predictive2 {bayesSurv}

Compute predictive quantities based on a Bayesian survival regression model fitted using bayesBisurvreg or bayessurvreg2 or bayessurvreg3 functions.

Description

This function computes predictive densities, survivor and hazard curves for specified combinations of covariates.

Firstly, either the function bayesBisurvreg or the function bayessurvreg2 or the function bayessurvreg3 has to be used to obtain a sample from the posterior distribution of unknown quantities.

Function predictive2.control serves only to perform some input checks inside the main function predictive2.

Usage

predictive2(formula, random, obs.dim, time0, data = parent.frame(),
     grid, na.action = na.fail, Gspline,
     quantile = c(0, 0.025, 0.5, 0.975, 1),
     skip = 0, by = 1, last.iter, nwrite,
     only.aver = TRUE,
     predict = list(density=FALSE, Surv=TRUE,
                    hazard=FALSE, cum.hazard=FALSE),
     dir, extens = "", extens.random="_b", version=0)

predictive2Para(formula, random, obs.dim, time0, data = parent.frame(),
     grid, na.action = na.fail, Gspline,
     quantile = c(0, 0.025, 0.5, 0.975, 1),
     skip = 0, by = 1, last.iter, nwrite,
     only.aver = TRUE,
     predict = list(density=FALSE, Surv=TRUE,
                    hazard=FALSE, cum.hazard=FALSE),
     dir, extens = "", extens.random="_b", version=0)

predictive2.control(predict, only.aver, quantile, obs.dim,
     time0, Gspline, n)

Arguments

formula

the same formula as that one used to sample from the posterior distribution of unknown quantities by the function bayesBisurvreg or bayessurvreg2 or bayessurvreg3. On the left hand side whichever Surv object of a~proper length can be used (it is ignored anyway).

REMARK: the prediction must be asked for at least two combinations of covariates. This is the restriction imposed by one of the internal functions I use.

random

the same random statement as that one used to sample from the posterior distribution of unknown quantities by the function bayessurvreg2 or bayessurvreg3, not applicable if bayesBisurvreg was used to sample from the posterior distribution.

obs.dim

a vector that has to be supplied if bivariate data were used for estimation (using the function bayesBisurvreg). This vector has to be of the same length as the number of covariate combinations for which the predictive quantities are to be computed. It determines to which dimension (1 or 2) each observation belong.

time0

a~vector of length Gspline$dim giving the starting time for the survival model. It does not have to be supplied if equal to zero (usually). This option is used to get hazard and density functions on the original time scale in the case that the model was \log(T-time0) = \dots. Note that time0 IS NOT the starting time of doubly censored observation since there after subtracting the onset time, the starting time is (usually) equal to zero.

data

optional data frame in which to interpret the variables occuring in the formulas. Usually, you create a new data.frame similar to that one used to obtain a sample from the posterior distribution. In this new data.frame, put covariate values equal to these for which predictive quantities are to be obtained. If cluster statement was used, assign a unique cluster identification to each observation. Response variable and a censoring indicator may be set to arbitrary values. They are only used in formula but are ignored for computation.

grid

a~vector giving the grid of values where predictive quantities are to be evaluated. The grid should normally start at some value slightly higher than time0.

na.action

function to be used to handle any NAs in the data. The user is discouraged to change a default value na.fail.

Gspline

a~list specifying the G-spline used for the error distribution in the model. It is a~list with the following components:

dim

dimension of the G-spline, in the case when the function bayesBisurvreg was used to fit the model this will usually be equal to 2, in the case when the function bayessurvreg2 was used to fit the model this MUST be equal to 1.

K

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

quantile

a vector of quantiles that are to be computed for each predictive quantity.

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

if TRUE only posterior predictive mean is computed for all quantities and no quantiles.

The word of warning: with only.aver set to FALSE, all quantities must be stored for all iterations of the MCMC to be able to compute the quantiles. This might require quite lots of memory.

predict

a list of logical values indicating which predictive quantities are to be computed. Components of the list:

density

predictive density

Surv

predictive survivor functions

hazard

predictive hazard functions

cum.hazard

predictive cumulative hazard functions

dir

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

extens

an extension used to distinguish different sampled G-splines if more formulas were used in one MCMC simulation (e.g. with doubly-censored data).

• if the data were not doubly-censored or if you wish to compute predictive quantities for the onset time of the doubly-censored data then

  extens = ""

• if the data were doubly-censored and you wish to compute predictive quantities for the event time then

  extens = "_2"

extens.random

only applicable if the function bayessurvreg3 was used to generate the MCMC sample.

This is an extension used to distinguish different sampled G-splines determining the distribution of the random intercept (under the presence of doubly-censored data).

• if the data were not doubly-censored or if you wish to compute predictive quantities for the onset time of the doubly-censored data then

  extens.random = "_b"

• if the data were doubly-censored and you wish to compute predictive quantities for the event time then

  extens.random = "_b2"

version

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

bayesBisurvreg:

version = 0;

bayessurvreg2:

version = 0;

bayessurvreg3:

with all distributions specified as G-splines: version = 3;

bayessurvreg3:

with error distributions specified as G-splines and bivariate normal random intercepts: version = 32.

n

number of covariate combinations for which the prediction will be performed.

Value

A list with possibly the following components (what is included depends on the value of the arguments predict and only.aver):

grid

a~vector with the grid values at which the survivor function, survivor density, hazard and cumulative hazard are computed.

Surv

predictive survivor functions.

A~matrix with as many columns as length(grid) and as many rows as the number of covariate combinations for which the predictive quantities were asked. One row per covariate combination.

density

predictive survivor densities.

The same structure as Surv component of the list.

hazard

predictive hazard functions.

The same structure as Surv component of the list.

cum.hazard

predictive cumulative hazard functions.

The same structure as Surv component of the list.

quant.Surv

pointwise quantiles for the predictive survivor functions.

This is a list with as many components as the number of covariate combinations. One component per covariate combination.

Each component of this list is a~matrix with as many columns as length(grid) and as many rows as the length of the argument quantile. Each row of this matrix gives values of one quantile. The rows are also labeled by the probabilities (in %) of the quantiles.

quant.density

pointwise quantiles for the predictive survivor densities.

The same structure as quant.Surv component of the list.

quant.hazard

pointwise quantiles for the predictive hazard functions.

The same structure as quant.Surv component of the list.

quant.cum.hazard

pointwise quantiles for the predictive cumulative hazard functions.

The same structure as quant.Surv component of the list.

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

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