S-PLUS : Copyright (c) 1988, 1996 MathSoft, Inc. S : Copyright AT&T. Version 3.4 Release 1 for Sun SPARC, SunOS 5.3 : 1996 Mayo local startup... loading survival loading date loading slocal.misc set missing value action to 'na.omit' set contrasts to ('contr.treatment', 'contr.poly') stop automatic character -> factor conversion in data frames Working data will be in .Data Warning: Cannot open audit file > # > # Set up for the test > # > dyn.load("../loadmod.o") > attach("../.Data") > options(na.action="na.omit", contrasts="contr.treatment") > # > # Test the logic of the new program, by fitting some no-frailty models > # (theta=0). It should give exactly the same answers as 'ordinary' coxph. > # By default frailty models run with eps=1e-7, ordinary with 1e-4. I match > # these to get the same number of iterations. > # > 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)) > > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > > zz <- rep(0, nrow(test1)) > tfit1 <- coxph(Surv(time,status) ~x, test1, eps=1e-7) > tfit2 <- coxph(Surv(time,status) ~x + frailty(zz, theta=0, sparse=T), test1) > tfit3 <- coxph(Surv(zz,time,status) ~x + frailty(zz, theta=0,sparse=T), test1) > > temp <- c("coefficients", "var", "loglik", "linear.predictors", + "means", "n") > > all.equal(tfit1[temp], tfit2[temp]) [1] T > all.equal(tfit1[temp], tfit3[temp]) [1] T > > zz <- rep(0, nrow(test2)) > tfit1 <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-7) > tfit2 <- coxph(Surv(start, stop, event) ~ x + frailty(zz, theta=0, sparse=T), + test2) > all.equal(tfit1[temp], tfit2[temp]) [1] T > > > > # Tests using the rats data > # > # (Female rats, from Mantel et al, Cancer Research 37, > # 3863-3868, November 77) > > rats <- read.table("data.rats", col.names=c("litter", "rx", "time", + "status")) > > rfit <- coxph(Surv(time,status) ~ rx + frailty(litter), rats, + method="breslow") > names(rfit) [1] "coefficients" "var" "var2" [4] "loglik" "iter" "linear.predictors" [7] "residuals" "means" "method" [10] "frail" "fvar" "df" [13] "df2" "penalty" "pterms" [16] "assign2" "history" "coxlist1" [19] "printfun" "n" "terms" [22] "assign" "wald.test" "y" [25] "formula" "call" > rfit Call: coxph(formula = Surv(time, status) ~ rx + frailty(litter), data = rats, method = "breslow") coef se(coef) se2 Chisq DF p rx 0.906 0.323 0.319 7.88 1.0 0.005 frailty(litter) 16.89 13.8 0.250 Iterations: 6 outer, 20 Newton-Raphson Variance of random effect= 0.474 EM likelihood = -181.1 Degrees of freedom for terms= 1.0 13.9 Likelihood ratio test=36.3 on 14.83 df, p=0.00145 n= 150 > > rfit$iter [1] 6 20 > rfit$df [1] 0.9759431 13.8548423 > rfit$history[[1]] $theta: [1] 0.4742848 $done: c.loglik T $history: theta loglik c.loglik [1,] 0.0000000 -181.8451 -181.8451 [2,] 1.0000000 -168.3683 -181.5458 [3,] 0.5000000 -173.3117 -181.0788 [4,] 0.3090061 -175.9446 -181.1490 [5,] 0.4645720 -173.7590 -181.0775 [6,] 0.4736209 -173.6431 -181.0773 $c.loglik: [1] -181.0773 > > rfit1 <- coxph(Surv(time,status) ~ rx + frailty(litter, theta=1), rats, + method="breslow") > rfit1 Call: coxph(formula = Surv(time, status) ~ rx + frailty(litter, theta = 1), data = rats, method = "breslow") coef se(coef) se2 Chisq DF p rx 0.918 0.327 0.321 7.85 1.0 0.0051 frailty(litter, theta = 1 27.25 22.7 0.2300 Iterations: 1 outer, 5 Newton-Raphson Variance of random effect= 1 EM likelihood = -181.5 Degrees of freedom for terms= 1.0 22.7 Likelihood ratio test=50.7 on 23.67 df, p=0.001 n= 150 > > rfit2 <- coxph(Surv(time,status) ~ frailty(litter), rats) > rfit2 Call: coxph(formula = Surv(time, status) ~ frailty(litter), data = rats) coef se(coef) se2 Chisq DF p frailty(litter) 18 14.6 0.24 Iterations: 6 outer, 17 Newton-Raphson Variance of random effect= 0.504 EM likelihood = -184.8 Degrees of freedom for terms= 14.6 Likelihood ratio test=30 on 14.61 df, p=0.0101 n= 150 > # > # Here is a test case with multiple smoothing terms > # > > fit0 <- coxph(Surv(time, status) ~ ph.ecog + age, lung) > fit1 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,3), lung) > fit2 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,4), lung) > fit3 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,8), lung) > > > > fit4 <- coxph(Surv(time, status) ~ ph.ecog + pspline(wt.loss,3), lung) > > fit5 <-coxph(Surv(time, status) ~ ph.ecog + pspline(age,3) + + pspline(wt.loss,3), lung) > > fit1 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 3), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.4480 0.11707 0.11678 14.64 1.00 0.00013 pspline(age, 3), linear 0.0113 0.00928 0.00928 1.47 1.00 0.22000 pspline(age, 3), nonlin 2.08 2.08 0.37000 Iterations: 