BayesSurv_AFT {SemiCompRisks} | R Documentation |
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.
BayesSurv_AFT(Formula, data, model = "LN", hyperParams, startValues, mcmcParams, na.action = "na.fail", subset=NULL, path=NULL)
Formula |
a |
data |
a data.frame in which to interpret the variables named in |
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,
|
startValues |
a list containing vectors of starting values for model parameters. It can be specified as the object returned by the function |
mcmcParams |
a list containing variables required for MCMC sampling. Components include,
|
na.action |
how NAs are treated. See |
subset |
a specification of the rows to be used: defaults to all rows. See |
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. (2018+),
SemiCompRisks: an R package for independent and cluster-correlated analyses of semi-competing risks data, submitted, arXiv:1801.03567.
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)