R version 4.4.0 beta (2024-04-12 r86413 ucrt) -- "Puppy Cup"
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> options(na.action=na.exclude) # preserve missings
> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
> library(survival)
> 
> #
> # Test aareg, for some simple data where the answers can be computed
> #  in closed form
> #
> aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...)
>    
> test1 <- data.frame(time=  c(4, 3,1,1,2,2,3),
+                     status=c(1,NA,1,0,1,1,0),
+                     x=     c(0, 2,1,1,1,0,0),
+ 		    wt=    c(1, 1:6))
> 
> tfit  <- aareg(Surv(time, status) ~ x, test1)
> aeq(tfit$times, c(1,2,2))
[1] TRUE
> aeq(tfit$nrisk, c(6,4,4))
[1] TRUE
> aeq(tfit$coefficient, matrix(c(0,0,1/3, 1/3, 1, -1/3), ncol=2))
[1] TRUE
> aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2))
[1] TRUE
> aeq(tfit$test.statistic, c(1,1))
[1] TRUE
> aeq(tfit$test.var,       c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16))
[1] TRUE
> 
> tfit <- aareg(Surv(time, status) ~ x, test1, test='nrisk')
> aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2)) #should be as before
[1] TRUE
> aeq(tfit$test.statistic, c(4/3, 6/3+ 4 - 4/3))
[1] TRUE
> aeq(tfit$test.var,       c(16/9, -16/9, -16/9, 36/9 + 16 + 16/9))
[1] TRUE
> 
> # In the 1-variable case, this is the same as the default Aalen weight
> tfit <- aareg(Surv(time, status) ~ x, test1, test='variance')
> aeq(tfit$test.statistic, c(1,1))
[1] TRUE
> aeq(tfit$test.var,       c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16))
[1] TRUE
> 
> #
> # Repeat the above, with case weights
> #
> tfit <- aareg(Surv(time, status) ~x, test1, weights=wt)  
> aeq(tfit$times, c(1,2,2))
[1] TRUE
> aeq(tfit$nrisk, c(21,16,16))
[1] TRUE
> aeq(tfit$coefficient, matrix(c(0,0,5/12, 2/9, 1, -5/12), ncol=2))
[1] TRUE
> aeq(tfit$tweight, matrix(c(12,12,12, 36/7, 3,3), ncol=2))
[1] TRUE
> aeq(tfit$test.statistic, c(5, 72/63 + 3 - 15/12))
[1] TRUE
> aeq(tfit$test.var,       c(25, -25/4, -25/4, (72/63)^2 + 9 + (5/4)^2))
[1] TRUE
> 
> tfit <- aareg(Surv(time, status) ~x, test1, weights=wt, test='nrisk')
> aeq(tfit$test.statistic, c(20/3,  42/9 + 16 - 16*5/12))
[1] TRUE
> aeq(tfit$test.var,       c(400/9, -400/9, -400/9, 
+ 			    (42/9)^2 + 16^2 + (16*5/12)^2))
[1] TRUE
> 
> #
> # Make a test data set with no NAs, in sorted order, no ties,
> #   15 observations
> tdata <- lung[15:29, c('time', 'status', 'age', 'sex', 'ph.ecog')]
> tdata$status <- tdata$status -1
> tdata <- tdata[order(tdata$time, tdata$status),]
> row.names(tdata) <- 1:15
> tdata$status[8] <- 0      #for some variety
> 
> afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, tdata, nmin=6)
> #
> # Now, do it "by hand"
> cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, tdata, iter=0,
+                method='breslow')
> dt1   <- coxph.detail(cfit)
> sch1  <- resid(cfit, type='schoen')
> 
> # First estimate of Aalen: from the Cox computations, first 9
> #  The first and last cols of the ninth are somewhat unstable (approx =0)
> mine <- rbind(solve(dt1$imat[,,1], sch1[1,]),
+               solve(dt1$imat[,,2], sch1[2,]),
+               solve(dt1$imat[,,3], sch1[3,]),
+               solve(dt1$imat[,,4], sch1[4,]),
+               solve(dt1$imat[,,5], sch1[5,]),
+               solve(dt1$imat[,,6], sch1[6,]),
+               solve(dt1$imat[,,7], sch1[7,]),
+               solve(dt1$imat[,,8], sch1[8,]),
+               solve(dt1$imat[,,9], sch1[9,])) 
> mine <- diag(1/dt1$nrisk[1:9]) %*% mine
> 
> aeq(mine, afit$coef[1:9, -1])
[1] TRUE
> 
> #
> # Check out the dfbeta matrix from aareg
> #   Note that it is kept internally in time order, not data set order
