BayesSurv_AFT: The function to implement Bayesian parametric and semi-parametric analyses for univariate survival data in the context of accelerated failure time (AFT) models.

Description

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.

Usage

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

Arguments

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 $\beta$; mu.prop.var, the variance of proposal density for $\mu$; zeta.prop.var, the variance of proposal density for $1/\sigma^2$).

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.

Value

BayesSurv_AFT returns an object of class Bayes_AFT.

Details

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: $$\log(T_i) = x_i^{\top}\beta + \epsilon_i,$$ where $\epsilon_i$ is a random variable whose distribution determines that of $T_i$ and $\beta$ is a vector of regression parameters. Considering the interval censoring, the time to the event for the $i^{\textrm{th}}$ subject satisfies $c_{ij}\leq T_i <c_{ij+1}$. Let $L_i$ denote the left-truncation time. For the Bayesian parametric analysis, we take $\epsilon_i$ to follow the Normal($\mu$, $\sigma^2$) distribution for $\epsilon_i$. The following prior distributions are adopted for the model parameters: $$\pi(\beta, \mu) \propto 1,$$ $$\sigma^2 \sim \textrm{Inverse-Gamma}(a_{\sigma}, b_{\sigma}).$$

For the Bayesian semi-parametric analysis, we assume that $\epsilon_i$ is taken as draws from the DPM of normal distributions: $$\epsilon\sim DPM(G_0, \tau).$$ 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 $\beta$ and a Gamma($a_{\tau}$, $b_{\tau}$) hyperprior for the precision parameter $\tau$.

References

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.

Examples

Run this code

# NOT RUN {
# }
# 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")
# }
# NOT RUN {
# }

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