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### R code from vignette source 'validate.Rnw'
###################################################
### code chunk number 1: init
###################################################
options(continue=" ", width=60)
options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1))))
pdf.options(pointsize=8) #text in graph about the same as regular text
library(survival, quietly=TRUE)
###################################################
### code chunk number 2: breslow1
###################################################
breslow1 <- function(beta) {
# first test data set, Breslow approximation
r = exp(beta)
lpl = 2*beta - (log(3*r +3) + 2*log(r+3))
U = (6+ 3*r - r^2)/((r+1)*(r+3))
H = r/(r+1)^2 + 6*r/(r+3)^2
c(beta=beta, loglik=lpl, U=U, H=H)
}
beta <- log((3 + sqrt(33))/2)
temp <- rbind(breslow1(0), breslow1(beta))
dimnames(temp)[[1]] <- c("beta=0", "beta=solution")
temp
###################################################
### code chunk number 3: validate.Rnw:186-209
###################################################
iter <- matrix(0, nrow=6, ncol=4,
dimnames=list(paste("iter", 0:5),
c("beta", "loglik", "U", "H")))
# Exact Newton-Raphson
beta <- 0
for (i in 1:5) {
iter[i,] <- breslow1(beta)
beta <- beta + iter[i,"U"]/iter[i,"H"]
}
print(iter, digits=9)
# coxph fits
test1 <- data.frame(time= c(1, 1, 6, 6, 8, 9),
status=c(1, 0, 1, 1, 0, 1),
x= c(1, 1, 1, 0, 0, 0))
temp <- matrix(0, nrow=6, ncol=4,
dimnames=list(1:6, c("iter", "beta", "loglik", "H")))
for (i in 0:5) {
tfit <- coxph(Surv(time, status) ~ x, data=test1,
ties="breslow", iter.max=i)
temp[i+1,] <- c(tfit$iter, coef(tfit), tfit$loglik[2], 1/vcov(tfit))
}
temp
###################################################
### code chunk number 4: mresid1
###################################################
mresid1 <- function(r) {
status <- c(1,0,1,1,0,1)
xbeta <- c(r,r,r,1,1,1)
temp1 <- 1/(3*r +3)
temp2 <- 2/(r+3) + temp1
status - xbeta*c(temp1, temp1, temp2, temp2, temp2, 1+ temp2)
}
r0 <- mresid1(1)
r1 <- round(mresid1((3 + sqrt(33))/2), 6)
###################################################
### code chunk number 5: iter
###################################################
temp <- matrix(0, 8, 3)
dimnames(temp) <- list(paste0("iteration ", 0:7, ':'), c("beta", "loglik", "H"))
bhat <- 0
for (i in 1:8) {
r <- exp(bhat)
temp[i,] <- c(bhat, 2*(bhat - log(3*r +3)), 2*r/(r+1)^2)
bhat <- bhat + (r+1)/r
}
round(temp,3)
###################################################
### code chunk number 6: breslow2
###################################################
ufun <- function(r) {
4 - (r/(r+1) + r/(r+2) + 3*r/(3*r+2) + 6*r/(3*r+1) + 6*r/(3*r+2))
}
rhat <- uniroot(ufun, c(.5, 1.5), tol=1e-8)$root
bhat <- log(rhat)
c(rhat=rhat, bhat=bhat)
###################################################
### code chunk number 7: temp
###################################################
true2 <- function(beta, newx=0) {
r <- exp(beta)
loglik <- 4*beta - log(r+1) - log(r+2) - 3*log(3*r+2) - 2*log(3*r+1)
u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) -
( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1))
imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 +
3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2
hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) )
xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1),
3*r/(3*r+2))
# The matrix of weights, one row per obs, one col per time
# deaths at 2,3,6,7,8,9
wtmat <- matrix(c(1,0,0,0,1,0,0,0,0,0,
0,1,0,1,1,0,0,0,0,0,
0,0,1,1,1,0,1,1,0,0,
0,0,0,1,1,0,1,1,0,0,
0,0,0,0,1,1,1,1,0,0,
0,0,0,0,0,1,1,1,1,1), ncol=6)
wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat
x <- c(1,0,0,1,0,1,1,1,0,0)
status <- c(1,1,1,1,1,1,1,0,0,0)
xbar <- colSums(wtmat*x)/ colSums(wtmat)
n <- length(x)
# Table of sums for score and Schoenfeld resids
hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time
dM <- -hazmat #Expected part
for (i in 1:6) dM[i,i] <- dM[i,i] +1 #observed
dM[7,6] <- dM[7,6] +1 # observed
mart <- rowSums(dM)
# Table of sums for score and Schoenfeld resids
# Looks like the last table of appendix E.2.1 of the book
resid <- dM * outer(x, xbar, '-')
score <- rowSums(resid)
scho <- colSums(resid)
# We need to split the two tied times up, to match coxph
scho <- c(scho[1:5], scho[6]/2, scho[6]/2)
var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2))
var.d <- cumsum( (xbar-newx)*hazard)
surv <- exp(-cumsum(hazard) * exp(beta*newx))
varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx)
list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard,
mart=mart, score=score, rmat=resid,
scho=scho, surv=surv, var=varhaz)
}
val2 <- true2(bhat)
rtemp <- round(val2$mart, 6)
###################################################
### code chunk number 8: wt1
###################################################
ufun <- function(r) {
xbar <- c( (2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r + 5), 2*r/(2*r +1))
11- (xbar[1] + 10* xbar[2] + 2* xbar[3])
}
rhat <- uniroot(ufun, c(1,3), tol= 1e-9)$root
bhat <- log(rhat)
c(rhat=rhat, bhat=bhat)
###################################################
### code chunk number 9: wt2
###################################################
wfun <- function(r) {
beta <- log(r)
pl <- 11*beta - (log(r^2 + 11*r + 7) + 10*log(11*r +5) + 2*log(2*r +1))
xbar <- c((2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r +5), 2*r/(2*r +1))
U <- 11 - (xbar[1] + 10*xbar[2] + 2*xbar[3])
H <- ((4*r^2 + 11*r)/(r^2 + 11*r +7)- xbar[1]^2) +
10*(xbar[2] - xbar[2]^2) + 2*(xbar[3]- xbar[3]^2)
c(loglik=pl, U=U, H=H)
}
temp <- matrix(c(wfun(1), wfun(rhat)), ncol=2,
dimnames=list(c("loglik", "U", "H"), c("beta=0", "beta-hat")))
round(temp, 6)
###################################################
### code chunk number 10: mstate1
###################################################
getOption("SweaveHooks")[["fig"]]()
states <- c("Entry", "a", "b", "c")
smat <- matrix(0, 4, 4, dimnames=list(states, states))
smat[1,2:3] <- 1
smat[2,3] <- smat[3,2] <- smat[3,4] <- smat[2,4] <- 1
statefig(c(1,2,1), smat)
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