4 outer, 10 Newton-Raphson Theta= 0.861 Degrees of freedom for terms= 1.0 3.1 Likelihood ratio test=21.9 on 4.08 df, p=0.000227 n=227 (1 observations deleted due to missing) > fit2 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 4), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.4505 0.11766 0.11723 14.66 1.00 0.00013 pspline(age, 4), linear 0.0112 0.00927 0.00927 1.45 1.00 0.23000 pspline(age, 4), nonlin 2.96 3.08 0.41000 Iterations: 4 outer, 10 Newton-Raphson Theta= 0.797 Degrees of freedom for terms= 1.0 4.1 Likelihood ratio test=22.7 on 5.07 df, p=0.000412 n=227 (1 observations deleted due to missing) > fit3 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 8), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.4764 0.12024 0.11925 15.70 1.00 7.4e-05 pspline(age, 8), linear 0.0117 0.00923 0.00923 1.61 1.00 2.0e-01 pspline(age, 8), nonlin 6.93 6.99 4.3e-01 Iterations: 5 outer, 13 Newton-Raphson Theta= 0.691 Degrees of freedom for terms= 1 8 Likelihood ratio test=27.6 on 8.97 df, p=0.00108 n=227 (1 observations deleted due to missing) > fit4 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(wt.loss, 3), data = lung ) coef se(coef) se2 Chisq DF p ph.ecog 0.51545 0.12960 0.12737 15.82 1.00 0.00007 pspline(wt.loss, 3), line -0.00702 0.00655 0.00655 1.15 1.00 0.28000 pspline(wt.loss, 3), nonl 2.45 2.09 0.31000 Iterations: 3 outer, 8 Newton-Raphson Theta= 0.776 Degrees of freedom for terms= 1.0 3.1 Likelihood ratio test=21.1 on 4.06 df, p=0.000326 n=213 (15 observations deleted due to missing) > fit5 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 3) + pspline( wt.loss, 3), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.47422 0.13495 0.13206 12.35 1.00 0.00044 pspline(age, 3), linear 0.01368 0.00976 0.00974 1.96 1.00 0.16000 pspline(age, 3), nonlin 1.90 2.07 0.40000 pspline(wt.loss, 3), line -0.00717 0.00661 0.00660 1.18 1.00 0.28000 pspline(wt.loss, 3), nonl 2.08 2.03 0.36000 Iterations: 4 outer, 10 Newton-Raphson Theta= 0.85 Theta= 0.779 Degrees of freedom for terms= 1.0 3.1 3.0 Likelihood ratio test=25.2 on 7.06 df, p=0.000726 n=213 (15 observations deleted due to missing) > > rm(fit1, fit2, fit3, fit4, fit5) > # > # Test on the ovarian data > > fit1 <- coxph(Surv(futime, fustat) ~ rx + age, ovarian) > fit2 <- coxph(Surv(futime, fustat) ~ rx + pspline(age, df=2), + data=ovarian) > fit2$iter [1] 2 7 > > fit2$df [1] 0.9426611 1.9293052 > > fit2$history $"pspline(age, df = 2)": $"pspline(age, df = 2)"$theta: [1] 0.4468868 $"pspline(age, df = 2)"$done: [1] T $"pspline(age, df = 2)"$history: thetas dfs [1,] 1.0000000 1.000000 [2,] 0.0000000 5.000000 [3,] 0.6000000 1.734267 [4,] 0.4845205 1.929305 $"pspline(age, df = 2)"$half: [1] 0 > > fit4 <- coxph(Surv(futime, fustat) ~ rx + pspline(age, df=4), + data=ovarian) > fit4 Call: coxph(formula = Surv(futime, fustat) ~ rx + pspline(age, df = 4), data = ovarian) coef se(coef) se2 Chisq DF p rx -0.373 0.761 0.749 0.24 1.00 0.6200 pspline(age, df = 4), lin 0.139 0.044 0.044 9.98 1.00 0.0016 pspline(age, df = 4), non 2.59 2.93 0.4500 Iterations: 3 outer, 13 Newton-Raphson Theta= 0.242 Degrees of freedom for terms= 1.0 3.9 Likelihood ratio test=19.4 on 4.9 df, p=0.00149 n= 26 > > > # Simulation for the ovarian data set > # > fit1 <- coxph(Surv(futime, fustat) ~ rx + ridge(age, ecog.ps, theta=1), + ovarian) > > dfs <- eigen(solve(fit1$var, fit1$var2))$values > > temp <- matrix(rnorm(30000), ncol=3) > temp2 <- apply((temp^2) %*% dfs, 1, sum) > > round(rbind(quantile(temp2, c(.8, .9, .95, .99)), + qchisq( c(.8, .9, .95, .99), sum(fit1$df))), 3) 80% 90% 95% 99% [1,] 4.287 5.779 7.156 10.458 [2,] 4.313 5.874 7.399 10.861 > # From: McGilchrist and Aisbett, Biometrics 47, 461-66, 1991 > # Data on the recurrence times to infection, at the point of insertion of > # the catheter, for kidney patients using portable dialysis equipment. > # Catheters may be removed for reasons other than infection, in which case > # the observation is censored. Each patient has exactly 2 observations. > > # Variables: patient, time, status, age, > # sex (1=male, 2=female), > # disease type (0=GN, 1=AN, 2=PKD, 3=Other) > # author's estimate of the frailty > > # I don't match their answers, and I think that I'm right > > kidney <- read.table("data.kidney", col.names=c("id", "time", "status", + "age", "sex", "disease", "frail")) > kidney$disease <- factor(kidney$disease, levels=c(3, 0:2), + labels=c("Other", "GN", "AN", "PKD")) > > kfit <- coxph(Surv(time, status)~ age + sex + disease + frailty(id), kidney) > kfit1<- coxph(Surv(time, status) ~age + sex + disease + + frailty(id, theta=1), kidney, iter=20) > kfit0 <- coxph(Surv(time, status)~ age + sex + disease, kidney) > temp <- coxph(Surv(time, status) ~age + sex + disease + + frailty(id, theta=1, sparse=F), kidney) > > > # Check out the EM based score equations > # temp1 and kfit1 should have essentially the same coefficients > # temp2 should equal kfit1$frail > # equality won't be exact because of the different iteration paths > temp1 <- coxph(Surv(time, status) ~ age + sex + disease + + offset(kfit1$frail[id]), kidney) > rr <- tapply(resid(temp1), kidney$id, sum) > temp2 <- log(rr/1 +1) > all.equal(temp1$coef, kfit1$coef) [1] "Mean relative difference: 9.243907e-06" > all.equal(temp2, kfit1$frail) [1] "names for target but not for current" [2] "Mean relative difference: 0.002409231" > > > > kfit Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id), data = kidney) coef se(coef) se2 Chisq DF p age 0.00318 0.0111 0.0111 0.08 1 7.8e-01 sex -1.48314 0.3582 0.3582 17.14 1 3.5e-05 diseaseGN 0.08796 0.4064 0.4064 0.05 1 8.3e-01 diseaseAN 0.35079 0.3997 0.3997 0.77 1 3.8e-01 diseasePKD -1.43111 0.6311 0.6311 5.14 1 2.3e-02 frailty(id) 0.00 0 9.3e-01 Iterations: 6 outer, 28 Newton-Raphson Variance of random effect= 5e-07 EM likelihood = -179.1 Degrees of freedom for terms= 1 1 3 0 Likelihood ratio test=17.6 on 5 df, p=0.00342 n= 76 > kfit1 Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, theta = 1), data = kidney, iter.max = 20) coef se(coef) se2 Chisq DF p age 0.00389 0.0196 0.00943 0.04 1.0 0.84000 sex -2.00788 0.5910 0.41061 11.54 1.0 0.00068 diseaseGN 0.35334 0.7165 0.38015 0.24 1.0 0.62000 diseaseAN 0.52363 0.7229 0.40462 0.52 1.0 0.47000 diseasePKD -0.45980 1.0898 0.66091 0.18 1.0 0.67000 frailty(id, theta = 1) 28.48 18.8 0.06900 Iterations: 1 outer, 10 Newton-Raphson Variance of random effect= 1 EM likelihood = -182.5 Degrees of freedom for terms= 0.2 0.5 1.1 18.8 Likelihood ratio test=63.8 on 20.55 df, p=2.55e-06 n= 76 > kfit0 Call: coxph(formula = Surv(time, status) ~ age + sex + disease, data = kidney) coef exp(coef) se(coef) z p age 0.00318 1.003 0.0111 0.285 7.8e-01 sex -1.48319 0.227 0.3582 -4.140 3.5e-05 diseaseGN 0.08796 1.092 0.4064 0.216 8.3e-01 diseaseAN 0.35078 1.420 0.3997 0.878 3.8e-01 diseasePKD -1.43111 0.239 0.6311 -2.268 2.3e-02 Likelihood ratio test=17.6 on 5 df, p=0.00342 n= 76 > temp Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, theta = 1, sparse = F), data = kidney) coef se(coef) se2 Chisq DF p age 0.00389 0.0186 0.0112 0.04 1.0 0.83000 sex -2.00763 0.5762 0.4080 12.14 1.0 0.00049 diseaseGN 0.35335 0.6786 0.4315 0.27 1.0 0.60000 diseaseAN 0.52340 0.6891 0.4404 0.58 1.0 0.45000 diseasePKD -0.45934 1.0139 0.7130 0.21 1.0 0.65000 frailty(id, theta = 1, sp 26.23 18.7 0.12000 Iterations: 1 outer, 5 Newton-Raphson Variance of random effect= 1 EM likelihood = -182.5 Degrees of freedom for terms= 0.4 0.5 1.4 18.7 Likelihood ratio test=63.8 on 20.97 df, p=3.27e-06 n= 76 > > # > # Now fit the data using REML > # > kfitm1 <- coxph(Surv(time,status) ~ age + sex + disease + + frailty(id, dist="gauss"), kidney) > kfitm2 <- coxph(Surv(time,status) ~ age + sex + disease + + frailty(id, dist="gauss", sparse=F), kidney) > kfitm1 Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, dist = "gauss"), data = kidney) coef se(coef) se2 Chisq DF p age 0.00489 0.015 0.0106 0.11 1.0 0.74000 sex -1.69703 0.461 0.3617 13.56 1.0 0.00023 diseaseGN 0.17980 0.545 0.3927 0.11 1.0 0.74000 diseaseAN 0.39283 0.545 0.3982 0.52 1.0 0.47000 diseasePKD -1.13630 0.825 0.6173 1.90 1.0 0.17000 frailty(id, dist = "gauss 17.89 12.1 0.12000 Iterations: 6 outer, 30 Newton-Raphson Variance of random effect= 0.493 Degrees of freedom for terms= 0.5 0.6 1.7 12.1 Likelihood ratio test=47.5 on 14.89 df, p=2.82e-05 n= 76 > summary(kfitm2) Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, dist = "gauss", sparse = F), data = kidney) n= 76 coef se(coef) se2 Chisq DF p age 0.00492 0.0149 0.0108 0.11 1.0 0.74000 sex -1.70204 0.4631 0.3613 13.51 1.0 0.00024 diseaseGN 0.18173 0.5413 0.4017 0.11 1.0 0.74000 diseaseAN 0.39442 0.5428 0.4052 0.53 1.0 0.47000 diseasePKD -1.13160 0.8175 0.6298 1.92 1.0 0.17000 frailty(id, dist = "gauss 18.13 12.3 0.12000 exp(coef) exp(-coef) lower .95 upper .95 age 1.005 0.995 0.9760 1.035 sex 0.182 5.485 0.0736 0.452 diseaseGN 1.199 0.834 0.4151 3.465 diseaseAN 1.484 0.674 0.5120 4.299 diseasePKD 0.323 3.101 0.0650 1.601 gamma:1 1.701 0.588 0.5181 5.586 gamma:2 1.424 0.702 0.3851 5.266 gamma:3 1.159 0.863 0.3828 3.511 gamma:4 0.623 1.606 0.2340 1.657 gamma:5 1.254 0.797 0.3981 3.953 gamma:6 1.135 0.881 0.3834 3.360 gamma:7 1.973 0.507 0.5694 6.834 gamma:8 0.620 1.614 0.2166 1.772 gamma:9 0.823 