309 lines
10 KiB
Plaintext
309 lines
10 KiB
Plaintext
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R Under development (unstable) (2024-04-17 r86441) -- "Unsuffered Consequences"
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Copyright (C) 2024 The R Foundation for Statistical Computing
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Platform: aarch64-unknown-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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> options(na.action=na.exclude) # preserve missings
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> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
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> library(survival)
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>
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> #
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> # Test aareg, for some simple data where the answers can be computed
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> # in closed form
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> #
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> aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...)
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>
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> test1 <- data.frame(time= c(4, 3,1,1,2,2,3),
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+ status=c(1,NA,1,0,1,1,0),
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+ x= c(0, 2,1,1,1,0,0),
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+ wt= c(1, 1:6))
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>
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> tfit <- aareg(Surv(time, status) ~ x, test1)
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> aeq(tfit$times, c(1,2,2))
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[1] TRUE
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> aeq(tfit$nrisk, c(6,4,4))
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[1] TRUE
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> aeq(tfit$coefficient, matrix(c(0,0,1/3, 1/3, 1, -1/3), ncol=2))
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[1] TRUE
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> aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2))
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[1] TRUE
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> aeq(tfit$test.statistic, c(1,1))
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[1] TRUE
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> aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16))
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[1] TRUE
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>
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> tfit <- aareg(Surv(time, status) ~ x, test1, test='nrisk')
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> aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2)) #should be as before
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[1] TRUE
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> aeq(tfit$test.statistic, c(4/3, 6/3+ 4 - 4/3))
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[1] TRUE
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> aeq(tfit$test.var, c(16/9, -16/9, -16/9, 36/9 + 16 + 16/9))
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[1] TRUE
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>
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> # In the 1-variable case, this is the same as the default Aalen weight
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> tfit <- aareg(Surv(time, status) ~ x, test1, test='variance')
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> aeq(tfit$test.statistic, c(1,1))
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[1] TRUE
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> aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16))
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[1] TRUE
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>
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> #
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> # Repeat the above, with case weights
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> #
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> tfit <- aareg(Surv(time, status) ~x, test1, weights=wt)
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> aeq(tfit$times, c(1,2,2))
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[1] TRUE
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> aeq(tfit$nrisk, c(21,16,16))
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[1] TRUE
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> aeq(tfit$coefficient, matrix(c(0,0,5/12, 2/9, 1, -5/12), ncol=2))
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[1] TRUE
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> aeq(tfit$tweight, matrix(c(12,12,12, 36/7, 3,3), ncol=2))
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[1] TRUE
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> aeq(tfit$test.statistic, c(5, 72/63 + 3 - 15/12))
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[1] TRUE
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> aeq(tfit$test.var, c(25, -25/4, -25/4, (72/63)^2 + 9 + (5/4)^2))
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[1] TRUE
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>
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> tfit <- aareg(Surv(time, status) ~x, test1, weights=wt, test='nrisk')
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> aeq(tfit$test.statistic, c(20/3, 42/9 + 16 - 16*5/12))
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[1] TRUE
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> aeq(tfit$test.var, c(400/9, -400/9, -400/9,
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+ (42/9)^2 + 16^2 + (16*5/12)^2))
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[1] TRUE
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>
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> #
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> # Make a test data set with no NAs, in sorted order, no ties,
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> # 15 observations
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> tdata <- lung[15:29, c('time', 'status', 'age', 'sex', 'ph.ecog')]
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> tdata$status <- tdata$status -1
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> tdata <- tdata[order(tdata$time, tdata$status),]
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> row.names(tdata) <- 1:15
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> tdata$status[8] <- 0 #for some variety
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>
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> afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, tdata, nmin=6)
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> #
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> # Now, do it "by hand"
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> cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, tdata, iter=0,
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+ method='breslow')
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> dt1 <- coxph.detail(cfit)
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> sch1 <- resid(cfit, type='schoen')
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>
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> # First estimate of Aalen: from the Cox computations, first 9
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> # The first and last cols of the ninth are somewhat unstable (approx =0)
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> mine <- rbind(solve(dt1$imat[,,1], sch1[1,]),
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+ solve(dt1$imat[,,2], sch1[2,]),
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+ solve(dt1$imat[,,3], sch1[3,]),
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+ solve(dt1$imat[,,4], sch1[4,]),
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+ solve(dt1$imat[,,5], sch1[5,]),
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+ solve(dt1$imat[,,6], sch1[6,]),
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+ solve(dt1$imat[,,7], sch1[7,]),
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+ solve(dt1$imat[,,8], sch1[8,]),
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+ solve(dt1$imat[,,9], sch1[9,]))
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> mine <- diag(1/dt1$nrisk[1:9]) %*% mine
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>
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> aeq(mine, afit$coefficient[1:9, -1])
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[1] TRUE
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>
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> #
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> # Check out the dfbeta matrix from aareg
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> # Note that it is kept internally in time order, not data set order
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> # Those who want residuals should use the resid function!
