388 lines
14 KiB
Plaintext
388 lines
14 KiB
Plaintext
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R Under development (unstable) (2024-04-01 r86255) -- "Unsuffered Consequences"
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Copyright (C) 2024 The R Foundation for Statistical Computing
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Platform: x86_64-pc-linux-gnu
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R is free software and comes with ABSOLUTELY NO WARRANTY.
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You are welcome to redistribute it under certain conditions.
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Type 'license()' or 'licence()' for distribution details.
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R is a collaborative project with many contributors.
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Type 'contributors()' for more information and
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'citation()' on how to cite R or R packages in publications.
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Type 'demo()' for some demos, 'help()' for on-line help, or
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'help.start()' for an HTML browser interface to help.
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Type 'q()' to quit R.
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> #
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> # A tiny multi-state example
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> #
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> library(survival)
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> aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
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> mtest <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5),
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+ t1= c(0, 4, 9, 0, 2, 0, 2, 8, 1, 3),
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+ t2= c(4, 9, 10, 5, 9, 2, 8, 9, 3, 11),
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+ st= c(1, 2, 1, 2, 3, 1, 3, 0, 2, 0))
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>
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> mtest$state <- factor(mtest$st, 0:3, c("censor", "a", "b", "c"))
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>
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> if (FALSE) {
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+ # this graph is very useful when debugging
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+ temp <- survcheck(Surv(t1, t2, state) ~1, mtest, id=id)
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+ plot(c(0,11), c(1,5.1), type='n', xlab="Time", ylab= "Subject")
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+ with(mtest, segments(t1+.1, id, t2, id, col=as.numeric(temp$istate)))
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+ event <- subset(mtest, state!='censor')
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+ text(event$t2, event$id+.2, as.character(event$state))
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+ }
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>
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> mtest <- mtest[c(1,3,2,4,5,7,6,10, 9, 8),] #not in time order
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>
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> mfit <- survfit(Surv(t1, t2, state) ~ 1, mtest, id=id, time0=FALSE)
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>
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> # True results
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> #
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> #time state probabilities
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> # entry a b c entry a b c
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> #
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> #0 124 1 0 0 0
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> #1+ 1245
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> #2+ 1235 4 3/4 1/4 0 0 4 -> a, add 3
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> #3+ 123 4 5 9/16 1/4 3/16 0 5 -> b
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> #4+ 23 14 5 6/16 7/16 3/16 0 1 -> a
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> #5+ 3 14 5 3/16 7/16 6/16 0 2 -> b, exits
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> #8+ 3 1 5 4 3/16 7/32 6/16 7/32 4 -> c
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> #9+ 15 0 0 19/32 13/32 1->b, 3->c & exit
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> # 10+ 1 5 19/64 19/64 13/32 1->a
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>
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> aeq(mfit$n.risk, matrix(c(4,4,3,2,1,1,0,0,
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+ 0,1,1,2,2,1,0,0,
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+ 0,0,1,1,1,1,2,1,
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+ 0,0,0,0,0,1,0,0), ncol=4))
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[1] TRUE
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> aeq(mfit$pstate, matrix(c(24, 18, 12, 6, 6, 0, 0, 0,
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+ 8, 8, 14, 14, 7, 0, 9.5, 9.5,
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+ 0, 6, 6, 12, 12,19,9.5, 9.5,
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+ 0, 0, 0, 0, 7, 13, 13, 13)/32, ncol=4))
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[1] TRUE
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> aeq(mfit$n.transition, matrix(c(1,0,1,0,0,0,0,0,
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+ 0,0,0,0,0,0,1,0,
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+ 0,1,0,1,0,0,0,0,
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+ 0,0,0,0,0,1,0,0,
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+ 0,0,0,0,0,1,0,0,
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+ 0,0,0,0,1,0,0,0), ncol=6))
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[1] TRUE
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> all.equal(mfit$time, c(2, 3, 4, 5, 8, 9, 10, 11))
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[1] TRUE
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>
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> # Somewhat more complex.
