Nothing
library(survival)
aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...)
#
# Test the multi-state version of the CI curve
#
tdata <- data.frame(id=c(1,1,1,1, 2,2,2, 3,3, 4,4,4,4, 5, 6, 6),
time1=c(0, 10,20,30, 0, 5, 15, 0, 20, 0, 6,18,34, 0, 0,15),
time2=c(10,20,30,40, 5, 15,25, 20, 22, 6,18,34,50,10,15,20),
status=c(1,1,1,1, 1,1,1, 1,0, 1,1,1,0,0,1,0),
event= letters[c(1,2,3,4, 2,4,3, 2,2, 3,1,2,2,1, 1,1)],
wt = c(2,2,2,2, 1,1,1, 3,3, 1,1,1,1, 2, 1,1),
stringsAsFactors=TRUE)
tdata$stat2 <- factor(tdata$status * as.numeric(tdata$event),
labels=c("censor", levels(tdata$event)))
fit <- survfit(Surv(time1, time2, stat2) ~1, id=id, weights=wt, tdata,
influence=TRUE)
# The exact figures for testci2.
# The subject data of id, weight, (transition time, transition)
#1: 2 (10, 0->a) (20, a->b) (30, b->c) (40, c->d) no data after 40=censored
#2: 1 ( 5, 0->b) (15, b->d) (25, d->c) no data after 25 implies censored then
#3: 3 (20, 0->b) (22, censor)
#4: 1 ( 6, 0->c) (18, c->a) (34, a->b) (50, censor)
#5: 2 (10, censor)
#6: 1 (15, 0->a) (20, censor)
# Each line below follows a subject through time as a (state, rdist weight) pair
# using the redistribute to the right algorithm.
# RDR algorithm: at each censoring (or last fu) a subject's weight is put into
# a "pool" for that state and their weight goes to zero. The pool is
# dynamically shared between all members of the state proportional to their
# original case weight, when someone leaves they take their portion of the
# pool to the new state.
# Table of case weights and state, blank is weight of zero
# time 5 6 10 15 18 20 25 30 34 40 50
# -----------------------------------------------------------------------
# id, wt
# 1, 2 - - a a a b b c c d
# 2, 1 b b b d d d c
# 3, 3 - - - - - b
# 4, 1 - c c c a a a a b b b
# 5, 2 - - -
# 6, 1 - - - a a a
# Pool weights
# 10 10+ 15 18 20 20+ 22+ 25 25+ 30 34 40 40+
# - 0 2 3/2 3/2 0
# a 0 0 1/2 1/2 1/4 5/4 5/4 5/4 5/4 5/4
# b 0 0 0 0 7/4 7/4 19/4 19/4 19/4 5/4 5/4 5/4
# c 0 0 0 0 0 1 23/4 23/4
# d 0 0 0 0 0 23/4 31/4
# fit$pstate for time i and state j = total weight at that time/state in the
# above table (original weight + redistrib), divided by 10.
# time 5 6 10 15 18 20 25 30 34 40 50
truth <- matrix(c(0, 0, 2, 3, 4, 2, 1, 1, 0, 0, 0,
1, 1, 1, 0, 0, 5, 2, 0, 1, 1, 1,
0, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0,
0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0) +
c(0, 0, 0, .5, .5, 1/4, 5/4, 5/4, 0, 0, 0,
0, 0, 0, 0, 0, 7/4, 19/4, 0, 5/4, 5/4, 5/4,
0, 0, 0, 0, 0, 0, 0, 23/4, 23/4, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 23/4, 31/4),
ncol=4)
truth <- truth[c(1:6, 6:11),]/10 #the explicit censor at 22
#dimnames(truth) <- list(c(5, 6, 10, 15, 18, 20, 25, 30, 34, 40, 50),
# c('a', 'b', 'c', 'd')
aeq(truth, fit$pstate[,2:5])
# Test the dfbetas
# It was a big surprise, but the epsilon where a finite difference approx to
# the derivative is most accurate is around 1e-7 = approx sqrt(precision).
# Smaller eps makes the approximate derivative worse.
# There is a now a formal test in mstate.R, not approximate.
# compute the per observation influence first
n <- nrow(tdata)
U <- array(0, dim=c(n, dim(fit$pstate)))
eps <- sqrt(.Machine$double.eps)
n <- nrow(tdata)
for (i in 1:n) {
twt <- tdata$wt
twt[i] <- twt[i] + eps
tfit <- survfit(Surv(time1, time2, stat2) ~ 1, id=id, tdata,
weights=twt)
U[i,,] <- (tfit$pstate - fit$pstate)/eps #finite difference approx
}
dfbeta <- rowsum(tdata$wt*matrix(U,nrow=n), tdata$id) # per subject
dfbeta <- array(dfbeta, dim=c(6,12,5))
aeq(dfbeta, fit$influence, tolerance= eps*10)
aeq(fit$std.err, sqrt(apply(fit$influence.pstate^2, 2:3, sum)))
if (FALSE) {
# a plot of the data that helped during creation of the example
plot(c(0,50), c(1,6), type='n', xlab='time', ylab='subject')
with(tdata, segments(time1, id, time2, id))
with(tdata, text(time2, id, as.numeric(stat2)-1, cex=1.5, col=2))
}
if (FALSE) {
# The following lines test out 4 error messages in the routine
#
# Gap in follow-up time, id 2
survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 4, 6, 3), factor(c(0,0,1,1,0,2))) ~1,
id=c(1,1,1,2,2,3))
# mismatched weights
survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,0,1,1,0,2))) ~1,
id=c(1,1,1,2,2,3), weights=c(1,1,2,1,1,4))
# in two groups at once
survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,0,1,1,0,2))) ~
c(1,1,2,1,1,2), id=c(1,1,1,2,2,3))
# state change that isn't a state change (went from 1 to 1)
survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,1,1,1,0,2))) ~1,
id=c(1,1,1,2,2,3))
}
# Check the start.time option
#
# Later work showed this test has to be false. At time 0 everyone starts in
# state (s0), but by time 20 many have shifted to another. fit2 picks up at
# the right place, but because there is no istate varaible, fit2x starts
# everyone in (s0) at time 20. There is no way for survfit to know.
if (FALSE) {
fit2 <- survfit(Surv(time1, time2, stat2) ~1, id=id, weights=wt, tdata,
start.time=20)
data2 <- subset(tdata, time2>= 20)
fit2x <- survfit(Surv(time1, time2, stat2) ~1, id=id, weights=wt, data2)
ii <- names(fit2)[!(names(fit2) %in% c("call", "start.time"))]
all.equal(unclass(fit2)[ii], unclass(fit2x)[ii])
}
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