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afths_circ
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afths_circ
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afths_circ <- function (ct, X, nburnin = 1000, nmc = 5000, thin = 1,
Xtest = NULL, cttest = NULL)
{
niter <- nburnin + nmc
effsamp <- (niter - nburnin)/thin
n <- nrow(X)
p <- ncol(X)
time <- ct[, 1]
status <- ct[, 2]
censored.id <- which(status == 0)
n.censored <- length(censored.id) # number of censored observations
n.observed <- n - n.censored
X.censored <- X[censored.id, ]
X.observed <- X[-censored.id, ]
y <- logtime <- log(time) # for coding convenience, since the whole code is written with y
y.censored <- y[censored.id]
y.observed <- y[-censored.id]
alpha <- 0
beta <- rep(0, p)
lambda <- rep(1, p/2)
tau <- 1
sigma_sq <- 1
I_n <- diag(n)
l0 <- rep(0, p)
l1 <- rep(1, n)
l2 <- rep(1, p)
Q_star <- t(X) %*% X
if(is.null(Xtest))
{
Xtest <- X
ntest <- n
cttest<- ct
} else {
ntest <- nrow(Xtest)
}
alphaout <- rep(0, effsamp)
betaout <- matrix(0, p, effsamp)
lambdaout <- matrix(0, p/2, effsamp)
sigmaSqout <- rep(0, effsamp)
predsurvout <- matrix(0, ntest, effsamp)
logtimeout <- matrix(0, ntest, effsamp)
likelihood.out <- matrix(0, n, effsamp)
loglikelihood.out <- rep(0, effsamp)
for (i in 1:niter)
{
## Impute the Censored data ##
mean.impute <- alpha + X.censored %*% beta
sd.impute <- sqrt(sigma_sq)
## update censored data ##
y[censored.id] <- rtnorm(n.censored, mean = mean.impute, sd = sd.impute, lower = logtime[censored.id]) # response
# Sample $ \alpha $
A <- crossprod(x = rep(1, n)) + chol2inv(chol(100 * diag(1)))
Ainv <- chol2inv(chol(A))
Sigma.alpha <- sigma_sq * Ainv
mean.alpha <- as.vector(Ainv %*% t(rep(1, n)) %*% (y - X %*% beta))
alpha <- as.vector(mvrnorm(n = 1, mu = mean.alpha, Sigma = Sigma.alpha))
## Update beta according to horseshoe
if (p > n)
{
lambda.temp <- c(lambda, lambda)
lambda_star = tau * lambda.temp
U = as.numeric(lambda_star^2) * t(X)
u = stats::rnorm(l2, l0, lambda_star)
v = X %*% u + stats::rnorm(n)
v_star = solve((X %*% U + I_n), (((y - alpha)/sqrt(sigma_sq)) - v))
beta = sqrt(sigma_sq) * (u + U %*% v_star)
} else {
lambda.temp <- c(lambda, lambda)
lambda_star = tau * lambda.temp
L = chol((1/sigma_sq) * (Q_star + diag(1/as.numeric(lambda_star^2), p, p)))
v = solve(t(L), t(t(y - alpha) %*% X)/sigma_sq)
mu = solve(L, v)
u = solve(L, stats::rnorm(p))
beta = mu + u
}
## Sample lambda
eta <- 1/(lambda^2)
upsi <- stats::runif((p/2), 0, 1/(1 + eta))
tempps <- c((beta[1]^2 + beta[11]^2), (beta[2]^2 + beta[12]^2), (beta[3]^2 + beta[13]^2),
(beta[4]^2 + beta[14]^2), (beta[5]^2 + beta[15]^2), (beta[6]^2 + beta[16]^2),
(beta[7]^2 + beta[17]^2), (beta[8]^2 + beta[18]^2), (beta[9]^2 + beta[19]^2),
