# DDPGPSurv-package: DDP-GP Survival Analysis Package In DDPGPSurv: DDP-GP Survival Analysis

## Description

A nonparametric Bayesian approach to survival analysis. The functions perform inference via MCMC simulations from the posterior distributions for a Dependent Dirichlet Process-Gaussian Process prior. To maximize computational efficiency, some of the computations are performed in 'Rcpp'.

## Details

The Dependent Dirichlet Process-Gaussian Process model is summarized below. The Dependent Dirichlet Process has a Gaussian Process as its base measure.

y_i|μ_h(x_i),σ^2=∑_{h=1}^{∞}w_{h}N(μ_{h}(x_i),σ^2)

μ_h(x)\sim GP(xβ_h,C(\cdot,\cdot))

C(x_{i},x_{j})=σ_0^2exp\{-\Vert \frac{x_{i}-x_{j}}{l^2}\Vert^{2}\}+I_{\{i=j\}}J^{2}

Here, the mean of the Gaussian Process is modeled using linear regression with regression coefficients β_h and J is a small diagonal perturbation to the squared exponential covariance function (set to 0.01).

To complete the model specification, independent hyperpriors are assumed:

β_{h}\sim N(β_{0},Σ_{0})

σ^{-2}\sim Gamma(δ_{1},δ_{2})

We use a hyperparamter M to control the weights (w_{h}) in the model:

M\sim Gamma(λ_{1},λ_{2})

## Author(s)

William Hua <[email protected]>, Yanxun Xu <[email protected]>

Maintainer: William Hua <[email protected]>

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 ######################################## #Source dependent packages library(MASS) library(mc2d) library(mvnfast) library(survival) #Simulate Data using built-in data generation ## seed=1 set.seed(seed) Npat=5 data <- simulate_data(Npat) ######################################## #Run MCMC ######################################## #Inputs for mcmc response <- log(data$OS) covariate <- cbind(scale(data$Age),data$AUC,data$CR) censor_status <- data$death mcmc_settings<-NULL mcmc_settings$nskip<-10 mcmc_settings$nburn<-50 mcmc_settings$ndisplay<-100 mcmc_settings$nsave<-20 mcmc_settings$sigma_jump<-c(0,4,2.5,4,2.6) ################### #Run MCMC function mcmc_Gibbs<-mcmc_DDPGP(response,covariate,censor_status,mcmc_settings) ######################################## #Plotting Density/Survival/Hazard Estimation ######################################## #Parameters in Plotting Estimation for Functions range=seq(2,8,1) example_AUC <- 5 example_CR <- 1 example_Age <- 0 new_pat<-cbind(example_Age,example_AUC,example_CR) if_plot=1 ################### #Plot DDP-GP Density Esimation a=DDPGP_Dens(mcmc_Gibbs,new_pat,range, if_plot) #Plot DDP-GP Survival Esimation b=DDPGP_Surv(mcmc_Gibbs,new_pat,range, if_plot) #Plot DDP-GP Hazard Esimation c=DDPGP_Haz(mcmc_Gibbs,new_pat,range, if_plot) ######################################## #Plotting Mean Survival Estimation ######################################## #Parameters in Plotting Mean Survival Estimation range_AUC <- seq(2.6, 7, 0.1) new_pat_1<-cbind(example_Age,range_AUC,example_CR) if_plot=1 DDPGP_mean<-DDPGP_meansurvival(mcmc_Gibbs,new_pat_1,if_plot,cov_col=2) 

DDPGPSurv documentation built on June 24, 2018, 5:06 p.m.