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>
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> #
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> # First, the simple test case where I know the anwers
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> #
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> afit <- aareg(Surv(time, status) ~ x, test1, dfbeta=T)
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> temp <- c(rep(0,6), #intercepts at time 1
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+ c(2,-1,-1,0,0,0)/9, #alpha at time 1
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+ c(0,0,0,2, -1, -1)/9, #intercepts at time 2
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+ c(0,0,0,-2,1,1)/9) #alpha at time 2
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> aeq(afit$dfbeta, temp)
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[1] TRUE
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>
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> #
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> #Now a multivariate data set
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> #
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> afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T)
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>
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> ord <- order(lung$time, -lung$status)
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> cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,],
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+ method='breslow', iter=0, x=T)
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> cdt <- coxph.detail(cfit, riskmat=T)
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>
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> # an arbitrary list of times
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> acoef <- rowsum(afit$coefficient, afit$times) #per death time coefs
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> indx <- match(cdt$time, afit$times)
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> for (i in c(2,5,27,54,101, 135)) {
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+ lwho <- (cdt$riskmat[,i]==1)
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+ lmx <- cfit$x[lwho,]
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+ lmy <- 1*( cfit$y[lwho,2]==1 & cfit$y[lwho,1] == cdt$time[i])
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+ fit <- lm(lmy~ lmx)
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+ cat("i=", i, "coef=", aeq(fit$coefficients, acoef[i,]))
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+
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+ rr <- diag(resid(fit))
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+ zz <- cbind(1,lmx)
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+ zzinv <- solve(t(zz) %*% zz)
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+ cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],]))
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+
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+ df <- t(zzinv %*% t(zz) %*% rr)
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+ cat(" dfbeta=", aeq(df, afit$dfbeta[lwho,,i]), "\n")
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+ }
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i= 2 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 5 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 27 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 54 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 101 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 135 coef= TRUE twt= TRUE dfbeta= TRUE
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>
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>
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> # Repeat it with case weights
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> ww <- rep(1:5, length.out=nrow(lung))/ 3.0
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> afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T,
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+ weights=ww)
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> cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,],
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+ method='breslow', iter=0, x=T, weights=ww[ord])
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> cdt <- coxph.detail(cfit, riskmat=T)
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>
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> acoef <- rowsum(afit$coefficient, afit$times) #per death time coefs
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> for (i in c(2,5,27,54,101, 135)) {
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+ who <- (cdt$riskmat[,i]==1)
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+ x <- cfit$x[who,]
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+ y <- 1*( cfit$y[who,2]==1 & cfit$y[who,1] == cdt$time[i])
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+ w <- cfit$weights[who]
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+ fit <- lm(y~x, weights=w)
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+ cat("i=", i, "coef=", aeq(fit$coefficients, acoef[i,]))
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+
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+ rr <- diag(resid(fit))
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+ zz <- cbind(1,x)
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+ zzinv <- solve(t(zz)%*% (w*zz))
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+ cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],]))
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+
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+ df <- t(zzinv %*% t(zz) %*% (w*rr))
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+ cat(" dfbeta=", aeq(df, afit$dfbeta[who,,i]), "\n")
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+ }
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i= 2 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 5 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 27 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 54 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 101 coef= TRUE twt= TRUE dfbeta= TRUE
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i= 135 coef= TRUE twt= TRUE dfbeta= TRUE
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>
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> #
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> # Check that the test statistic computed within aareg and
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> # the one recomputed within summary.aareg are the same.
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> # Of course, they could both be wrong, but at least they'll agree!