> # Those who want residuals should use the resid function!
> 
> #
> # First, the simple test case where I know the anwers
> #
> afit <- aareg(Surv(time, status) ~ x, test1, dfbeta=T)
> temp <- c(rep(0,6),             #intercepts at time 1
+           c(2,-1,-1,0,0,0)/9,   #alpha at time 1
+           c(0,0,0,2, -1, -1)/9, #intercepts at time 2
+           c(0,0,0,-2,1,1)/9)    #alpha at time 2
> aeq(afit$dfbeta, temp)
[1] TRUE
> 
> #
> #Now a multivariate data set
> #
> afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T)
> 
> ord <- order(lung$time, -lung$status)
> cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,],
+ 	        method='breslow', iter=0, x=T)
> cdt  <- coxph.detail(cfit, riskmat=T)
> 
> # an arbitrary list of times
> acoef <- rowsum(afit$coef, afit$times) #per death time coefs
> indx <- match(cdt$time, afit$times)
> for (i in c(2,5,27,54,101, 135)) {
+     lwho <- (cdt$riskmat[,i]==1)
+     lmx <- cfit$x[lwho,]
+     lmy <- 1*( cfit$y[lwho,2]==1 & cfit$y[lwho,1] == cdt$time[i])
+     fit <- lm(lmy~ lmx)
+     cat("i=", i, "coef=", aeq(fit$coef, acoef[i,]))
+ 
+     rr <- diag(resid(fit))
+     zz <- cbind(1,lmx)
+     zzinv <- solve(t(zz) %*% zz)
+     cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],]))
+ 
+     df <- t(zzinv %*% t(zz)  %*% rr)
+     cat(" dfbeta=", aeq(df, afit$dfbeta[lwho,,i]), "\n")
+     }
i= 2 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 5 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 27 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 54 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 101 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 135 coef= TRUE twt= TRUE dfbeta= TRUE 
> 	  
> 
> # Repeat it with case weights
> ww <- rep(1:5, length=nrow(lung))/ 3.0
> afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T,
+ 	      weights=ww)
> cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,],
+ 	        method='breslow', iter=0, x=T, weight=ww[ord])
> cdt  <- coxph.detail(cfit, riskmat=T)
> 
> acoef <- rowsum(afit$coef, afit$times) #per death time coefs
> for (i in c(2,5,27,54,101, 135)) {
+     who <- (cdt$riskmat[,i]==1)
+     x <- cfit$x[who,]
+     y <- 1*( cfit$y[who,2]==1 & cfit$y[who,1] == cdt$time[i])
+     w <- cfit$weight[who]
+     fit <- lm(y~x, weights=w)
+     cat("i=", i, "coef=", aeq(fit$coef, acoef[i,]))
+ 
+     rr <- diag(resid(fit))
+     zz <- cbind(1,x)
+     zzinv <- solve(t(zz)%*% (w*zz))
+     cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],]))
+  
+     df <- t(zzinv %*% t(zz) %*% (w*rr))
+     cat(" dfbeta=", aeq(df, afit$dfbeta[who,,i]), "\n")
+     }
i= 2 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 5 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 27 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 54 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 101 coef= TRUE twt= TRUE dfbeta= TRUE 
i= 135 coef= TRUE twt= TRUE dfbeta= TRUE 
> 	  
> #
> # Check that the test statistic computed within aareg and
> #  the one recomputed within summary.aareg are the same.
> # Of course, they could both be wrong, but at least they'll agree!
> # If the maxtime argument is used in summary, it recomputes the test,
> #  even if we know that it wouldn't have had to.
> #
> # Because the 1-variable and >1 variable case have different code, test
> #  them both.
> #
> afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T)
> asum <- summary(afit, maxtime=max(afit$times))
> aeq(afit$test.stat, asum$test.stat)
[1] TRUE
> aeq(afit$test.var,  asum$test.var)
[1] TRUE
> aeq(afit$test.var2, asum$test.var2)
[1] TRUE
> 
> print(afit)
Call:
aareg(formula = Surv(time, status) ~ age, data = lung, dfbeta = T)

