aftprobiths: Horseshoe shrinkage prior in integrated survival and binary...

In intsurvbin: Survival and Binary Data Integration

Description

This function provides the implementation of integrated survival and binary high dimensiona regression utilizing Horseshoe prior on the paramters

Usage

aftprobiths(ct, z, X, burn = 1000, nmc = 5000, thin = 1,
  alpha = 0.05, Xtest = NULL, cttest = NULL, ztest = NULL)

Arguments

ct	survival response, a n*2 matrix with first column as response and second column as right censored indicator, 1 is event time and 0 is right censored.
z	binary response, a n*1 vector with numeric values 0 or 1.
X	Matrix of covariates, dimension n*p.
burn	Number of burn-in MCMC samples. Default is 1000.
nmc	Number of posterior draws to be saved. Default is 5000.
thin	Thinning parameter of the chain. Default is 1 (no thinning).
alpha	Level for the credible intervals. For example, alpha = 0.05 results in 95% credible intervals.
Xtest	test design matrix.
cttest	test survival response.
ztest	test binary response.

Value

Beta.sHat	Posterior mean of β for survival model, a p by 1 vector.
Beta.bHat	Posterior mean of β for binary model, a p by 1 vector.
LeftCI.s	The left bounds of the credible intervals for Beta.sHat.
RightCI.s	The right bounds of the credible intervals for Beta.sHat.
LeftCI.b	The left bounds of the credible intervals for Beta.bHat.
RightCI.b	The right bounds of the credible intervals for Beta.bHat.
Beta.sMedian	Posterior median of beta for survival model, a p by 1 vector.
Beta.bMedian	Posterior median of beta for binary model, a p by 1 vector.
SigmaHat	Posterior mean of variance covariance matrix.
LambdaHat	Posterior mean of λ, a p*1 vector.
TauHat	Posterior mean of τ, a 2*1 vector.
Beta.sSamples	Posterior samples of β for survival model.
Beta.bSamples	Posterior samples of β for binary model.
LambdaSamples	Posterior samples of λ.
TauSamples	Posterior samples of τ.
SigmaSamples	Posterior samples of variance covariance matrix.
DIC.s	DIC for survival model.
DIC.b	DIC for binary model.
SurvivalHat	Predictive survival probability.
LogTimeHat	Predictive log time.

References

Maity, A. K., Carroll, R. J., and Mallick, B. K. (2019) "Integration of Survival and Binary Data for Variable Selection and Prediction: A Bayesian Approach", Journal of the Royal Statistical Society: Series C (Applied Statistics).

Examples

burnin <- 50
nmc    <- 150
thin <- 1
y.sd   <- 1  # standard deviation of the response

p <- 100  # number of predictors
ntrain <- 100  # training size
ntest  <- 50   # test size
n <- ntest + ntrain  # sample size
q <- 10   # number of true predictos

beta.t <- c(sample(x = c(1, -1), size = q, replace = TRUE), rep(0, p - q))  # randomly assign sign

Sigma <- matrix(0.9, nrow = p, ncol = p)
for(j in 1:p)
{
Sigma[j, j] <- 1
}

x <- mvtnorm::rmvnorm(n, mean = rep(0, p), sigma = Sigma)    # correlated design matrix

zmean <- x %*% beta.t
tmean <- x %*% beta.t
yCorr <- 0.5
yCov <- matrix(c(1, yCorr, yCorr, 1), nrow = 2)


y <- mvtnorm::rmvnorm(n, sigma = yCov)
t <- y[, 1] + tmean
z <- ifelse((y[, 2] + zmean) > 0, 1, 0)
X <- scale(as.matrix(x))  # standarization

z <- as.numeric(as.matrix(c(z)))
t <- as.numeric(as.matrix(c(t)))
T <- exp(t)   # AFT model
C <- rgamma(n, shape = 1.75, scale = 3)   # 42% censoring time
time <- pmin(T, C)  # observed time is min of censored and true
status = time == T   # set to 1 if event is observed
ct <- as.matrix(cbind(time = time, status = status))  # censored time


# Training set
ztrain <- z[1:ntrain]
cttrain <- ct[1:ntrain, ]
Xtrain  <- X[1:ntrain, ]

# Test set
ztest <- z[(ntrain + 1):n]
cttest <- ct[(ntrain + 1):n, ]
Xtest  <- X[(ntrain + 1):n, ]

posterior.fit.joint <- aftprobiths(ct = cttrain, z = ztrain, X = Xtrain,
                                   burn = burnin, nmc = nmc, thin = thin,
                                   Xtest = Xtest, cttest = cttest, ztest = ztest)
                             
posterior.fit.joint$Beta.sHat

intsurvbin documentation built on Oct. 3, 2019, 9:02 a.m.