241 lines
7.9 KiB
R
241 lines
7.9 KiB
R
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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# Tests of the weighted Cox model
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#
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# Similar data set to test1, but add weights,
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# a double-death/censor tied time
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# a censored last subject
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# The latter two are cases covered only feebly elsewhere.
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#
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# The data set testw2 has the same data, but done via replication
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#
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aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
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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 <- c(1,2,3,4,3,2,1,2,1)
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testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx),
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status= rep(c(1,0,1,1,1,0,0,1,0), xx),
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x= rep(c(2,0,1,1,0,1,0,1,0), xx),
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id= rep(1:9, xx))
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indx <- match(1:9, testw2$id)
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testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx),
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status= rep(c(1,0,1,1,1,0,0,1,0), xx),
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x= rep(c(2,0,1,1,0,1,0,1,0), xx),
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id= rep(1:9, xx))
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indx <- match(1:9, testw2$id)
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fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt,
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method='breslow', iter=0)
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fit0b <- coxph(Surv(time, status) ~x, testw2, ties='breslow', iter=0)
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fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, ties='breslow')
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fitb <- coxph(Surv(time, status) ~x, testw2, ties='breslow')
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texp <- function(beta) { # expected, Breslow estimate
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r <- exp(beta)
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temp <- cumsum(c(1/(r^2 + 11*r +7), 10/(11*r +5), 2/(2*r+1)))
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c(r^2, 1,r,r,1,r,1,r,1)* temp[c(1,1,2,2,2,2,2,3,3)]
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}
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aeq(texp(0), c(1/19, 1/19, rep(103/152, 5), rep(613/456,2))) #verify texp()
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xbar <- function(beta) { # xbar, Breslow estimate
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r <- exp(beta)
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temp <- r* rep(c(2*r + 11, 11/10, 1), c(2, 5, 2))
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temp * texp(beta)
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}
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fit0
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summary(fit)
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aeq(resid(fit0), testw1$status - texp(0))
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resid(fit0, type='score')
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resid(fit0, type='scho')
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aeq(resid(fit0, type='mart'), (resid(fit0b, type='mart'))[indx])
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aeq(resid(fit0, type='scor'), (resid(fit0b, type='scor'))[indx])
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aeq(unique(resid(fit0, type='scho')), unique(resid(fit0b, type='scho')))
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aeq(resid(fit, type='mart'), testw1$status - texp(fit$coef))
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resid(fit, type='score')
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resid(fit, type='scho')
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aeq(resid(fit, type='mart'), (resid(fitb, type='mart'))[indx])
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aeq(resid(fit, type='scor'), (resid(fitb, type='scor'))[indx])
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aeq(unique(resid(fit, type='scho')), unique(resid(fitb, type='scho')))
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rr1 <- resid(fit, type='mart')
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rr2 <- resid(fit, type='mart', weighted=T)
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aeq(rr2/rr1, testw1$wt)
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rr1 <- resid(fit, type='score')
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rr2 <- resid(fit, type='score', weighted=T)
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aeq(rr2/rr1, testw1$wt)
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fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, ties='efron')
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fit
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resid(fit, type='mart')
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resid(fit, type='score')
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resid(fit, type='scho')
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# Tests of the weighted Cox model, AG form of the data
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# Same solution as doweight1.s
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#
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testw3 <- data.frame(id = c( 1, 1, 2, 3, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9),
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begin= c( 0, 5, 0, 0,10,15, 0, 0,14, 0, 0, 0,23, 0),
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time= c( 5,10,10,10,15,20,20,14,20,20,30,23,40,50),
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status= c( 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0),
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x= c( 2, 2, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0),
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wt = c( 1, 1, 2, 3, 3, 3, 4, 3, 3, 2, 1, 2, 2, 1))
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fit0 <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt,
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ties='breslow', iter=0)
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fit <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, ties='breslow')
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fit0
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summary(fit)
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resid(fit0, type='mart', collapse=testw3$id)
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resid(fit0, type='score', collapse=testw3$id)
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resid(fit0, type='scho')
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resid(fit, type='mart', collapse=testw3$id)
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resid(fit, type='score', collapse=testw3$id)
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resid(fit, type='scho')
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fit0 <- coxph(Surv(begin, time, status) ~x,testw3, weights=wt, iter=0)
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resid(fit0, 'mart', collapse=testw3$id)
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resid(coxph(Surv(begin, time, status) ~1, testw3, weights=wt)
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, collapse=testw3$id) #Null model
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fit <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, ties='efron')
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fit
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resid(fit, type='mart', collapse=testw3$id)
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resid(fit, type='score', collapse=testw3$id)
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resid(fit, type='scho')
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#
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# Check out the impact of weights on the dfbetas
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# Am I computing them correctly?
