70 lines
2.6 KiB
R
70 lines
2.6 KiB
R
# A short test on coxph.detail, to ensure that the computed hazard is
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# equal to the theoretical value
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library(survival)
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aeq <- function(a,b) all.equal(as.vector(a), as.vector(b))
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# taken from book4.R
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test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8),
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stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17),
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event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0),
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x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) )
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byhand <- function(beta, newx=0) {
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r <- exp(beta)
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loglik <- 4*beta - (log(r+1) + log(r+2) + 2*log(3*r+2) + 2*log(3*r+1) +
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log(2*r +2))
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u <- 1/(r+1) + 1/(3*r+1) + 2*(1/(3*r+2) + 1/(2*r+2)) -
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( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1))
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imat <- r*(1/(r+1)^2 + 2/(r+2)^2 + 6/(3*r+2)^2 +
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6/(3*r+1)^2 + 6/(3*r+2)^2 + 4/(2*r +2)^2)
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hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1),
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1/(3*r+2), 1/(2*r +2) )
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# The matrix of weights, one row per obs, one col per time
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# deaths at 2,3,6,7,8,9
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wtmat <- matrix(c(1,0,0,0,1, 0, 0,0,0,0,
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0,1,0,1,1, 0, 0,0,0,0,
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0,0,1,1,1, 0, 1,1,0,0,
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0,0,0,1,1, 0, 1,1,0,0,
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0,0,0,0,1, 1, 1,1,0,0,
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0,0,0,0,0, 1, 1,1,1,1,
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0,0,0,0,0,.5,.5,1,1,1), ncol=7)
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wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat
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x <- c(1,0,0,1,0,1,1,1,0,0)
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status <- c(1,1,1,1,1,1,1,0,0,0)
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xbar <- colSums(wtmat*x)/ colSums(wtmat)
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n <- length(x)
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# Table of sums for score and Schoenfeld resids
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hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time
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dM <- -hazmat #Expected part
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for (i in 1:5) dM[i,i] <- dM[i,i] +1 #observed
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dM[6:7,6:7] <- dM[6:7,6:7] +.5 # observed
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mart <- rowSums(dM)
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# Table of sums for score and Schoenfeld resids
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# Looks like the last table of appendix E.2.1 of the book
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resid <- dM * outer(x, xbar, '-')
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score <- rowSums(resid)
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scho <- colSums(resid)
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# We need to add the ties back up (they are symmetric)
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scho[6:7] <- rep(mean(scho[6:7]), 2)
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list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard* exp(beta*newx),
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mart=mart, score=score, rmat=resid,
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scho=scho)
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}
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# The actual coefficient of the fit is close to zero. Using a larger
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# number pushes the test harder, but it should still work without
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# the init and iter arguments, i.e., for any coefficient.
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fit1 <- coxph(Surv(start, stop, event) ~x, test2,init=-1, iter=0)
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temp <- coxph.detail(fit1)
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temp2 <- byhand(fit1$coef, fit1$means)
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aeq(temp$haz, c(temp2$haz[1:5], sum(temp2$haz[6:7])))
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