( grid1	...	grid1 )

and

	(	grid2	)
x2 =	(	...	)
	(	grid2	)

There exists a method to plot objects of the class bayesGspline.

Attributes

Additionally, the object of class bayesGspline has the following attributes:

sample.size

a length of the McMC sample used to compute the McMC average.

sample

G-spline evaluated in a grid of values. This attribute is present only if only.aver = FALSE.

For a univariate G-spline this is a matrix with sample.size columns and length(grid1) rows.

For a bivariate G-spline this is a matrix with sample.size columns and length(grid1)*length(grid2) rows.

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.

Komárek, A. and Lesaffre, E. (2008). Bayesian accelerated failure time model with multivariate doubly-interval-censored data and flexible distributional assumptions. Journal of the American Statistical Association, 103, 523–533.

Komárek, A., Lesaffre, E., and Legrand, C. (2007). Baseline and treatment effect heterogeneity for survival times between centers using a random effects accelerated failure time model with flexible error distribution. Statistics in Medicine, 26, 5457–5472.

Examples

## See the description of R commands for
## the models described in
## Komarek (2006),
## Komarek and Lesaffre (2006),
## Komarek and Lesaffre (2008),
## Komarek, Lesaffre, and Legrand (2007).
## 
## R commands available
## in the documentation
## directory of this package
##  - ex-tandmobPA.R and
##    https://www2.karlin.mff.cuni.cz/~komarek/software/bayesSurv/ex-tandmobPA.pdf
##  - ex-tandmobCS.R and
##    https://www2.karlin.mff.cuni.cz/~komarek/software/bayesSurv/ex-tandmobCS.pdf
##  - ex-eortc.R and
##    https://www2.karlin.mff.cuni.cz/~komarek/software/bayesSurv/ex-eortc.pdf
##