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#
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wtemp <- rep(1,26)
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wtemp[c(5,10,15)] <- 2:4
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fit <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp)
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rr <- resid(fit, 'dfbeta')
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fit1 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp,
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subset=(-5))
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fit2 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp,
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subset=(-10))
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fit3 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp,
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subset=(-15))
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#
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# Effect of case weights on expected survival curves post Cox model
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#
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fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, ties='breslow',
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iter=0)
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fit0b <- coxph(Surv(time, status) ~x, testw2, ties='breslow', iter=0)
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surv1 <- survfit(fit0, newdata=list(x=0))
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surv2 <- survfit(fit0b, newdata=list(x=0))
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aeq(surv1$surv, surv2$surv)
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#
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# Check out the Efron approx.
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#
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fit0 <- coxph(Surv(time, status) ~x,testw1, weights=wt, iter=0)
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fit <- coxph(Surv(time, status) ~x,testw1, weights=wt)
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resid(fit0, 'mart')
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resid(coxph(Surv(time, status) ~1, testw1, weights=wt)) #Null model
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# lfun is the known log-likelihood for this data set, worked out in the
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# appendix of Therneau and Grambsch
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# ufun is the score vector and ifun the information matrix
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lfun <- function(beta) {
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r <- exp(beta)
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a <- 7*r +3
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b <- 4*r +2
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11*beta - ( log(r^2 + 11*r +7) +
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(10/3)*(log(a+b) + log(2*a/3 +b) + log(a/3 +b)) + 2*log(2*r +1))
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}
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aeq(fit0$log[1], lfun(0))
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aeq(fit$log[2], lfun(fit$coef))
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ufun <- function(beta, efron=T) { #score statistic
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r <- exp(beta)
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xbar1 <- (2*r^2+11*r)/(r^2+11*r +7)
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xbar2 <- 11*r/(11*r +5)
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xbar3 <- 2*r/(2*r +1)
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xbar2b<- 26*r/(26*r+12)
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xbar2c<- 19*r/(19*r + 9)
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temp <- 11 - (xbar1 + 2*xbar3)
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if (efron) temp - (10/3)*(xbar2 + xbar2b + xbar2c)
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else temp - 10*xbar2
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}
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print(ufun(fit$coef) < 1e-4) # Should be true
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ifun <- function(beta, efron=T) { # information matrix
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r <- exp(beta)
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xbar1 <- (2*r^2+11*r)/(r^2+11*r +7)
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xbar2 <- 11*r/(11*r +5)
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xbar3 <- 2*r/(2*r +1)
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xbar2b<- 26*r/(26*r+12)
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xbar2c<- 19*r/(19*r + 9)
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temp <- ((4*r^2 + 11*r)/(r^2+11*r +7) - xbar1^2) +
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2*(xbar3 - xbar3^2)
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if (efron) temp + (10/3)*((xbar2- xbar2^2) + (xbar2b - xbar2b^2) +
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(xbar2c -xbar2c^2))
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else temp + 10 * (xbar2- xbar2^2)
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}
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aeq(fit0$var, 1/ifun(0))
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aeq(fit$var, 1/ifun(fit$coef))
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# Make sure that the weights pass through the residuals correctly
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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$wt)
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rr1 <- resid(fit, type='score')
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rr2 <- resid(fit, type='score', weighted=T)
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aeq(rr2/rr1, testw1$wt)
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#
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# Look at the individual components
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#
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dt0 <- coxph.detail(fit0)
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dt <- coxph.detail(fit)
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aeq(sum(dt$score), ufun(fit$coef)) #score statistic
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aeq(sum(dt0$score), ufun(0))
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aeq(dt0$hazard, c(1/19, (10/3)*(1/16 + 1/(6+20/3) + 1/(6+10/3)), 2/3))
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rm(fit, fit0, rr1, rr2, dt, dt0)
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#
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# Effect of weights on the robust variance
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#
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test1 <- data.frame(time= c(9, 3,1,1,6,6,8),
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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(3,0,1,1,1,1,1),
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id= 1:7)
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testx <- data.frame(time= c(4,4,4,1,1,2,2,3),
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status=c(1,1,1,1,0,1,1,0),
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x= c(0,0,0,1,1,1,0,0),
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wt= c(1,1,1,1,1,1,1,1),
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id= 1:8)
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fit1 <- coxph(Surv(time, status) ~x, cluster=id, test1, ties='breslow',
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weights=wt)
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fit2 <- coxph(Surv(time, status) ~x, cluster=id, testx, ties='breslow')
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db1 <- resid(fit1, 'dfbeta', weighted=F)
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db1 <- db1[-2] #toss the missing
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db2 <- resid(fit2, 'dfbeta')
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aeq(db1, db2[3:8])
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W <- c(3,1,1,1,1,1) #Weights, after removal of the missing value
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aeq(fit2$var, sum(db1*db1*W))
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aeq(fit1$var, sum(db1*db1*W*W))
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