  n= 228 
    139 out of 139 unique event times used

              slope      coef se(coef) robust se      z      p
Intercept -0.000872 -0.000905 4.26e-03  4.13e-03 -0.219 0.8270
age        0.000110  0.000142 6.96e-05  6.75e-05  2.110 0.0351

Chisq=4.44 on 1 df, p=0.0351; test weights=aalen
> 
> afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T, test='nrisk')
> asum <- summary(afit, maxtime=max(afit$times))
> aeq(afit$test.stat, asum$test.stat)
[1] TRUE
> aeq(afit$test.var,  asum$test.var)
[1] TRUE
> aeq(afit$test.var2, asum$test.var2)
[1] TRUE
> 
> summary(afit)
              slope   coef se(coef) robust se      z      p
Intercept -0.000954 -0.117  0.53500   0.53300 -0.219 0.8260
age        0.000105  0.018  0.00875   0.00873  2.060 0.0398

Chisq=4.23 on 1 df, p=0.0398; test weights=nrisk
> 
> #
> # Mulitvariate
> #
> afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung,
+ 	      dfbeta=T)
> asum <- summary(afit, maxtime=max(afit$times))
> aeq(afit$test.stat, asum$test.stat)
[1] TRUE
> aeq(afit$test.var,  asum$test.var)
[1] TRUE
> aeq(afit$test.var2, asum$test.var2)
[1] TRUE
> 
> print(afit)
Call:
aareg(formula = Surv(time, status) ~ age + sex + ph.karno + pat.karno, 
    data = lung, dfbeta = T)

  n=224 (4 observations deleted due to missingness)
    132 out of 136 unique event times used

              slope      coef se(coef) robust se     z       p
Intercept  2.15e-02  0.025000 8.45e-03  7.72e-03  3.25 0.00117
age        3.09e-05  0.000076 7.32e-05  6.49e-05  1.17 0.24100
sex       -2.96e-03 -0.004020 1.25e-03  1.23e-03 -3.27 0.00109
ph.karno  -6.77e-05 -0.000083 6.69e-05  8.30e-05 -1.00 0.31700
pat.karno -1.01e-04 -0.000112 5.59e-05  5.70e-05 -1.96 0.05010

Chisq=23.36 on 4 df, p=0.000107; test weights=aalen
> 
> afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung,
+ 	      dfbeta=T, test='nrisk')
> asum <- summary(afit, maxtime=max(afit$times))
> aeq(afit$test.stat, asum$test.stat)
[1] TRUE
> aeq(afit$test.var,  asum$test.var)
[1] TRUE
> aeq(afit$test.var2, asum$test.var2)
[1] TRUE
> 
> summary(afit)
              slope    coef se(coef) robust se     z       p
Intercept  2.12e-02  3.0600  1.04000   0.95600  3.20 0.00138
age        3.18e-05  0.0107  0.00928   0.00818  1.31 0.19100
sex       -2.99e-03 -0.4940  0.15300   0.15200 -3.26 0.00112
ph.karno  -8.37e-05 -0.0113  0.00783   0.00965 -1.17 0.24100
pat.karno -8.50e-05 -0.0133  0.00724   0.00767 -1.73 0.08320

Chisq=22.39 on 4 df, p=0.000168; test weights=nrisk
> 
> # Weights play no role in the final computation of the test statistic, given
> #  the coefficient matrix, nrisk, and dfbeta as inputs.  (Weights do
> #  change the inputs).  So there is no need to reprise the above with
> #  case weights.
> 
> proc.time()
   user  system elapsed 
   1.04    0.18    1.21