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> # If the maxtime argument is used in summary, it recomputes the test,
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> # even if we know that it wouldn't have had to.
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> #
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> # Because the 1-variable and >1 variable case have different code, test
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> # them both.
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> #
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> afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T)
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> asum <- summary(afit, maxtime=max(afit$times))
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> aeq(afit$test.statistic, asum$test.statistic)
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[1] TRUE
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> aeq(afit$test.var, asum$test.var)
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[1] TRUE
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> aeq(afit$test.var2, asum$test.var2)
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[1] TRUE
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>
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> print(afit)
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Call:
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aareg(formula = Surv(time, status) ~ age, data = lung, dfbeta = T)
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n= 228
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139 out of 139 unique event times used
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slope coef se(coef) robust se z p
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Intercept -0.000872 -0.000905 4.26e-03 4.13e-03 -0.219 0.8270
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age 0.000110 0.000142 6.96e-05 6.75e-05 2.110 0.0351
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Chisq=4.44 on 1 df, p=0.0351; test weights=aalen
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>
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> afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T, test='nrisk')
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> asum <- summary(afit, maxtime=max(afit$times))
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> aeq(afit$test.statistic, asum$test.statistic)
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[1] TRUE
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> aeq(afit$test.var, asum$test.var)
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[1] TRUE
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> aeq(afit$test.var2, asum$test.var2)
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[1] TRUE
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>
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> summary(afit)
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slope coef se(coef) robust se z p
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Intercept -0.000954 -0.117 0.53500 0.53300 -0.219 0.8260
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age 0.000105 0.018 0.00875 0.00873 2.060 0.0398
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Chisq=4.23 on 1 df, p=0.0398; test weights=nrisk
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>
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> #
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> # Mulitvariate
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> #
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> afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung,
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+ dfbeta=T)
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> asum <- summary(afit, maxtime=max(afit$times))
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> aeq(afit$test.statistic, asum$test.statistic)
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[1] TRUE
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> aeq(afit$test.var, asum$test.var)
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[1] TRUE
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> aeq(afit$test.var2, asum$test.var2)
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[1] TRUE
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>
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> print(afit)
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Call:
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aareg(formula = Surv(time, status) ~ age + sex + ph.karno + pat.karno,
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data = lung, dfbeta = T)
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n=224 (4 observations deleted due to missingness)
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132 out of 136 unique event times used
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slope coef se(coef) robust se z p
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Intercept 2.15e-02 0.025000 8.45e-03 7.72e-03 3.25 0.00117
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age 3.09e-05 0.000076 7.32e-05 6.49e-05 1.17 0.24100
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sex -2.96e-03 -0.004020 1.25e-03 1.23e-03 -3.27 0.00109
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ph.karno -6.77e-05 -0.000083 6.69e-05 8.30e-05 -1.00 0.31700
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pat.karno -1.01e-04 -0.000112 5.59e-05 5.70e-05 -1.96 0.05010
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Chisq=23.36 on 4 df, p=0.000107; test weights=aalen
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>
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> afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung,
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+ dfbeta=T, test='nrisk')
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> asum <- summary(afit, maxtime=max(afit$times))
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> aeq(afit$test.statistic, asum$test.statistic)
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[1] TRUE
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> aeq(afit$test.var, asum$test.var)
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[1] TRUE
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> aeq(afit$test.var2, asum$test.var2)
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[1] TRUE
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>
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> summary(afit)
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slope coef se(coef) robust se z p
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Intercept 2.12e-02 3.0600 1.04000 0.95600 3.20 0.00138
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age 3.18e-05 0.0107 0.00928 0.00818 1.31 0.19100
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sex -2.99e-03 -0.4940 0.15300 0.15200 -3.26 0.00112
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ph.karno -8.37e-05 -0.0113 0.00783 0.00965 -1.17 0.24100
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pat.karno -8.50e-05 -0.0133 0.00724 0.00767 -1.73 0.08320
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Chisq=22.39 on 4 df, p=0.000168; test weights=nrisk
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>
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> # Weights play no role in the final computation of the test statistic, given
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> # the coefficient matrix, nrisk, and dfbeta as inputs. (Weights do
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> # change the inputs). So there is no need to reprise the above with
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> # case weights.
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>
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> proc.time()
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user system elapsed
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0.540 0.008 0.545
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