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> # Scramble the input data
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> # Not everyone starts at the same time or in the same state
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> # Case weights
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> #
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> tdata <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5),
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+ t1= c(0, 4, 9, 1, 2, 0, 2, 8, 1, 3),
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+ t2= c(4, 9, 10, 5, 9, 2, 8, 9, 3, 11),
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+ st= c(1, 2, 1, 2, 3, 1, 3, 0, 3, 0),
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+ i0= c(4, 1, 2, 1, 4, 4, 1, 3, 2, 3),
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+ wt= 1:10)
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>
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> tdata$st <- factor(tdata$st, c(0:3),
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+ labels=c("censor", "a", "b", "c"))
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> tdata$i0 <- factor(tdata$i0, c(4, 1:3),
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+ labels=c("entry", "a", "b", "c"))
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> if (FALSE) {
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+ #useful picture
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+ temp <- survcheck(Surv(t1, t2, st) ~1, tdata, id=id, istate=i0)
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+ plot(c(0,11), c(1,5.5), type='n', xlab="Time", ylab= "Subject")
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+ with(tdata, segments(t1+.1, id, t2, id, col=as.numeric(temp$istate)))
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+ with(subset(tdata, st!= "censor"),
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+ text(t2, id+.15, as.character(st)))
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+ with(tdata, text((t1+t2)/2, id+.25, wt))
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+ with(subset(tdata, !duplicated(id)),
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+ text(t1, id+.15, as.character(i0)))
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+ #abline(v=c(2:5, 8:11), lty=3, col='gray')
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+ }
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>
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> tfun <- function(data=tdata) {
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+ reorder <- c(10, 9, 1, 2, 5, 4, 3, 7, 8, 6)
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+ new <- data[reorder,]
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+ new
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+ }
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>
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> # These weight vectors are in the order of tdata
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> # w[9] is the weight for subject 5 at time 1.5, for instance
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> # p0 is defined as all those at risk just before the first event, which in
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> # this data set is entry:a at time 2 for id=4; id 1,2,4,5 at risk
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>
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> # When the functions below were written, the entry state was listed last.
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> # Currently the entry state is first, so "[swap]" was added to the aj routines
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> # rather than rearranging the formulas
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> swap <- c(4,1,2,3)
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> p0 <- function(w) c( w[1]+ w[6], w[4], w[9], 0)/ (w[1]+ w[4] + w[6] + w[9])
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>
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> # aj2 = Aalen-Johansen H matrix at time 2, etc.
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> aj2 <- function(w) {
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+ #subject 4 moves from entry to 'a'
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+ rbind(c(1, 0, 0, 0),
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+ c(0, 1, 0, 0),
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+ c(0, 0, 1, 0),
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+ c(w[6], 0, 0, w[1])/(w[1] + w[6]))[swap, swap]
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+ }
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> aj3 <- function(w) rbind(c(1, 0, 0, 0),
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+ c(0, 0, 1, 0), # 5 moves from b to c
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+ c(0, 0, 1, 0),
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+ c(0, 0, 0, 1))[swap,swap]
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> aj4 <- function(w) {
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+ # subject 1 moves from entry to a
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+ rbind(c(1, 0, 0, 0),
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+ c(0, 1, 0, 0),
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+ c(0, 0, 1, 0),
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+ c(w[1], 0, 0, w[5])/(w[1] + w[5])) [swap, swap]
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+ }
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> aj5 <- function(w) {
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+ # subject 2 from a to b
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+ rbind(c(w[2]+w[7], w[4], 0, 0)/(w[2]+ w[4] + w[7]),
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+ c(0, 1, 0, 0),
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+ c(0, 0, 1, 0),
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+ c(0, 0, 0, 1))[swap, swap]
