204 lines
7.0 KiB
R
204 lines
7.0 KiB
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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# 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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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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tfit <- aareg(Surv(time, status) ~ x, test1)
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aeq(tfit$times, c(1,2,2))
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aeq(tfit$nrisk, c(6,4,4))
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aeq(tfit$coefficient, matrix(c(0,0,1/3, 1/3, 1, -1/3), ncol=2))
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aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2))
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aeq(tfit$test.statistic, c(1,1))
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aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16))
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tfit <- aareg(Surv(time, status) ~ x, test1, test='nrisk')
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aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2)) #should be as before
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aeq(tfit$test.statistic, c(4/3, 6/3+ 4 - 4/3))
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aeq(tfit$test.var, c(16/9, -16/9, -16/9, 36/9 + 16 + 16/9))
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# In the 1-variable case, this is the same as the default Aalen weight
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tfit <- aareg(Surv(time, status) ~ x, test1, test='variance')
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aeq(tfit$test.statistic, c(1,1))
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aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16))
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#
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# Repeat the above, with case weights
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#
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tfit <- aareg(Surv(time, status) ~x, test1, weights=wt)
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aeq(tfit$times, c(1,2,2))
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aeq(tfit$nrisk, c(21,16,16))
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aeq(tfit$coefficient, matrix(c(0,0,5/12, 2/9, 1, -5/12), ncol=2))
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aeq(tfit$tweight, matrix(c(12,12,12, 36/7, 3,3), ncol=2))
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aeq(tfit$test.statistic, c(5, 72/63 + 3 - 15/12))
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aeq(tfit$test.var, c(25, -25/4, -25/4, (72/63)^2 + 9 + (5/4)^2))
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tfit <- aareg(Surv(time, status) ~x, test1, weights=wt, test='nrisk')
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aeq(tfit$test.statistic, c(20/3, 42/9 + 16 - 16*5/12))
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aeq(tfit$test.var, c(400/9, -400/9, -400/9,
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(42/9)^2 + 16^2 + (16*5/12)^2))
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#
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# Make a test data set with no NAs, in sorted order, no ties,
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# 15 observations
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tdata <- lung[15:29, c('time', 'status', 'age', 'sex', 'ph.ecog')]
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tdata$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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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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# 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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aeq(mine, afit$coefficient[1:9, -1])
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#
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# Check out the dfbeta matrix from aareg
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# Note that it is kept internally in time order, not data set order
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# Those who want residuals should use the resid function!
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#
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# First, the simple test case where I know the anwers
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#
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afit <- aareg(Surv(time, status) ~ x, test1, dfbeta=T)
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temp <- c(rep(0,6), #intercepts at time 1
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c(2,-1,-1,0,0,0)/9, #alpha at time 1
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c(0,0,0,2, -1, -1)/9, #intercepts at time 2
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c(0,0,0,-2,1,1)/9) #alpha at time 2
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aeq(afit$dfbeta, temp)
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#
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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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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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# 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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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$tweight[indx[i],]))
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df <- t(zzinv %*% t(zz) %*% rr)
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cat(" dfbeta=", aeq(df, afit$dfbeta[lwho,,i]), "\n")
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}
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# 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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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$coefficients, acoef[i,]))
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rr <- diag(resid(fit))
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zz <- cbind(1,x)
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zzinv <- solve(t(zz)%*% (w*zz))
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cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],]))
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df <- t(zzinv %*% t(zz) %*% (w*rr))
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cat(" dfbeta=", aeq(df, afit$dfbeta[who,,i]), "\n")
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}
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#
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# Check that the test statistic computed within aareg and
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# the one recomputed within summary.aareg are the same.
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# Of course, they could both be wrong, but at least they'll agree!
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# If the maxtime argument is used in summary, it recomputes the test,
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# even if we know that it wouldn't have had to.
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#
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# Because the 1-variable and >1 variable case have different code, test
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# them both.
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#
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afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T)
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asum <- summary(afit, maxtime=max(afit$times))
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aeq(afit$test.statistic, asum$test.statistic)
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aeq(afit$test.var, asum$test.var)
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aeq(afit$test.var2, asum$test.var2)
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print(afit)
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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$test.statistic)
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aeq(afit$test.var, asum$test.var)
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aeq(afit$test.var2, asum$test.var2)
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summary(afit)
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#
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# Mulitvariate
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#
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afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung,
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dfbeta=T)
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asum <- summary(afit, maxtime=max(afit$times))
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aeq(afit$test.statistic, asum$test.statistic)
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aeq(afit$test.var, asum$test.var)
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aeq(afit$test.var2, asum$test.var2)
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print(afit)
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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$test.statistic)
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aeq(afit$test.var, asum$test.var)
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aeq(afit$test.var2, asum$test.var2)
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summary(afit)
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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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