BayesSurv_AFT: The function to implement Bayesian parametric and...
In SemiCompRisks: Hierarchical Models for Parametric and Semi-Parametric Analyses of Semi-Competing Risks Data

Description Usage Arguments Details Value Author(s) References See Also Examples

Independent univariate survival data can be analyzed using AFT models that have a hierarchical structure. The proposed models can accomodate left-truncated and/or interval-censored data. An efficient computational algorithm that gives users the flexibility to adopt either a fully parametric (log-Normal) or a semi-parametric (Dirichlet process mixture) model specification is developed.

1 2	BayesSurv_AFT(Formula, data, model = "LN", hyperParams, startValues, mcmcParams, na.action = "na.fail", subset=NULL, path=NULL)

`Formula`	a `Formula` object, with the outcomes on the left of a \sim, and covariates on the right. It is of the form, left truncation time \| interval- (or right-) censored time to event \sim covariates : i.e., L \| y_{L}+y_{U} ~ x.
`data`	a data.frame in which to interpret the variables named in `Formula`.
`model`	The specification of baseline survival distribution: "LN" or "DPM".
`hyperParams`	a list containing lists or vectors for hyperparameter values in hierarchical models. Components include, `LN` (a list containing numeric vectors for log-Normal hyperparameters: `LN.ab`), `DPM` (a list containing numeric vectors for DPM hyperparameters: `DPM.mu`, `DPM.sigSq`, `DPM.ab`, `Tau.ab`). See Details and Examples below.
`startValues`	a list containing vectors of starting values for model parameters. It can be specified as the object returned by the function `initiate.startValues_AFT`.
`mcmcParams`	a list containing variables required for MCMC sampling. Components include, `run` (a list containing numeric values for setting for the overall run: `numReps`, total number of scans; `thin`, extent of thinning; `burninPerc`, the proportion of burn-in). `tuning` (a list containing numeric values relevant to tuning parameters for specific updates in Metropolis-Hastings (MH) algorithm: `beta.prop.var`, the variance of proposal density for β; `mu.prop.var`, the variance of proposal density for μ; `zeta.prop.var`, the variance of proposal density for 1/σ^2).
`na.action`	how NAs are treated. See `model.frame`.
`subset`	a specification of the rows to be used: defaults to all rows. See `model.frame`.
`path`	the name of directory where the results are saved.

The function BayesSurv_AFT implements Bayesian semi-parametric (DPM) and parametric (log-Normal) models to univariate time-to-event data in the presence of left-truncation and/or interval-censoring. Consider a univariate AFT model that relates the covariate x_i to survival time T_i for the i^{\textrm{th}} subject:

\log(T_i) = x_i^{\top}β + ε_i,

where ε_i is a random variable whose distribution determines that of T_i and β is a vector of regression parameters. Considering the interval censoring, the time to the event for the i^{\textrm{th}} subject satisfies c_{ij}≤q T_i <c_{ij+1}. Let L_i denote the left-truncation time. For the Bayesian parametric analysis, we take ε_i to follow the Normal(μ, σ^2) distribution for ε_i. The following prior distributions are adopted for the model parameters:

π(β, μ) \propto 1,

σ^2 \sim \textrm{Inverse-Gamma}(a_{σ}, b_{σ}).

For the Bayesian semi-parametric analysis, we assume that ε_i is taken as draws from the DPM of normal distributions:

ε\sim DPM(G_0, τ).

We refer readers to print.Bayes_AFT for a detailed illustration of DPM specification. We adopt a non-informative flat prior on the real line for the regression parameters β and a Gamma(a_{τ}, b_{τ}) hyperprior for the precision parameter τ.

BayesSurv_AFT returns an object of class Bayes_AFT.

Kyu Ha Lee and Sebastien Haneuse
Maintainer: Kyu Ha Lee <klee15239@gmail.com>

Lee, K. H., Rondeau, V., and Haneuse, S. (2017), Accelerated failure time models for semicompeting risks data in the presence of complex censoring, Biometrics, 73, 4, 1401-1412.

Alvares, D., Haneuse, S., Lee, C., Lee, K. H. (2019), SemiCompRisks: An R package for the analysis of independent and cluster-correlated semi-competing risks data, The R Journal, 11, 1, 376-400.

initiate.startValues_AFT, print.Bayes_AFT, summary.Bayes_AFT, predict.Bayes_AFT

## Not run: 
# loading a data set
data(survData)
survData$yL <- survData$yU <- survData[,1]
survData$yU[which(survData[,2] == 0)] <- Inf
survData$LT <- rep(0, dim(survData)[1])

form <- Formula(LT | yL + yU ~ cov1 + cov2)

#####################
## Hyperparameters ##
#####################

## log-Normal model
##
LN.ab <- c(0.3, 0.3)

## DPM model
##
DPM.mu <- log(12)
DPM.sigSq <- 100
DPM.ab <-  c(2, 1)
Tau.ab <- c(1.5, 0.0125)

##
hyperParams <- list(LN=list(LN.ab=LN.ab),
DPM=list(DPM.mu=DPM.mu, DPM.sigSq=DPM.sigSq, DPM.ab=DPM.ab, Tau.ab=Tau.ab))

###################
## MCMC SETTINGS ##
###################

## Setting for the overall run
##
numReps    <- 100
thin       <- 1
burninPerc <- 0.5

## Tuning parameters for specific updates
##
##  - those common to all models
beta.prop.var	<- 0.01
mu.prop.var	<- 0.1
zeta.prop.var	<- 0.1

##
mcmcParams	<- list(run=list(numReps=numReps, thin=thin, burninPerc=burninPerc),
tuning=list(beta.prop.var=beta.prop.var, mu.prop.var=mu.prop.var,
zeta.prop.var=zeta.prop.var))

################################################################
## Analysis of Independent univariate survival data ############
################################################################

###############
## logNormal ##
###############

##
myModel <- "LN"
myPath  <- "Output/01-Results-LN/"

startValues      <- initiate.startValues_AFT(form, survData, model=myModel, nChain=2)

##
fit_LN <- BayesSurv_AFT(form, survData, model=myModel, hyperParams,
startValues, mcmcParams, path=myPath)

fit_LN
summ.fit_LN <- summary(fit_LN); names(summ.fit_LN)
summ.fit_LN
pred_LN <- predict(fit_LN, time = seq(0, 35, 1), tseq=seq(from=0, to=30, by=5))
plot(pred_LN, plot.est="Haz")
plot(pred_LN, plot.est="Surv")

#########
## DPM ##
#########

##
myModel <- "DPM"
myPath  <- "Output/02-Results-DPM/"

startValues      <- initiate.startValues_AFT(form, survData, model=myModel, nChain=2)

##
fit_DPM <- BayesSurv_AFT(form, survData, model=myModel, hyperParams,
startValues, mcmcParams, path=myPath)

fit_DPM
summ.fit_DPM <- summary(fit_DPM); names(summ.fit_DPM)
summ.fit_DPM
pred_DPM <- predict(fit_DPM, time = seq(0, 35, 1), tseq=seq(from=0, to=30, by=5))
plot(pred_DPM, plot.est="Haz")
plot(pred_DPM, plot.est="Surv")

## End(Not run)