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+ }
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> aj8 <- function(w) rbind(c(w[2], 0, w[7], 0)/(w[2]+ w[7]), # 4 a to c
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+ c(0, 1, 0, 0),
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+ c(0, 0, 1, 0),
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+ c(0, 0, 0, 1))[swap, swap]
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> aj9 <- function(w) rbind(c(0, 1, 0, 0), # 1 a to b
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+ c(0, 1, 0, 0),
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+ c(0, 0, 1, 0),
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+ c(0, 0, 1 ,0)) [swap, swap] # 3 entry to c
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> aj10 <- function(w)rbind(c(1, 0, 0, 0),
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+ c(1, 0, 0, 0), #1 b to a
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+ c(0, 0, 1, 0),
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+ c(0, 0, 0, 1))[swap, swap]
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>
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> #time state
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> # a b c entry
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> #
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> #1 2 5 14 initial distribution
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> #2 24 5 1 4 -> a, add 3
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> #3 24 5 13 5 from b to c
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> #4 124 5 3 1 -> a
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> #5 14 5 3 2 -> b, exits
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> #8 1 45 3 4 -> c
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> #9 1 45 1->b, 3->c & exit
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> #10 1 45 1->a
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>
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> # P is a product of matrices
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> dopstate <- function(w) {
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+ p1 <- p0(w)
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+ p2 <- p1 %*% aj2(w)
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+ p3 <- p2 %*% aj3(w)
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+ p4 <- p3 %*% aj4(w)
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+ p5 <- p4 %*% aj5(w)
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+ p8 <- p5 %*% aj8(w)
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+ p9 <- p8 %*% aj9(w)
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+ p10<- p9 %*% aj10(w)
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+ rbind(p2, p3, p4, p5, p8, p9, p10, p10)
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+ }
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>
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> # Check the pstate estimate
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> w1 <- rep(1,10)
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> mtest2 <- tfun(tdata) # scrambled order
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> mfit2 <- survfit(Surv(t1, t2, st) ~ 1, tdata, id=id, istate=i0,
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+ time0=FALSE) # ordered
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> aeq(mfit2$pstate, dopstate(w1))
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[1] TRUE
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> aeq(mfit2$p0, p0(w1))
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[1] TRUE
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>
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> mfit2b <- survfit(Surv(t1, t2, st) ~ 1, mtest2, id=id, istate=i0, time0=FALSE)
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> aeq(mfit2b$pstate, dopstate(w1))
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[1] TRUE
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> aeq(mfit2b$p0, p0(w1))
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[1] TRUE
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>
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> mfit2b$call <- mfit2$call <- NULL
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> all.equal(mfit2b, mfit2)
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[1] TRUE
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> aeq(mfit2$transitions, c(2,0,1,0, 0,2,0,0, 1,1,1,0, 0,0,0,2))
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[1] TRUE
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>
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> # Now the harder one, where subjects change weights
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> mfit3 <- survfit(Surv(t1, t2, st) ~ 1, tdata, id=id, istate=i0,
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+ weights=wt, influence=TRUE, time0=FALSE)
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> aeq(mfit3$p0, p0(1:10))
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[1] TRUE
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> aeq(mfit3$pstate, dopstate(1:10))
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[1] TRUE
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>
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>
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> # The derivative of a matrix product AB is (dA)B + A(dB) where dA is the
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> # elementwise derivative of A and etc for B.
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> # dp0 creates the derivatives of p0 with respect to each subject, a 5 by 4
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> # matrix
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> # All the functions below are hand coded for a weight vector that is in
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> # exactly the same order as the rows of mtest.