1.215 0.2888 2.346 gamma:10 0.503 1.988 0.1747 1.448 gamma:11 0.757 1.322 0.2708 2.113 gamma:12 1.105 0.905 0.3343 3.651 gamma:13 1.302 0.768 0.4275 3.967 gamma:14 0.591 1.691 0.1854 1.885 gamma:15 0.545 1.835 0.1858 1.598 gamma:16 1.044 0.958 0.3142 3.470 gamma:17 0.914 1.095 0.3000 2.782 gamma:18 0.918 1.089 0.3248 2.597 gamma:19 0.643 1.556 0.1951 2.117 gamma:20 1.170 0.855 0.3453 3.963 gamma:21 0.334 2.997 0.1020 1.091 gamma:22 0.687 1.455 0.2353 2.006 gamma:23 1.478 0.677 0.4756 4.592 gamma:24 1.017 0.983 0.3156 3.278 gamma:25 0.810 1.235 0.2749 2.384 gamma:26 0.614 1.627 0.2149 1.757 gamma:27 1.088 0.919 0.3282 3.610 gamma:28 1.542 0.649 0.4923 4.829 gamma:29 1.379 0.725 0.4377 4.342 gamma:30 1.375 0.727 0.4444 4.253 gamma:31 1.445 0.692 0.4703 4.438 gamma:32 1.199 0.834 0.3521 4.085 gamma:33 1.945 0.514 0.5523 6.849 gamma:34 0.862 1.161 0.2769 2.682 gamma:35 1.703 0.587 0.5266 5.508 gamma:36 0.827 1.209 0.2281 3.002 gamma:37 1.471 0.680 0.3894 5.555 gamma:38 1.048 0.954 0.3068 3.579 Iterations: 6 outer, 17 Newton-Raphson Variance of random effect= 0.509 Degrees of freedom for terms= 0.5 0.6 1.7 12.3 Rsquare= 0.788 (max possible= 0.997 ) Likelihood ratio test= 118 on 15.14 df, p=0 Wald test = 37.4 on 15.14 df, p=0.00119 > # > # Fit the kidney data using AIC > # > > # gamma, corrected aic > coxph(Surv(time, status) ~ age + sex + frailty(id, method="aic", caic=T), + kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, method = "aic", caic = T), data = kidney) coef se(coef) se2 Chisq DF p age 0.00364 0.0105 0.00891 0.12 1.0 0.73000 sex -1.31907 0.3955 0.32493 11.13 1.0 0.00085 frailty(id, method = "aic 13.54 7.8 0.08700 Iterations: 9 outer, 47 Newton-Raphson Variance of random effect= 0.202 EM likelihood = -182.1 Degrees of freedom for terms= 0.7 0.7 7.8 Likelihood ratio test=33.3 on 9.2 df, p=0.000137 n= 76 > > coxph(Surv(time, status) ~ age + sex + frailty(id, dist="t"), kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "t"), data = kidney) coef se(coef) se2 Chisq DF p age 0.00558 0.012 0.00873 0.22 1.0 0.6400 sex -1.65036 0.481 0.38545 11.77 1.0 0.0006 frailty(id, dist = "t") 20.05 13.8 0.1200 Iterations: 9 outer, 44 Newton-Raphson Variance of random effect= 0.807 Degrees of freedom for terms= 0.5 0.6 13.8 Likelihood ratio test=48.2 on 14.93 df, p=2.24e-05 n= 76 > coxph(Surv(time, status) ~ age + sex + frailty(id, dist="gauss", method="aic", + caic=T), kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "gauss", method = "aic", caic = T), data = kidney) coef se(coef) se2 Chisq DF p age 0.00303 0.0103 0.00895 0.09 1.00 0.7700 sex -1.15153 0.3637 0.30556 10.03 1.00 0.0015 frailty(id, dist = "gauss 12.36 6.76 0.0800 Iterations: 7 outer, 30 Newton-Raphson Variance of random effect= 0.185 Degrees of freedom for terms= 0.8 0.7 6.8 Likelihood ratio test=28.4 on 8.22 df, p=0.000476 n= 76 > > > # uncorrected aic > coxph(Surv(time, status) ~ age + sex + frailty(id, method="aic", caic=F), + kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, method = "aic", caic = F), data = kidney) coef se(coef) se2 Chisq DF p age 0.00758 0.0146 0.00836 0.27 1.0 0.60000 sex -1.86230 0.5503 0.39401 11.45 1.0 0.00071 frailty(id, method = "aic 35.99 19.1 0.01100 Iterations: 10 outer, 74 Newton-Raphson Variance of random effect= 0.824 EM likelihood = -182.6 Degrees of freedom for terms= 0.3 0.5 19.1 Likelihood ratio test=60 on 19.91 df, p=6.83e-06 n= 76 Warning messages: Inner loop failed to coverge for iterations 4 in: coxpenal.fit(X, Y, strats, offset, init = init, iter.max = iter.max, outer.max .... > > coxph(Surv(time, status) ~ age + sex + frailty(id, dist="t", caic=F), kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "t", caic = F), data = kidney) coef se(coef) se2 Chisq DF p age 0.00558 0.012 0.00873 0.22 1.0 0.6400 sex -1.65036 0.481 0.38545 11.77 1.0 0.0006 frailty(id, dist = "t", c 20.05 13.8 0.1200 Iterations: 9 outer, 44 Newton-Raphson Variance of random effect= 0.807 Degrees of freedom for terms= 0.5 0.6 13.8 Likelihood ratio test=48.2 on 14.93 df, p=2.24e-05 n= 76 > #temp <- sas.get("../../../../data/moertel/sasdata", "anal") > #colon <- temp[temp$study==1,] > #rm(temp) > #colon$rx <- factor(colon$rx, levels=1:3, labels=c("Obs", "Lev", "Lev+5FU")) > > data.restore("data.colon") [1] "data.colon" > # > # Fit models to the Colon cancer data used in Lin > # > fitc1 <- coxph(Surv(time, status) ~ rx + extent + node4 + cluster(id) + + strata(etype), colon) > fitc1 Call: coxph(formula = Surv(time, status) ~ rx + extent + node4 + cluster(id) + strata( etype), data = colon) coef exp(coef) se(coef) robust se z p rxLev -0.0362 0.964 0.0768 0.1056 -0.343 