Description Usage Arguments Details Value Author(s) References See Also Examples
This function generates a posterior density sample for a Linear Dependent Tailfree Process model for conditional survival estimation of time-to-event data.
1 2 3 4 5 |
y |
a vector giving the response variables. |
x |
a matrix giving the design matrix for the median function. |
xtf |
a matrix giving the design matrix for the conditional probabilities. |
prediction |
a list giving the information used to obtain conditional
inferences. The list includes the following
elements: |
prior |
a list giving the prior information. The list includes the following
parameter: |
mcmc |
a list giving the MCMC parameters. The list must include
the following elements: |
state |
a list giving the current value of the parameters. This list is used if the current analysis is the continuation of a previous analysis. |
status |
a logical variable indicating whether this run is new ( |
grid |
vector of grid points where the conditional survival functions are evaluated. The default value is NULL and the grid is chosen according to the range of the data. |
compute.band |
logical variable indicating whether the credible band for the conditional density and mean function must be computed. |
type.band |
string indication the type of credible band to be computed; if equal to "HPD" or "PD" then the 95 percent pointwise HPD or PD band is computed, respectively. |
data |
data frame. |
na.action |
a function that indicates what should happen when the data
contain |
work.dir |
working directory. |
This generic function fits a Linear Dependent Tailfree process (Jara and Hanson, 2011), for (potentially) interval-censored data. Let T_i in R+ be the time-to-event for subject i and set z_i = log T_i. The model for the log time-to.event data is given by:
zi = xi' beta + vi, i=1,…,n
vi | Gxtfi ~ Gxtfi
{Gxtf: xtf in X} | maxm, alpha, sigma2 ~ LDTFP^maxm(h,Pi^{sigma2},\textit{A}^{alpha,rhi})
where, h is the logistic CDF, and Gxtf is median-zero and centered around an N(0,sigma2) distribution. To complete the model specification, independent hyperpriors are assumed,
alpha | a0, b0 ~ Gamma(a0,b0)
sigma^-2 | tau1, tau2 ~ Gamma(tau1/2,tau2/2)
The precision parameter, alpha, of the LDTFP
prior
can be considered as random, having a gamma
distribution, Gamma(a0,b0),
or fixed at some particular value. To let alpha to be fixed at a particular
value, set a0 to NULL in the prior specification.
The computational implementation of the model is based on Slice sampling (Neal, 2003).
An object of class LDTFPsurvival
representing the LDTFP model fit.
Generic functions such as print
, plot
,
and summary
have methods to show the results of the fit. The results include
beta
, alpha
and sigma^2
.
The list state
in the output object contains the current value of the parameters
necessary to restart the analysis. If you want to specify different starting values
to run multiple chains set status=TRUE
and create the list state based on
this starting values. In this case the list state
must include the following objects:
alpha |
a double precision giving the value of the precision parameter. |
betace |
a vector giving the value of the median regression coefficient. |
sigma^2 |
a double precision giving the value of the centering variance. |
betatf |
a matrix giving the regression coefficients for each conditional probability. |
z |
a vector giving the current value of the (imputed) survival times. |
Alejandro Jara <atjara@uc.cl>
Jara, A., Hanson, T. (2011). A class of mixtures of dependent tail-free processes. Biometrika, 98(3): 553 - 566.
Neal, R. (2003) Slice sampling. Anals of Statistics, 31: 705 - 767.
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#############################################################
# Time to Cosmetic Deterioration of Breast Cancer Patients
#############################################################
data(deterioration)
attach(deterioration)
y <- cbind(left,right)
# Design matrix
x <- cbind(rep(1,length(trt)),trt)
xtf <- cbind(rep(1,length(trt)),trt)
colnames(x) <- c("(Intercept)","trt")
colnames(xtf) <- c("(Intercept)","trt")
# Prediction
xdenpred <- cbind(rep(1,2),c(0,1))
xtfdenpred <- cbind(rep(1,2),c(0,1))
xmedpred <- cbind(rep(1,2),c(0,1))
xtfmedpred <- cbind(rep(1,2),c(0,1))
prediction <- list(xdenpred=xdenpred,
xtfdenpred=xtfdenpred,
xmedpred=xmedpred,
xtfmedpred=xtfmedpred,
quans=c(0.03,0.50,0.97))
# Prior information
prior <- list(maxm=5,
a0=1,
b0=1,
mub=rep(0,2),
Sb=diag(1000,2),
tau1=2,002,
tau2=2.002)
# Initial state
state <- NULL
# MCMC parameters
mcmc <- list(nburn=5000,
nsave=5000,
nskip=4,
ndisplay=200)
# Fitting the model
fit1 <- LDTFPsurvival(y=y,
x=x,
xtf=xtf,
prediction=prediction,
prior=prior,
mcmc=mcmc,
state=state,
grid=seq(0.01,70,len=200),
status=TRUE,
compute.band=TRUE)
fit1
summary(fit1)
plot(fit1)
# Plotting survival functions estimates
par(cex=1.7,mar=c(4.1, 4.1, 1, 1))
x1 <- fit1$grid
y1 <- fit1$survml[1,]
x2 <- fit1$grid
y2 <- fit1$survmu[1,]
aa <- rbind(x2,y2)[, order(-x2, y2)]
x2 <- aa[1,]
y2 <- aa[2,]
plot(fit1$grid,fit1$survmu[1,],type="l",
xlab="months",ylab="survival",
lty=1,lwd=2,ylim=c(0,1),col="lightgray")
polygon(x=c(x1,x2),y=c(y1,y2),border=NA,col="lightgray")
lines(fit1$grid,fit1$survmm[1,],lty=1,lwd=3)
par(cex=1.7,mar=c(4.1, 4.1, 1, 1))
x1 <- fit1$grid
y1 <- fit1$survml[2,]
x2 <- fit1$grid
y2 <- fit1$survmu[2,]
aa <- rbind(x2,y2)[, order(-x2, y2)]
x2 <- aa[1,]
y2 <- aa[2,]
plot(fit1$grid,fit1$survmu[2,],type="l",
xlab="months",ylab="survival",
lty=1,lwd=2,ylim=c(0,1),col="lightgray")
polygon(x=c(x1,x2),y=c(y1,y2),border=NA,col="lightgray")
lines(fit1$grid,fit1$survmm[2,],lty=1,lwd=3)
## End(Not run)
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