Penalized Semiparametric Bayesian Cox Models

Run a Bayesian Lasso Cox with mandatory variables

Data set exampleData consists of six components: survival times t, event status di, covariates x, number of genomics variables p, number of clinical variables q and true effects of covariates beta_true. See ?exampleData for more information of the data.

To run a Bayesian Lasso Cox model for variable selection of the first \(p\) genomics variables and inclusion of \(q\) mandatory variables, one can specify arguments of the main function psbcSpeedUp() with p = p and q = q. If the arguments p and q are unspecified, the Bayesian Lasso Cox model does variable selection for all covariates, i.e., by default p = ncol(survObj$x) and q = 0.

# Load the example dataset
data("exampleData", package = "psbcSpeedUp")
p <- exampleData$p
q <- exampleData$q
survObj <- exampleData[1:3]

# Set hyperparameters (see help file for specifying more hyperparameters)
mypriorPara <- list('eta0'=0.02, 'kappa0'=1, 'c0'=2, 'r'=10/9, 'delta'=1e-05,
'lambdaSq'=1, 'sigmaSq'= runif(1, 0.1, 10), 'beta.prop.var'=1, 'beta.clin.var'=1)

# run Bayesian Lasso Cox
library("psbcSpeedUp")
set.seed(123)
fitBayesCox <- psbcSpeedUp(survObj, p=p, q=q, hyperpar=mypriorPara,
nIter=1000, burnin=500, outFilePath="/tmp")

Plot posterior estimates of regression cofficients

The function psbcSpeedUp::plot() can show the posterior mean and 95% credible intervals of regression coefficients.

plot(fitBayesCox)

Plot time-dependent Brier scores

The function psbcSpeedUp::plotBrier() can show the time-dependent Brier scores based on posterior mean of coefficients or Bayesian model averaging.

plotBrier(fitBayesCox, times = 80)

##     Null.model Bayesian.Cox
## IBS  0.2089742   0.08195375

Predict survival probabilities and cumulative hazards

The function psbcSpeedUp::predict() can estimate the survival probabilities and cumulative hazards.

predict(fitBayesCox, type = c("cumhazard", "survival"))

##        observation   times cumhazard  survival
##     1:           1   0.264  1.14e-05  1.00e+00
##     2:           2   0.264  4.66e-05  1.00e+00
##     3:           3   0.264  6.07e-05  1.00e+00
##     4:           4   0.264  1.71e-05  1.00e+00
##     5:           5   0.264  7.55e-05  1.00e+00
##    ---                                        
## 39996:         196 107.641  2.76e+00  6.36e-02
## 39997:         197 107.641  5.65e-01  5.68e-01
## 39998:         198 107.641  5.37e+01  4.86e-24
## 39999:         199 107.641  4.25e+02 2.25e-185
## 40000:         200 107.641  1.89e-01  8.28e-01