hsaftgroupcorr: This function extends the main function 'hsaft' to create...

In PanCanVarSel: Pan-Cancer Variable Selection

Description

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

Usage

hsaftgroupcorr(ct, X, method.tau = c("fixed", "truncatedCauchy",
  "halfCauchy"), tau = 1, method.sigma = c("fixed", "Jeffreys"),
  Sigma2 = 1, burn = 1000, nmc = 5000, 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 τ. 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 τ 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 σ^2, or "fixed" to use a fixed value (an empirical Bayes estimate, for example).
Sigma2	A fixed value for the error variance σ^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 σ^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 β.
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 hsaftgroupcorr 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 <- hsaftgroupcorr(ct, X, method.tau = "truncatedCauchy", method.sigma = "Jeffreys",
                                burn = burnin, nmc = nmc,
                                r = r, n.seq = n.seq, pk = p)
summary(posterior.fit$BetaHat)

PanCanVarSel documentation built on Sept. 20, 2019, 5:04 p.m.