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> # Since p0 = (w[1]+ w[6], w[4], w[9], 0)/ (w[1]+ w[4] + w[6] + w[9])
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> # and subject id is 1,1,1, 2, 3, 4,4,4, 5,5
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> # we get the derivative below
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> #
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>
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> dp0 <- function(w) { # influence just before the first event
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+ p <- p0(w)
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+ w0 <- w[c(1,4,6,9)] # the 4 obs at the start, subjects 1, 2, 4, 5
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+ rbind(c(1,0, 0, 0) - p, # subject 1 affects p[entry]
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+ c(0,1, 0, 0) - p, # subject 2 affects p[a]
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+ 0, # subject 3 affects none
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+ c(1, 0, 0, 0) - p, # subject 4 affect p[entry]
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+ c(0, 0, 1, 0) - p)/ # subject 5 affects p[b]
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+ sum(w0)
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+ }
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>
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>
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> dp2 <- function(w) {
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+ h2 <- aj2(w) # H matrix at time 2
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+ part1 <- dp0(w) %*% h2
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+
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+ # 1 and 4 in entry, obs 4 moves from entry to a
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+ mult <- p0(w)[1]/(w[1] + w[6]) #p(t-) / weights in state
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+ part2 <- rbind((c(1,0,0,0)- h2[1,]) * mult,
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+ 0,
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+ 0,
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+ (c(0,1,0,0) - h2[1,]) * mult,
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+ 0)
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+ part1 + part2
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+ }
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>
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> dp3 <- function(w) {
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+ dp2(w) %*% aj3(w)
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+ }
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>
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> dp4 <- function(w) {
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+ h4 <- aj4(w) # H matrix at time 4
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+ part1 <- dp3(w) %*% h4
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+
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+ # subjects 1 and 3 in state entry (obs 1 and 5) 1 moves to a
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+ mult <- dopstate(w)[2,1]/ (w[1] + w[5]) # p_1(time 4-0) / wt
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+ part2 <- rbind((c(0,1,0,0)- h4[1,]) * mult,
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+ 0,
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+ (c(1,0,0,0)- h4[1,]) * mult,
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+ 0,
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+ 0)
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+ part1 + part2
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+ }
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> dp5 <- function(w) {
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+ h5 <- aj5(w) # H matrix at time 5
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+ part1 <- dp4(w) %*% h5
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+
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+ # subjects 124 in state a (obs 2,4,7), 2 goes to b
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+ mult <- dopstate(w)[3,2]/ (w[2] + w[4] + w[7])
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+ part2 <- rbind((c(0,1,0,0)- h5[2,]) * mult,
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+ (c(0,0,1,0)- h5[2,]) * mult,
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+ 0,
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+ (c(0,1,0,0)- h5[2,]) * mult,
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+ 0)
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+ part1 + part2
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+ }
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> dp8 <- function(w) {
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+ h8 <- aj8(w) # H matrix at time 8
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+ part1 <- dp5(w) %*% h8
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+
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+ # subjects 14 in state a (obs 2 &7), 4 goes to c
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+ mult <- dopstate(w)[4, 2]/ (w[2] + w[7])
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+ part2 <- rbind((c(0,1,0,0)- h8[2,]) * mult,
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+ 0,
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+ 0,
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+ (c(0,0,0,1)- h8[2,]) * mult,
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+ 0)
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+ part1 + part2
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+ }
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> dp9 <- function(w) dp8(w) %*% aj9(w)
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> dp10<- function(w) dp9(w) %*% aj10(w)
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>
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> #
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> # Feb 4 2024: discovered that the variance computation above is incorrect.
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> # Let U = influence for phat, with one row per observation in the data
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> # The weighted per subject influence is Z(t)= BDU(t) where
|
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|
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> # B= rbind(c(1,1,1,0,0,0,0,0,0,0),
|
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|
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> # c(0,0,0,1,0,0,0,0,0,0),
|
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|
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> # c(0,0,0,0,1,0,0,0,0,0),
|
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|
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> # c(0,0,0,0,0,1,1,1,0,0),
|
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|
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> # c(0,0,0,0,0,0,0,0,1,1))
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||
|
|
> # and D= diag(1:10)
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||
|
|
> # which can be summarized as "weight each row, then add over subjects".
|
||
|
|
> # The variance at time t is the column sums of Z^2(t) (elementwise squares)
|
||
|
|
> #
|
||
|
|
> # The code above for dp0, dp2, etc returns BU, which matches the computation of
|
||
|
|
> # the influence in survfitci.c. If the weight for a given subject is constant
|
||
|
|
> # over time, then BDU= WBU where W is the diagonal matrix of per-subject
|
||
|
|
> # weights: survfitci.c implicitly made this assumption, and was correct
|
||
|
|
> # in this case. It returned U as the influence, which matches dp0 etc.
|
||
|
|
> #
|
||
|
|
> # survfitci.c has been replaced by survfitaj.c, which uses the careful
|
||
|
|
> # derivations in the methods vignette, and returns BDU.
