# The function to implement Bayesian parametric and semi-parametric analyses for univariate survival data in the context of accelerated failure time (AFT) models. 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. ```r 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. ## 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 $c_{ij}\leq T_i ## See Also `initiate.startValues_AFT`, `print.Bayes_AFT`, `summary.Bayes_AFT`, `predict.Bayes_AFT` ## Examples ```r ## Not run: # loading a data set data(survData) survData$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) ```

BayesSurv_AFT function