---
title: "Penalized Semiparametric Bayesian Cox Models"
output: rmarkdown::html_vignette
vignette: >
%\VignetteEngine{knitr::rmarkdown}
%\VignetteIndexEntry{Penalized Semiparametric Bayesian Cox Models}
\usepackage[utf8]{inputenc}
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, eval = FALSE)
options(rmarkdown.html_vignette.check_title = FALSE)
```
This is a C++ speed-up and extended version of the R-pakcage [psbcGroup](https://CRAN.R-project.org/package=psbcGroup).
It implements the Bayesian Lasso Cox model ([Lee et al., 2011](https://doi.org/10.2202/1557-4679.1301)) and the Bayesian Lasso Cox with mandatory variables ([Zucknick et al., 2015](https://doi.org/10.1002/bimj.201400160)).
Bayesian Lasso Cox models with other shrinkage and group priors ([Lee et al., 2015](https://doi.org/10.1002/sam.11266)) are to be implemented later on.
## Installation
Install the latest released version from [CRAN](https://CRAN.R-project.org/package=psbcSpeedUp)
```{r install1, eval = FALSE}
install.packages("psbcSpeedUp")
```
Install the latest development version from GitHub
```{r install2, eval = FALSE}
#install.packages("remotes")
remotes::install_github("ocbe-uio/psbcSpeedUp")
```
## Examples
### 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$x)` and `q = 0`.
```{r, results='hide', warning=FALSE}
# Load the example dataset
data("exampleData", package = "psbcSpeedUp")
p <- exampleData$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.
```{r, fig.width=5, fig.height=8}
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.
```{r, fig.width=6, fig.heigh=5}
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.
```{r}
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
```
## References
> Kyu Ha Lee, Sounak Chakraborty, Jianguo Sun (2011).
> Bayesian variable selection in semiparametric proportional hazards model for high dimensional survival data.
> _The International Journal of Biostatistics_, 7:1. DOI: [10.2202/1557-4679.1301](https://doi.org/10.2202/1557-4679.1301).
> Kyu Ha Lee, Sounak Chakraborty, Jianguo Sun (2015).
> Survival prediction and variable selection with simultaneous shrinkage and grouping priors.
> _Statistical Analysis and Data Mining_, 8:114-127. DOI:[10.1002/sam.11266](https://doi.org/10.1002/sam.11266).
> Manuela Zucknick, Maral Saadati, Axel Benner (2015).
> Nonidentical twins: Comparison of frequentist and Bayesian lasso for Cox models.
> _Biometrical Journal_, 57:959-981. DOI:[10.1002/bimj.201400160](https://doi.org/10.1002/bimj.201400160).