7.3e-01 rxLev+5FU -0.4488 0.638 0.0840 0.1168 -3.842 1.2e-04 extent 0.5155 1.674 0.0796 0.1097 4.701 2.6e-06 node4 0.8799 2.411 0.0681 0.0961 9.160 0.0e+00 Likelihood ratio test=248 on 4 df, p=0 n= 1858 > > fitc2 <- coxph(Surv(time, status) ~ rx + extent + node4 + + frailty(id, dist="gauss", trace=T) + + strata(etype), colon) theta resid fsum trace [1,] 1 0.5721865 677.2472 498.2323 [2,] 3 0.8244916 2430.3958 880.5538 new theta= 6 theta resid fsum trace [1,] 1 0.5721865 677.2472 498.2323 [2,] 3 0.8244916 2430.3958 880.5538 [3,] 6 0.3152272 4520.0041 1279.6138 new theta= 12 theta resid fsum trace [1,] 1 0.5721865 677.2472 498.2323 [2,] 3 0.8244916 2430.3958 880.5538 [3,] 6 0.3152272 4520.0041 1279.6138 [4,] 12 -2.1486199 7550.5646 1950.6313 new theta= 7.554873 theta resid fsum trace [1,] 1.000000 0.5721865 677.2472 498.2323 [2,] 3.000000 0.8244916 2430.3958 880.5538 [3,] 6.000000 0.3152272 4520.0041 1279.6138 [4,] 12.000000 -2.1486199 7550.5646 1950.6313 [5,] 7.554873 -0.1827268 5420.8778 1463.2371 new theta= 7.004443 theta resid fsum trace [1,] 1.000000 0.57218652 677.2472 498.2323 [2,] 3.000000 0.82449159 2430.3958 880.5538 [3,] 6.000000 0.31522725 4520.0041 1279.6138 [4,] 12.000000 -2.14861992 7550.5646 1950.6313 [5,] 7.554873 -0.18272677 5420.8778 1463.2371 [6,] 7.004443 0.02102504 5123.0634 1399.3956 new theta= 7.06674 theta resid fsum trace [1,] 1.000000 0.57218652 677.2472 498.2323 [2,] 3.000000 0.82449159 2430.3958 880.5538 [3,] 6.000000 0.31522725 4520.0041 1279.6138 [4,] 12.000000 -2.14861992 7550.5646 1950.6313 [5,] 7.554873 -0.18272677 5420.8778 1463.2371 [6,] 7.004443 0.02102504 5123.0634 1399.3956 [7,] 7.066740 -0.01293658 5148.9076 1406.6504 new theta= 7.04162 theta resid fsum trace [1,] 1.000000 0.572186518 677.2472 498.2323 [2,] 3.000000 0.824491593 2430.3958 880.5538 [3,] 6.000000 0.315227245 4520.0041 1279.6138 [4,] 12.000000 -2.148619920 7550.5646 1950.6313 [5,] 7.554873 -0.182726773 5420.8778 1463.2371 [6,] 7.004443 0.021025043 5123.0634 1399.3956 [7,] 7.066740 -0.012936579 5148.9076 1406.6504 [8,] 7.041620 0.003463959 5140.3971 1403.7958 new theta= 7.047698 theta resid fsum trace [1,] 1.000000 0.572186518 677.2472 498.2323 [2,] 3.000000 0.824491593 2430.3958 880.5538 [3,] 6.000000 0.315227245 4520.0041 1279.6138 [4,] 12.000000 -2.148619920 7550.5646 1950.6313 [5,] 7.554873 -0.182726773 5420.8778 1463.2371 [6,] 7.004443 0.021025043 5123.0634 1399.3956 [7,] 7.066740 -0.012936579 5148.9076 1406.6504 [8,] 7.041620 0.003463959 5140.3971 1403.7958 [9,] 7.047698 -0.001163083 5142.0167 1404.4463 new theta= 7.046096 theta resid fsum trace [1,] 1.000000 5.721865e-01 677.2472 498.2323 [2,] 3.000000 8.244916e-01 2430.3958 880.5538 [3,] 6.000000 3.152272e-01 4520.0041 1279.6138 [4,] 12.000000 -2.148620e+00 7550.5646 1950.6313 [5,] 7.554873 -1.827268e-01 5420.8778 1463.2371 [6,] 7.004443 2.102504e-02 5123.0634 1399.3956 [7,] 7.066740 -1.293658e-02 5148.9076 1406.6504 [8,] 7.041620 3.463959e-03 5140.3971 1403.7958 [9,] 7.047698 -1.163083e-03 5142.0167 1404.4463 [10,] 7.046096 -1.820316e-05 5141.5307 1404.2792 new theta= 7.046071 Warning messages: Inner loop failed to coverge for iterations 4 in: coxpenal.fit(X, Y, strats, offset, init = init, iter.max = iter.max, outer.max .... > fitc2 Call: coxph(formula = Surv(time, status) ~ rx + extent + node4 + frailty(id, dist = "gauss", trace = T) + strata(etype), data = colon) coef se(coef) se2 Chisq DF p rxLev -0.0267 0.241 0.0824 0.01 1 9.1e-01 rxLev+5FU -0.7880 0.243 0.1071 10.50 1 1.2e-03 extent 1.1305 0.218 0.1068 26.81 1 2.2e-07 node4 2.1266 0.210 0.0984 102.56 1 0.0e+00 frailty(id, dist = "gauss 5464.64 730 0.0e+00 Iterations: 10 outer, 77 Newton-Raphson Variance of random effect= 7.05 Degrees of freedom for terms= 0.3 0.2 0.2 729.7 Likelihood ratio test=3544 on 730.49 df, p=0 n= 1858 > > fitc3 <- coxph(Surv(time, status) ~ rx + extent + node4 + frailty(id, trace=T) + + strata(etype), colon) theta loglik c.loglik [1,] 0 -5846.216 -5846.216 [2,] 1 -5305.049 -5590.102 new theta= 2 theta loglik c.loglik [1,] 0 -5846.216 -5846.216 [2,] 1 -5305.049 -5590.102 [3,] 2 -5036.927 -5479.479 new theta= 4 theta loglik c.loglik [1,] 0 -5846.216 -5846.216 [2,] 1 -5305.049 -5590.102 [3,] 2 -5036.927 -5479.479 [4,] 4 -4740.394 -5385.887 new theta= 8 theta loglik c.loglik [1,] 0 -5846.216 -5846.216 [2,] 1 -5305.049 -5590.102 [3,] 2 -5036.927 -5479.479 [4,] 4 -4740.394 -5385.887 [5,] 8 -4457.094 -5347.375 new theta= 16 theta loglik c.loglik [1,] 0 -5846.216 -5846.216 [2,] 1 -5305.049 -5590.102 [3,] 2 -5036.927 -5479.479 [4,] 4 -4740.394 -5385.887 [5,] 8 -4457.094 -5347.375 [6,] 16 -4223.785 -5393.362 new theta= 8.740343 