R Under development (unstable) (2024-08-21 r87038 ucrt) -- "Unsuffered Consequences"
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> library(coxme)
Loading required package: survival
Loading required package: bdsmatrix

Attaching package: 'bdsmatrix'

The following object is masked from 'package:base':

    backsolve

> options(na.action='na.exclude', contrasts=c('contr.treatment', 'contr.poly'))
> aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
> 
> #
> # A further test of mixed sparse/ non-sparse computation
> #  Make sure all the terms are added in and taken out properly,
> #  when people enter and leave the risk set. 
> #
> # The choice of "sparse" below forces group 1 to be non-sparse and
> #   group 2-4 to be sparse.  It will also force the coefficients to be
> #   in 2,3,4,1 order
> 
> tdata1 <- data.frame(time  =c(5,4,1,1,2,2,2,2,3, 1:8), 
+                      status=c(0,1,1,0,1,1,1,0,0, rep(1:0,4)),
+                      x1    =c(0,1,2,0,1,1,0,1,0, rep(4:1,2)),
+                      wt    =c(1,2,1,2,3,4,3,2,1, rep(1:2,4)),
+                      x2    =c(1,3,5,2,3,6,4,3,1, rep(1:2,4)),
+                      grp   =c(1,1,2,2,1,1,2,2,1, rep(3,4), rep(4,4)))
> temp1 <-  5*tdata1$time -3  # each subject spends 4 days not at risk
> tdata2 <- data.frame(t1 = c(rep(0, length(temp1)), temp1+4),
+ 		     t2 = c(temp1, 10*tdata1$time),
+                      status=c(tdata1$status, rev(tdata1$status)),
+ 		     x1 = rep(tdata1$x1, 2),
+ 		     wt = rep(tdata1$wt, 2),
+ 		     x2 = rep(tdata1$x2, 2),
+ 		     grp= rep(tdata1$grp, 2),
+ 		     id = rep(1:17, 2))
> 
> # What's it look like?
> #plot(c(0,80), c(0,17), type='n')
> #segments(tdata2$t1, tdata2$id, tdata2$t2, tdata2$id)
> #points(tdata2$t2[tdata2$status==1], tdata2$id[tdata2$status==1], pch=1)
> 
> theta <- .83
> fit1 <- coxme(Surv(t1, t2, status) ~ x1 + x2 +(1|grp), data=tdata2,
+ 	      vfixed=theta, ties='breslow', 
+               sparse=c(2, .25))
> 
> # This fit will complain when it tries to invert the information matrix--
> #  ignore the complaint
> fit2 <- coxph(Surv(t1, t2, status) ~ I(grp==2) + I(grp==3) + I(grp==4) +
+ 	      I(grp==1) + x1 + x2, data=tdata2, method='breslow',
+ 	      init=c(unlist(ranef(fit1)), fixef(fit1)),
+ 	      iter=0)
> 
> lp <- c(cbind(tdata2$x1, tdata2$x2) %*% fixef(fit1) + 
+ 	unlist(ranef(fit1))[c(4,1,2,3)[tdata2$grp]])
> aeq(lp, fit1$linear)
[1] TRUE
> fit3 <- coxph(Surv(t1, t2, status) ~ offset(lp), data=tdata2, method='breslow')
> 
> aeq(fit1$loglik[3] + fit1$penalty, fit3$loglik)
[1] TRUE
> aeq(fit3$loglik, fit2$loglik[2])
[1] TRUE
> 
> 
> #
> # And now, do it mostly by hand as the definitive check
> #
> lp2 <- fit1$linear - sum(fit1$mean * fixef(fit1))
> temp.risk <- exp(lp2)
> dtimes <- sort(unique(tdata2$t2[tdata2$status==1]))
> nd <- length(dtimes)
> denom <- double(nd)
> xbar  <- matrix(0., nrow=nd, ncol=6)
> xtemp <- cbind(1*(tdata2$grp==2), 1*(tdata2$grp==3), 1*(tdata2$grp==4),
+ 	       1*(tdata2$grp==1), tdata2$x1, tdata2$x2)
> 
> for (i in 1:nd) {
+     who <- (tdata2$t1 <dtimes[i] & tdata2$t2 >= dtimes[i])
+     denom[i] <- sum(temp.risk[who])
+     xbar[i,] <- colSums(temp.risk[who] * xtemp[who,])/denom[i]
+     }
> temp.log <- sum(lp2[tdata2$status==1] -
+ 		log(denom[match(tdata2$t2[tdata2$status==1], dtimes)]))
> aeq(fit1$loglik[3] + fit1$pen, temp.log)
[1] TRUE
> aeq(fit1$penalty, sum(unlist(ranef(fit1))^2)/(2*theta))
[1] TRUE
> # The linear predictors will differ by a constant, since fit2 will have
> #   subtracted means from the factor terms.
> aeq(diff(range(fit1$linear-fit2$linear)),0)
[1] TRUE
> 
> # Score statistic
> temp.score <- xtemp[tdata2$status==1,] - 
+ 	      xbar[match(tdata2$t2[tdata2$status==1], dtimes),]
> aeq(colSums(temp.score) - c(unlist(ranef(fit1)),0,0)/theta, fit1$u)
[1] TRUE
> 
> 
> dt <- coxph.detail(fit2, riskmat=T)
> aeq(dt$x, xtemp[as.numeric(dimnames(dt$x)[[1]]),])
[1] TRUE
> nevent <- table(tdata2$t2, tdata2$status)[,2]
> nevent <- nevent[nevent>0]
> aeq(dt$nevent, nevent)
[1] TRUE
> aeq(dt$means, xbar)
[1] TRUE
> aeq(colSums(temp.score), colSums(dt$score))
[1] TRUE
> 
> # Check out the information matrix.
> #  The coxme model has extra added to the diagonal, and due to
> #  the sparseness the off-diagonal elements for vars 1-3 are zero.
> temp1 <- as.matrix(fit1$hmat) %*% diag(sqrt(diag(fit1$hmat)))
> temp.imat <- temp1 %*% t(temp1)
> dt.imat <- apply(dt$imat,1:2, sum)
> aeq(diag(temp.imat), diag(dt.imat) + c(rep(1/theta,4),0,0))
[1] TRUE
> aeq(temp.imat[4:6, 3], dt.imat[4:6,3])
[1] TRUE
> aeq(temp.imat[5:6, 4:6], dt.imat[5:6,4:6])
[1] TRUE
> 
> 
> proc.time()
   user  system elapsed 
   1.64    0.26    1.84