#
# These results can be found in Miller
#
fit <- coxph(Surv(aml$time, aml$status) ~ aml$x, method='breslow')
fit
resid(fit, type='mart')
resid(fit, type='score')
resid(fit, type='scho')

fit <- survfit(Surv(aml$time, aml$status) ~ aml$x)
fit
summary(fit)
survdiff(Surv(aml$time, aml$status)~ aml$x)

#
# Test out the weighted K-M
#
#  First, equal case weights- shouldn't change the survival, but will
#    halve the variance
temp2 <-survfit(Surv(aml$time, aml$status), type='kaplan', weight=rep(2,23))
temp  <-survfit(Surv(time, status)~1, aml)
temp$surv/temp2$surv
(temp$std.err/temp2$std.err)^2

# Risk weights-- use a null Cox model
tfit <- coxph(Surv(aml$time, aml$status) ~ offset(log(1:23)))
sfit <- survfit(tfit, type='aalen')

# Now compute it by hand
#  Ties are a challenge
atime <- sort(aml$time)
denom <- rev(cumsum(rev((1:23)[order(aml$time)])))
denom <- denom[match(unique(atime), atime)]
deaths <- tapply(aml$status, aml$time, sum)
chaz <- cumsum(deaths/denom)
all.equal(sfit$surv, as.vector(exp(-chaz[deaths>0])))
cvar <- cumsum(deaths/denom^2)
all.equal(sfit$std^2, as.vector(cvar[deaths>0]))
summary(sfit)

# And the Efron result
summary(survfit(tfit))

# Lots of ties, so its a good test case
x1 <- coxph(Surv(time, status)~x, aml, method='efron')
x1
x2 <- coxph(Surv(rep(0,23),time, status) ~x, aml, method='efron')
x1$coef - x2$coef

rm(x1, x2, atime, denom, deaths, chaz,cvar, tfit, sfit, temp, temp2, fit)