191 lines
6.2 KiB
Plaintext
191 lines
6.2 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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> library(survival)
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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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>
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> # Tests of the weighted Cox model
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> # This is section 1.3 of my appendix -- no yet found in any of the
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> # printings though, it awaits the next edition
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> #
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> # Efron approximation
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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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> testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5),
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+ status= c(1,0,1,1,1,0,0,1,0),
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+ x= c(2,0,1,1,0,1,0,1,0),
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+ wt = c(1,2,3,4,3,2,1,2,1))
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> xx <- testw1$wt
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>
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> # Efron estimate
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> byhand <- function(beta, newx=0) {
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+ r <- exp(beta)
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+ a <- 7*r +3; b<- 4*r+2
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+ loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5)/3 +
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+ 10*log(a*2/3 +b)/3 + 10*log(a/3 +b)/3 +2*log(2*r+1))
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+
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+ hazard <- c(1/(r^2 + 11*r +7),
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+ 10/(3*c(11*r +5, a*2/3 +b, a/3+b)), 2/(2*r+1))
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+ temp <- c(hazard[1], hazard[1]+hazard[2] + hazard[3]*2/3 + hazard[4]/3,
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+ cumsum(hazard)[4:5])
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+ risk <- c(r^2, 1,r,r,1,r,1,r,1)
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+ expected <- risk* temp[c(1,1,2,2,2,3,3,4,4)]
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+
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+ # The matrix of weights, one row per obs, one col per death
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+ # deaths at 1,2,2,2, and 4
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+ riskmat <- matrix(c(1,1,1,1,1,1,1,1,1,
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+ 0,0,1,1,1,1,1,1,1,
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+ 0,0,2/3,2/3,2/3,1,1,1,1,
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+ 0,0,1/3,1/3,1/3,1,1,1,1,
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+ 0,0,0,0,0,0,0,1,1), ncol=5)
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+ wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat
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+
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+ x <- c(2,0,1,1,0,1,0,1,0)
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+ xbar <- colSums(x*wtmat)/ colSums(wtmat)
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+ imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 +
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+ 10* mean(xbar[2:4] - xbar[2:4]^2) + 2*(xbar[5] - xbar[5]^2)
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+
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+ status <- c(1,0,1,1,1,0,0,1,0)
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+ wt <- c(1,2,3,4,3,2,1,2,1)
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+ # Table of sums for score resids
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+ hazmat <- riskmat %*% diag(c(1,10/3,10/3, 10/3,2)/colSums(wtmat))
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+ dM <- -risk*hazmat #Expected part
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+ dM[1,1] <- dM[1,1] +1 # deaths at time 1
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+ for (i in 2:4) dM[3:5, i] <- dM[3:5,i] + 1/3
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+ dM[8,5] <- dM[8,5] +1
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+ mart <- rowSums(dM)
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+ resid <-dM * outer(x, xbar ,'-')
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+
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+ # Increments to the variance of the hazard
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+ var.g <- cumsum(hazard^2* c(1,3/10, 3/10, 3/10, 1/2))
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+ var.d <- cumsum((xbar-newx)*hazard)
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+
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+ sxbar <- c(xbar[1], mean(xbar[2:4]), xbar[5]) #xbar for Schoen
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+ list(loglik=loglik, imat=imat, hazard=hazard, xbar=xbar,
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+ mart=status-expected, expected=expected,
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+ score=rowSums(resid), schoen=c(2,1,1,0,1) - sxbar[c(1,2,2,2,3)],
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+ varhaz=((var.g + var.d^2/imat)* exp(2*beta*newx))[c(1,4,5)])
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+ }
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>
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> # Verify
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> temp <- byhand(0,0)
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> aeq(temp$xbar, c(13/19, 11/16, 26/38, 19/28, 2/3))
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[1] TRUE
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> aeq(temp$hazard, c(1/19, 5/24, 5/19, 5/14, 2/3))
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[1] TRUE
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>
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> fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, iter=0)
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> fit <- coxph(Surv(time, status) ~x, testw1, weights=wt)
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>
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> truth0 <- byhand(0,pi)
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> aeq(fit0$loglik[1], truth0$loglik)
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[1] TRUE
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> aeq(1/truth0$imat, fit0$var)
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[1] TRUE
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> aeq(truth0$mart, fit0$residuals)
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[1] TRUE
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> aeq(truth0$schoen, resid(fit0, 'schoen'))
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[1] TRUE
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> aeq(truth0$score, resid(fit0, 'score'))
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[1] TRUE
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> sfit <- survfit(fit0, list(x=pi), censor=FALSE)
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> aeq(sfit$std.err^2, truth0$varhaz)
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[1] TRUE
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> aeq(-log(sfit$surv), cumsum(truth0$hazard)[c(1,4,5)])
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[1] TRUE
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>
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> truth <- byhand(fit$coefficients, .3)
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> aeq(truth$loglik, fit$loglik[2])
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[1] TRUE
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> aeq(1/truth$imat, fit$var)
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[1] TRUE
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> aeq(truth$mart, fit$residuals)
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[1] TRUE
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> aeq(truth$schoen, resid(fit, 'schoen'))
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[1] TRUE
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> aeq(truth$score, resid(fit, 'score'))
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[1] TRUE
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>
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> sfit <- survfit(fit, list(x=.3), censor=FALSE)
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> aeq(sfit$std.err^2, truth$varhaz)
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[1] TRUE
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> aeq(-log(sfit$surv), (cumsum(truth$hazard)* exp(fit$coefficients*.3))[c(1,4,5)])
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[1] TRUE
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>
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>
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> fit0
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Call:
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coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt,
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iter = 0)
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coef exp(coef) se(coef) z p
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x 0.0000 1.0000 0.5843 0 1
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Likelihood ratio test=0 on 1 df, p=1
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n= 9, number of events= 5
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> summary(fit)
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Call:
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coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt)
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n= 9, number of events= 5
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coef exp(coef) se(coef) z Pr(>|z|)
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x 0.8726 2.3931 0.7126 1.225 0.221
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exp(coef) exp(-coef) lower .95 upper .95
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x 2.393 0.4179 0.5921 9.672
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Concordance= 0.637 (se = 0.161 )
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Likelihood ratio test= 1.75 on 1 df, p=0.2
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Wald test = 1.5 on 1 df, p=0.2
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Score (logrank) test = 1.58 on 1 df, p=0.2
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> resid(fit0, type='score')
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1 2 3 4 5 6
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1.24653740 0.03601108 0.14118105 0.14118105 -0.30336782 -0.27962308
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7 8 9
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0.60164259 -0.16851197 1.04608703
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> resid(fit0, type='scho')
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1 2 2 2 4
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1.3157895 0.3165727 0.3165727 -0.6834273 0.3333333
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>
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> resid(fit, type='score')
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1 2 3 4 5 6
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0.88116056 0.02477248 0.06057806 0.06057806 -0.59724033 -0.16737066
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7 8 9
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0.38040295 -0.13750290 0.66631324
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> resid(fit, type='scho')
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1 2 2 2 4
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1.0325955 0.1621759 0.1621759 -0.8378241 0.1728229
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>
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> rr1 <- resid(fit, type='mart')
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> rr2 <- resid(fit, type='mart', weighted=T)
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> aeq(rr2/rr1, testw1$wt)
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[1] TRUE
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>
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> rr1 <- resid(fit, type='score')
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> rr2 <- resid(fit, type='score', weighted=T)
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> aeq(rr2/rr1, testw1$wt)
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[1] TRUE
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>
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>
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> proc.time()
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user system elapsed
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0.440 0.024 0.462
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