|
||
|
|
> # The checks below have been changed to a case with constant weights per
|
||
|
|
> # subject. R code to test for general weights is in mstate2.R
|
||
|
|
> #
|
||
|
|
> w1 <- tdata$id
|
||
|
|
> mfit4 <- survfit(Surv(t1, t2, st) ~1, tdata, id=id, weights=id, istate=i0,
|
||
|
|
+ influence=TRUE, time0= FALSE)
|
||
|
|
> aeq(mfit4$influence[,1,], 1:5*dp2(w1)) #time 2
|
||
|
|
[1] TRUE
|
||
|
|
> aeq(mfit4$influence[,2,], 1:5*dp3(w1))
|
||
|
|
[1] TRUE
|
||
|
|
> aeq(mfit4$influence[,3,], 1:5*dp4(w1))
|
||
|
|
[1] TRUE
|
||
|
|
> aeq(mfit4$influence[,4,], 1:5*dp5(w1))
|
||
|
|
[1] TRUE
|
||
|
|
> aeq(mfit4$influence[,5,], 1:5*dp8(w1)) # time 8
|
||
|
|
[1] TRUE
|
||
|
|
> aeq(mfit4$influence[,6,], 1:5* dp9(w1))
|
||
|
|
[1] TRUE
|
||
|
|
> aeq(mfit4$influence[,7,], 1:5* dp10(w1))
|
||
|
|
[1] TRUE
|
||
|
|
> aeq(mfit4$influence[,8,], 1:5* dp10(w1)) # no changes at time 11
|
||
|
|
[1] TRUE
|
||
|
|
>
|
||
|
|
> ssq <- function(x) sqrt(sum(x^2))
|
||
|
|
> temp2 <- apply(mfit4$influence.pstate, 2:3, ssq)
|
||
|
|
> aeq(temp2, mfit4$std.err)
|
||
|
|
[1] TRUE
|
||
|
|
>
|
||
|
|
> if (FALSE) { # old test, survfitci returned the time 0 influence as well
|
||
|
|
+ w1 <- 1:10
|
||
|
|
+ aeq(mfit3$influence[,1,], dp0(w1))
|
||
|
|
+ aeq(mfit3$influence[,2,], dp2(w1))
|
||
|
|
+ aeq(mfit3$influence[,3,], dp3(w1))
|
||
|
|
+ aeq(mfit3$influence[,4,], dp4(w1))
|
||
|
|
+ aeq(mfit3$influence[,5,], dp5(w1))
|
||
|
|
+ aeq(mfit3$influence[,6,], dp8(w1))
|
||
|
|
+ aeq(mfit3$influence[,7,], dp9(w1))
|
||
|
|
+ aeq(mfit3$influence[,8,], dp10(w1))
|
||
|
|
+ aeq(mfit3$influence[,9,], dp10(w1)) # no changes at time 11
|
||
|
|
+ } # end of if (FALSE)
|
||
|
|
>
|
||
|
|
> # The cumulative hazard at each time point is remapped from a matrix
|
||
|
|
> # into a vector (in survfit)
|
||
|
|
> # First check out the names
|
||
|
|
> nstate <- length(mfit4$states)
|
||
|
|
> temp <- matrix(0, nstate, nstate)
|
||
|
|
> indx1 <- match(rownames(mfit4$transitions), mfit4$states)
|
||
|
|
> indx2 <- match(colnames(mfit4$transitions), mfit4$states, nomatch=0)
|
||
|
|
> temp[indx1, indx2] <- mfit4$transitions[, indx2>0]
|
||
|
|
> # temp is an nstate by nstate version of the transitions matrix
|
||
|
|
> from <- row(temp)[temp>0]
|
||
|
|
> to <- col(temp)[temp>0]
|
||
|
|
> all.equal(colnames(mfit4$cumhaz), paste(from, to, sep='.'))
|
||
|
|
[1] TRUE
|
||
|
|
>
|
||
|
|
> # check the cumulative hazard
|
||
|
|
> temp <- mfit4$n.risk[,from]
|
||
|
|
> hazard <- mfit4$n.transition/ifelse(temp==0, 1, temp)
|
||
|
|
> aeq(apply(hazard, 2, cumsum), mfit4$cumhaz)
|
||
|
|
[1] TRUE
|
||
|
|
>
|
||
|
|
>
|
||
|
|
> proc.time()
|
||
|
|
user system elapsed
|
||
|
|
0.958 0.105 1.055
|