theta loglik c.loglik [1,] 0.000000 -5846.216 -5846.216 [2,] 1.000000 -5305.049 -5590.102 [3,] 2.000000 -5036.927 -5479.479 [4,] 4.000000 -4740.394 -5385.887 [5,] 8.000000 -4457.094 -5347.375 [6,] 16.000000 -4223.785 -5393.362 [7,] 8.740343 -4423.925 -5348.128 new theta= 8.058 theta loglik c.loglik [1,] 0.000000 -5846.216 -5846.216 [2,] 1.000000 -5305.049 -5590.102 [3,] 2.000000 -5036.927 -5479.479 [4,] 4.000000 -4740.394 -5385.887 [5,] 8.000000 -4457.094 -5347.375 [6,] 16.000000 -4223.785 -5393.362 [7,] 8.740343 -4423.925 -5348.128 [8,] 8.058000 -4454.347 -5347.375 new theta= 8.025556 theta loglik c.loglik [1,] 0.000000 -5846.216 -5846.216 [2,] 1.000000 -5305.049 -5590.102 [3,] 2.000000 -5036.927 -5479.479 [4,] 4.000000 -4740.394 -5385.887 [5,] 8.000000 -4457.094 -5347.375 [6,] 16.000000 -4223.785 -5393.362 [7,] 8.740343 -4423.925 -5348.128 [8,] 8.058000 -4454.347 -5347.375 [9,] 8.025556 -4455.875 -5347.369 new theta= 8.028123 Warning messages: Inner loop failed to coverge for iterations 5 6 in: coxpenal.fit(X, Y, strats, offset, init = init, iter.max = iter.max, outer.max .... > fitc3 Call: coxph(formula = Surv(time, status) ~ rx + extent + node4 + frailty(id, trace = T) + strata(etype), data = colon) coef se(coef) se2 Chisq DF p rxLev 0.0434 0.305 0.140 0.02 1 8.9e-01 rxLev+5FU -0.5125 0.310 0.170 2.73 1 9.8e-02 extent 1.3373 0.251 0.137 28.45 1 9.6e-08 node4 2.3381 0.233 0.156 100.81 1 0.0e+00 frailty(id, trace = T) 5939.97 867 0.0e+00 Iterations: 9 outer, 112 Newton-Raphson Variance of random effect= 8.03 EM likelihood = -5347.4 Degrees of freedom for terms= 0.5 0.3 0.4 866.7 Likelihood ratio test=3787 on 868.01 df, p=0 n= 1858 > > fitc4 <- coxph(Surv(time, status) ~ rx + extent + node4 + frailty(id, df=30) + + strata(etype), colon) > fitc4 Call: coxph(formula = Surv(time, status) ~ rx + extent + node4 + frailty(id, df = 30) + strata(etype), data = colon) coef se(coef) se2 Chisq DF p rxLev -0.0374 0.0789 0.0769 0.22 1 6.4e-01 rxLev+5FU -0.4565 0.0859 0.0840 28.27 1 1.1e-07 extent 0.5289 0.0815 0.0798 42.13 1 8.5e-11 node4 0.9078 0.0701 0.0681 167.85 1 0.0e+00 frailty(id, df = 30) 58.56 30 1.4e-03 Iterations: 3 outer, 9 Newton-Raphson Variance of random effect= 0.0337 EM likelihood = -5832.4 Degrees of freedom for terms= 1.9 1.0 0.9 30.0 Likelihood ratio test=363 on 33.81 df, p=0 n= 1858 > > # Do a fit, removing the no-event people > temp <- tapply(colon$status, colon$id, sum) > keep <- !(is.na(match(colon$id, names(temp[temp>0])))) > fitc5 <- coxph(Surv(time, status) ~ rx + extent + node4 +cluster(id) + + strata(etype), colon, subset=keep) > > # > # Do the factor fit, but first remove the no-event people > # > # Ha! This routine has a factor with 506 levels. It uses all available > # memory, and can't finish in my patience window. Commented out. > > #fitc4 <- coxph(Surv(time, status) ~ rx + extent + node4 + factor(id), colon, > # subset=keep) > > > > > > > # > # The residual methods treat a sparse frailty as a fixed offset with > # no variance > # > > kfit1 <- coxph(Surv(time, status) ~ age + sex + + frailty(id, dist="gauss"), kidney) > tempf <- predict(kfit1, type="terms")[,3] > temp <- kfit1$frail[match(kidney$id, sort(unique(kidney$id)))] > #all.equal(unclass(tempf), unclass(temp)) > all.equal(as.vector(tempf), as.vector(temp)) [1] T > > # Now fit a model with explicit offset > kfitx <- coxph(Surv(time, status) ~ age + sex + offset(tempf),kidney, + eps=1e-7) > > # These are not precisely the same, due to different iteration paths > all.equal(kfitx$coef, kfit1$coef) [1] T > > # This will make them identical > kfitx <- coxph(Surv(time, status) ~ age + sex + offset(temp),kidney, + iter=0, init=kfit1$coef) > all.equal(resid(kfit1), resid(kfitx)) [1] T > all.equal(resid(kfit1, type="score"), resid(kfitx, type="score")) [1] T > all.equal(resid(kfit1, type="schoe"), resid(kfitx, type="schoe")) [1] T > > # These are not the same, due to a different variance matrix > # The frailty model's variance is about 2x the naive "assume an offset" var > # The score residuals are equal, however. > all.equal(resid(kfit1, type="dfbeta"), resid(kfitx, type="dfbeta")) [1] "Mean relative difference: 0.5214642" > zed <- kfitx > zed$var <- kfit1$var > all.equal(resid(kfit1, type="dfbeta"), resid(zed, type="dfbeta")) [1] T > > > temp1 <- resid(kfit1, type="score") > temp2 <- resid(kfitx, type="score") > all.equal(temp1, temp2) [1] T > > # > # Now for some tests of predicted values > # > all.equal(predict(kfit1, type="expected"), predict(kfitx, type="expected")) [1] T > all.equal(predict(kfit1, type="lp"), predict(kfitx, type="lp")) [1] T > > temp1 <- predict(kfit1, type="terms", se.fit=T) > temp2 <- predict(kfitx, type="terms", se.fit=T) > all.equal(temp1$fit[,1:2], temp2$fit) [1] T > all.equal(temp1$se.fit[,1:2], temp2$se.fit) #should be false [1] "Mean relative difference: 0.3023202" > mean(temp1$se.fit[,1:2]/ temp2$se.fit) [1] 1.432742 > all.equal(as.vector(temp1$se.fit[,3])^2, + as.vector(kfit1$fvar[match(kidney$id, sort(unique(kidney$id)))])) [1] T > > print(temp1) $fit: age sex frailty(id, dist = "gauss") 1 -0.073958502 1.0394106 0.59786111 2 -0.073958502 1.0394106 0.59786111 3 0.020271945 -0.3712181 0.38485832 4 0.020271945 -0.3712181 0.38485832 5 -0.055112412 1.0394106 0.20207583 6 -0.055112412 1.0394106 0.20207583 7 -0.059823935 -0.3712181 -0.55911485 8 -0.055112412 -0.3712181 -0.55911485 9 -0.158765904 1.0394106 0.28549873 10 -0.158765904 1.0394106 0.28549873 11 -0.130496770 -0.3712181 0.06626061 12 -0.125785247 -0.3712181 0.06626061 13 0.034406512 1.0394106 0.80459000 14 0.034406512 1.0394106 0.80459000 15 0.053252601 -0.3712181 -0.43812823 16 0.057964123 -0.3712181 -0.43812823 17 0.119213914 -0.3712181 -0.05626582 18 0.119213914 -0.3712181 -0.05626582 19 0.034406512 1.0394106 -0.49952683 20 0.039118034 1.0394106 -0.49952683 21 0.001425855 -0.3712181 -0.13020461 22 0.001425855 -0.3712181 -0.13020461 23 -0.045689368 -0.3712181 0.06374081 24 -0.045689368 -0.3712181 0.06374081 25 -0.040977845 -0.3712181 0.38796289 26 -0.040977845 -0.3712181 0.38796289 27 -0.007997189 -0.3712181 -0.47624190 28 -0.007997189 -0.3712181 -0.47624190 29 -0.125785247 -0.3712181 -0.66954879 30 -0.125785247 -0.3712181 -0.66954879 31 0.076810213 1.0394106 0.19352414 32 0.076810213 1.0394106 0.19352414 33 0.076810213 -0.3712181 -0.16474469 34 0.076810213 -0.3712181 -0.16474469 35 -0.003285667 -0.3712181 -0.15787841 36 0.001425855 -0.3712181 -0.15787841 37 0.043829556 -0.3712181 -0.46209283 38 0.043829556 -0.3712181 -0.46209283 39 0.001425855 -0.3712181 0.12596115 40 0.001425855 -0.3712181 0.12596115 41 0.010848900 1.0394106 -1.74241816 42 0.015560422 1.0394106 -1.74241816 43 -0.064535457 -0.3712181 -0.45191179 44 -0.064535457 -0.3712181 -0.45191179 45 0.086233257 -0.3712181 0.51548896 46 0.090944780 -0.3712181 0.51548896 47 -0.007997189 -0.3712181 0.09469348 48 -0.003285667 -0.3712181 0.09469348 49 -0.003285667 1.0394106 0.05795548 50 -0.003285667 1.0394106 0.05795548 51 0.062675646 -0.3712181 -0.37915463 52 0.067387168 -0.3712181 -0.37915463 53 -0.158765904 -0.3712181 0.11243130 54 -0.158765904 -0.3712181 0.11243130 55 0.039118034 -0.3712181 0.54762574 56 0.039118034 -0.3712181 0.54762574 57 0.043829556 1.0394106 0.45856914 58 0.043829556 1.0394106 0.45856914 59 0.048541079 -0.3712181 0.35623967 60 0.048541079 -0.3712181 0.35623967 61 0.057964123 -0.3712181 0.48779202 62 0.057964123 -0.3712181 0.48779202 63 0.029694989 -0.3712181 0.25581783 64 0.034406512 -0.3712181 0.25581783 65 0.062675646 -0.3712181 0.23046401 66 0.062675646 -0.3712181 0.23046401 67 0.001425855 -0.3712181 -0.13672108 68 0.006137378 -0.3712181 -0.13672108 69 -0.102227636 -0.3712181 0.51950930 70 -0.102227636 -0.3712181 0.51950930 71 -0.007997189 -0.3712181 -0.23862674 72 -0.007997189 -0.3712181 -0.23862674 73 0.039118034 -0.3712181 0.17164824 74 0.039118034 -0.3712181 0.17164824 75 0.076810213 1.0394106 -0.35798941 76 0.076810213 1.0394106 -0.35798941 $se.fit: age sex frailty(id, dist = "gauss") 1 0.195822035 0.3279661 0.6244919 2 0.195822035 0.3279661 0.6244919 3 0.053674606 0.1171308 0.6952595 4 0.053674606 0.1171308 0.6952595 5 0.145922707 0.3279661 0.5704061 6 0.145922707 0.3279661 0.5704061 7 0.158397539 0.1171308 0.4893554 8 0.145922707 0.1171308 0.4893554 9 0.420369012 0.3279661 0.6069822 10 0.420369012 0.3279661 0.6069822 11 0.345520020 0.1171308 0.5632659 12 0.333045188 0.1171308 0.5632659 13 0.091099103 0.3279661 0.6639923 14 0.091099103 0.3279661 0.6639923 15 0.140998431 0.1171308 0.5100815 16 0.153473263 0.1171308 0.5100815 17 0.315646080 0.1171308 0.5490307 18 0.315646080 0.1171308 0.5490307 19 0.091099103 0.3279661 0.5262813 20 0.103573935 0.3279661 0.5262813 21 0.003775278 0.1171308 0.5179992 22 0.003775278 0.1171308 0.5179992 23 0.120973042 0.1171308 0.6207106 24 0.120973042 0.1171308 0.6207106 25 0.108498210 0.1171308 0.5810134 26 0.108498210 0.1171308 0.5810134 27 0.021174386 0.1171308 0.6245776 28 0.021174386 0.1171308 0.6245776 29 0.333045188 0.1171308 0.5614453 30 0.333045188 0.1171308 0.5614453 31 0.203372591 0.3279661 0.6530508 32 0.203372591 0.3279661 0.6530508 33 0.203372591 0.1171308 0.5246117 34 0.203372591 0.1171308 0.5246117 35 0.008699554 0.1171308 0.5105633 36 0.003775278 0.1171308 0.5105633 37 0.116048767 0.1171308 0.6282338 38 