(beta[10]^2 + beta[20]^2))/(2 * sigma_sq * tau^2)
ub = (1 - upsi)/upsi
# Fub = stats::pgamma(ub,(p/2+1)/2,scale = 1/tempps)
Fub = 1 - exp(-tempps * ub)
Fub[Fub < (1e-04)] = 1e-04
up = stats::runif(p/2, 0, Fub)
# eta = stats::qgamma(up,(p/2+1)/2,scale = 1/tempps)
eta = -log(1 - up)/tempps
lambda = 1/sqrt(eta)
## sample tau
tempt <- sum((beta[1:(p/2)]/lambda)^2 + (beta[(p/2 + 1):p]/lambda)^2)/(2 * sigma_sq)
et = 1/tau^2
utau = stats::runif(1, 0, 1/(1 + et))
ubt = (1 - utau)/utau
Fubt = stats::pgamma(ubt, (p/2 + 1)/2, scale = 1/tempt)
Fubt = max(Fubt, 1e-08)
ut = stats::runif(1, 0, Fubt)
et = stats::qgamma(ut, (p/2 + 1)/2, scale = 1/tempt)
tau = 1/sqrt(et)
## Sample sigma square
E1 = max(t(y - alpha - X %*% beta) %*% (y - alpha - X %*% beta), (1e-10))
E2 = max(sum((beta[1:(p/2)]/lambda)^2 + (beta[(p/2 + 1):p]/lambda)^2)/(tau^2), (1e-10))
E3 <- crossprod(x = alpha)
sigma_sq = 1/stats::rgamma(1, (n + p/2 + 1)/2, scale = 2/(E1 + E2 + E3))
logt <- alpha + Xtest %*% beta
predictive.survivor <- pnorm(log(cttest[, 1]), mean = logt, sd = sd.impute, lower.tail = FALSE)
loglikelihood <- sum(c(dnorm(y.observed, mean = alpha + X.observed %*% beta, sd = sqrt(sigma_sq),
log = TRUE),
log(1 - pnorm(y.censored, mean = alpha + X.censored %*% beta,
sd = sqrt(sigma_sq)))))
likelihood <- exp(loglikelihood)
if (i%%1000 == 0)
{
print(i)
}
if (i > nburnin && i%%thin == 0)
{
alphaout[(i - nburnin)/thin] <- alpha
betaout[, (i - nburnin)/thin] <- beta
lambdaout[, (i - nburnin)/thin] <- lambda
sigmaSqout[(i - nburnin)/thin] <- sigma_sq
predsurvout[ ,(i - nburnin)/thin] <- predictive.survivor
logtimeout[, (i - nburnin)/thin] <- logt
likelihood.out[, (i - nburnin)/thin] <- likelihood
loglikelihood.out[(i - nburnin)/thin] <- loglikelihood
}
}
pMean.alpha <- mean(alphaout)
pMean <- apply(betaout, 1, mean)
pMedian <- apply(betaout, 1, stats::median)
pLambda <- apply(lambdaout, 1, mean)
pSigma <- mean(sigmaSqout)
pPS <- apply(predsurvout, 1, mean)
pLogtime <- apply(logtimeout, 1, mean)
plikelihood <- apply(likelihood.out, 1, mean)
pLoglikelihood <- mean(loglikelihood.out)
loglikelihood.posterior <- sum(c(dnorm(y.observed, mean = pMean.alpha + X.observed %*% pMean, sd = sqrt(pSigma), log = TRUE),
log(1 - pnorm(y.censored, mean = pMean.alpha + X.censored %*% pMean,
sd = sqrt(pSigma)))))
DIC <- -4 * pLoglikelihood + 2 * loglikelihood.posterior
lppd <- sum(log(plikelihood))
WAIC <- -2 * (lppd - 2 * (loglikelihood.posterior - pLoglikelihood))
result = list(BetaHat = pMean, BetaMedian = pMedian, Sigma2Hat = pSigma, AlphaHat = pMean.alpha,
BetaSamples = betaout, Sigma2Samples = sigmaSqout, SurvivalHat = pPS,
LogTimeHat = pLogtime, DIC = DIC, WAIC = WAIC, LambdaHat = pLambda)
return(result)
}