hsaftcovariatecorr {PanCanVarSel}

This function extends the main function hsaft to create correlation among covariates.

Description

This function extends the main function hsaft to create correlation among covariates.

Usage

hsaftcovariatecorr(ct, X, method.tau = c("fixed", "truncatedCauchy",
  "halfCauchy"), tau = 1, method.sigma = c("fixed", "Jeffreys"),
  Sigma2 = 1, burn = 100, nmc = 500, thin = 1, alpha = 0.05, r,
  n.seq, pk)

Arguments

ct

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.

X

Matrix of covariates, dimension n*p.

method.tau

Method for handling \tau. Select "truncatedCauchy" for full Bayes with the Cauchy prior truncated to [1/p, 1], "halfCauchy" for full Bayes with the half-Cauchy prior, or "fixed" to use a fixed value (an empirical Bayes estimate, for example).

tau

Use this argument to pass the (estimated) value of \tau in case "fixed" is selected for method.tau. Not necessary when method.tau is equal to"halfCauchy" or "truncatedCauchy". The default (tau = 1) is not suitable for most purposes and should be replaced.

method.sigma

Select "Jeffreys" for full Bayes with Jeffrey's prior on the error variance \sigma^2, or "fixed" to use a fixed value (an empirical Bayes estimate, for example).

Sigma2

A fixed value for the error variance \sigma^2. Not necessary when method.sigma is equal to "Jeffreys". Use this argument to pass the (estimated) value of Sigma2 in case "fixed" is selected for method.sigma. The default (Sigma2 = 1) is not suitable for most purposes and should be replaced.

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.

r

number of groups.

n.seq

a vector of sample sizes for all groups.

pk

number of covariates in each group.

Value

SurvivalHat

Predictive survival probability.

LogTimeHat

Predictive log time.

BetaHat

Posterior mean of Beta, a p by 1 vector.

LeftCI

The left bounds of the credible intervals.

RightCI

The right bounds of the credible intervals.

BetaMedian

Posterior median of Beta, a p by 1 vector.

Sigma2Hat

Posterior mean of error variance \sigma^2. If method.sigma = "fixed" is used, this value will be equal to the user-selected value of Sigma2 passed to the function.

TauHat

Posterior mean of global scale parameter tau, a positive scalar. If method.tau = "fixed" is used, this value will be equal to the user-selected value of tau passed to the function.

BetaSamples

Posterior samples of Beta.

TauSamples

Posterior samples of tau.

Sigma2Samples

Posterior samples of Sigma2.

BHat

Posterior samples of b which is the mean of \beta.

LikelihoodSamples

Posterior Samples of likelihood.

References

Stephanie van der Pas, James Scott, Antik Chakraborty and Anirban Bhattacharya (2016). horseshoe: Implementation of the Horseshoe Prior. R package version 0.1.0. https://CRAN.R-project.org/package=horseshoe

Arnab Kumar Maity, Anirban Bhattacharya, Bani K. Mallick, and Veerabhadran Baladandayuthapani (2017). Joint Bayesian Estimation and Variable Selection for TCPA Protein Expression Data

Examples

# Examples for hsaftcovariatecorr function
burnin <- 50   # number of burnin
nmc    <- 100  # number of Markov Chain samples
y.sd   <- 1     # standard deviation of the data
p      <- 80    # number of covariates
r      <- 5     # number of groups
p      <- 80    # number of covariate in each group
n1     <- 40    # sample size of 1st group
n2     <- 50    # sample size of 2nd group
n3     <- 70    # sample size of 3rd group
n4     <- 100   # sample size of 4th group
n5     <- 120   # sample size of 5th group
n      <- sum(c(n1, n2, n3, n4, n5))  # total sample size
n.seq  <- c(n1, n2, n3, n4, n5)
Beta   <- matrix(smoothmest::rdoublex(p * r), nrow = r, ncol = p, byrow = TRUE)
# from double exponential distribution
beta   <- as.vector(t(Beta))  # vectorize Beta
x1     <- mvtnorm::rmvnorm(n1, mean = rep(0, p))
x2     <- mvtnorm::rmvnorm(n2, mean = rep(0, p))
x3     <- mvtnorm::rmvnorm(n3, mean = rep(0, p))
x4     <- mvtnorm::rmvnorm(n4, mean = rep(0, p))
x5     <- mvtnorm::rmvnorm(n5, mean = rep(0, p))  # from multivariate normal distribution
y.mu1  <- x1 %*% Beta[1, ]
y.mu2  <- x2 %*% Beta[2, ]
y.mu3  <- x3 %*% Beta[3, ]
y.mu4  <- x4 %*% Beta[4, ]
y.mu5  <- x5 %*% Beta[5, ]
y1     <- stats::rnorm(n1, mean = y.mu1, sd = y.sd)
y2     <- stats::rnorm(n2, mean = y.mu2, sd = y.sd)
y3     <- stats::rnorm(n3, mean = y.mu3, sd = y.sd)
y4     <- stats::rnorm(n4, mean = y.mu4, sd = y.sd)
y5     <- stats::rnorm(n5, mean = y.mu5, sd = y.sd)
y      <- c(y1, y2, y3, y4, y5)
x      <- Matrix::bdiag(x1, x2, x3, x4, x5)
X      <- as.matrix(x)
y      <- as.numeric(as.matrix(y))  # from normal distribution
T      <- exp(y)   # AFT model
C      <- rgamma(n, shape = 1.75, scale = 3)  # 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

posterior.fit <- hsaftcovariatecorr(ct, X, method.tau = "truncatedCauchy",
                                    method.sigma = "Jeffreys",
                                    burn = burnin, nmc = nmc,
                                    r = r, n.seq = n.seq, pk = p)
                                    summary(posterior.fit$BetaHat)