0.116048767 0.1171308 0.6282338 39 0.003775278 0.1171308 0.6318230 40 0.003775278 0.1171308 0.6318230 41 0.028724942 0.3279661 0.5233805 42 0.041199774 0.3279661 0.5233805 43 0.170872371 0.1171308 0.5490773 44 0.170872371 0.1171308 0.5490773 45 0.228322255 0.1171308 0.6057277 46 0.240797087 0.1171308 0.6057277 47 0.021174386 0.1171308 0.6266224 48 0.008699554 0.1171308 0.6266224 49 0.008699554 0.3279661 0.5525454 50 0.008699554 0.3279661 0.5525454 51 0.165948095 0.1171308 0.5555328 52 0.178422927 0.1171308 0.5555328 53 0.420369012 0.1171308 0.5848260 54 0.420369012 0.1171308 0.5848260 55 0.103573935 0.1171308 0.6080357 56 0.103573935 0.1171308 0.6080357 57 0.116048767 0.3279661 0.6008923 58 0.116048767 0.3279661 0.6008923 59 0.128523599 0.1171308 0.5760879 60 0.128523599 0.1171308 0.5760879 61 0.153473263 0.1171308 0.5981138 62 0.153473263 0.1171308 0.5981138 63 0.078624270 0.1171308 0.6612065 64 0.091099103 0.1171308 0.6612065 65 0.165948095 0.1171308 0.5608325 66 0.165948095 0.1171308 0.5608325 67 0.003775278 0.1171308 0.5843468 68 0.016250110 0.1171308 0.5843468 69 0.270671027 0.1171308 0.6088168 70 0.270671027 0.1171308 0.6088168 71 0.021174386 0.1171308 0.6793365 72 0.021174386 0.1171308 0.6793365 73 0.103573935 0.1171308 0.6419952 74 0.103573935 0.1171308 0.6419952 75 0.203372591 0.3279661 0.5778115 76 0.203372591 0.3279661 0.5778115 > kfit1 Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "gauss"), data = kidney) coef se(coef) se2 Chisq DF p age 0.00471 0.0125 0.00856 0.14 1.0 0.7100 sex -1.41063 0.4451 0.31503 10.04 1.0 0.0015 frailty(id, dist = "gauss 26.54 14.7 0.0290 Iterations: 6 outer, 28 Newton-Raphson Variance of random effect= 0.569 Degrees of freedom for terms= 0.5 0.5 14.7 Likelihood ratio test=47.5 on 15.69 df, p=4.65e-05 n= 76 > kfitx Call: coxph(formula = Surv(time, status) ~ age + sex + offset(temp), data = kidney, init = kfit1$coef, iter.max = 0) coef exp(coef) se(coef) z p age 0.00471 1.005 0.00875 0.538 5.9e-01 sex -1.41063 0.244 0.30916 -4.563 5.0e-06 Likelihood ratio test=0 on 2 df, p=1 n= 76 > > rm(temp1, temp2, kfitx, zed, tempf) > # > # The special case of a single sparse frailty > # > > kfit1 <- coxph(Surv(time, status) ~ frailty(id, dist="gauss"), kidney) > tempf <- predict(kfit1, type="terms") > temp <- kfit1$frail[match(kidney$id, sort(unique(kidney$id)))] > all.equal(as.vector(tempf), as.vector(temp)) [1] T > > # Now fit a model with explicit offset > kfitx <- coxph(Surv(time, status) ~ offset(tempf),kidney, eps=1e-7) > > all.equal(resid(kfit1), resid(kfitx)) [1] T > all.equal(resid(kfit1, type="deviance"), resid(kfitx, type="deviance")) [1] T > > # > # Some tests of predicted values > # > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > aeq(predict(kfit1, type="expected"), predict(kfitx, type="expected")) [1] T > aeq(predict(kfit1, type="lp"), predict(kfitx, type="lp")) [1] T > > temp1 <- predict(kfit1, type="terms", se.fit=T) > all.equal(temp1$fit, kfitx$linear) [1] T > all.equal(temp1$se.fit^2, + kfit1$fvar[match(kidney$id, sort(unique(kidney$id)))]) [1] T > > temp1 $fit: [1] 0.695322941 0.695322941 0.244363776 0.244363776 0.493777896 [6] 0.493777896 -0.658879753 -0.658879753 0.520994314 0.520994314 [11] -0.114379760 -0.114379760 0.799261991 0.799261991 -0.487795409 [16] -0.487795409 -0.120271844 -0.120271844 0.131081160 0.131081160 [21] -0.214822375 -0.214822375 -0.054773695 -0.054773695 0.184575874 [26] 0.184575874 -0.509525783 -0.509525783 -0.790241403 -0.790241403 [31] 0.324356959 0.324356959 -0.239177390 -0.239177390 -0.264230973 [36] -0.264230973 -0.472242362 -0.472242362 0.006350496 0.006350496 [41] -0.872904122 -0.872904122 -0.530513459 -0.530513459 0.351179181 [46] 0.351179181 -0.037129299 -0.037129299 0.441718240 0.441718240 [51] -0.418876639 -0.418876639 -0.107887816 -0.107887816 0.346099359 [56] 0.346099359 0.658680102 0.658680102 0.197185714 0.197185714 [61] 0.304679320 0.304679320 0.139630271 0.139630271 0.093562534 [66] 0.093562534 -0.209483283 -0.209483283 0.301887374 0.301887374 [71] -0.278636264 -0.278636264 0.068590872 0.068590872 0.078473259 [76] 0.078473259 $se.fit: [1] 0.6147113 0.6147113 0.6157024 0.6157024 0.5713312 0.5713312 0.4392271 [8] 0.4392271 0.5759022 0.5759022 0.4832712 0.4832712 0.6417752 0.6417752 [15] 0.4573402 0.4573402 0.4812024 0.4812024 0.5118065 0.5118065 0.4762681 [22] 0.4762681 0.5530110 0.5530110 0.5193604 0.5193604 0.5531610 0.5531610 [29] 0.4773814 0.4773814 0.6361045 0.6361045 0.4707460 0.4707460 0.4669424 [36] 0.4669424 0.5597930 0.5597930 0.5639378 0.5639378 0.4648879 0.4648879 [43] 0.4902904 0.4902904 0.5446419 0.5446419 0.5567662 0.5567662 0.5606017 [50] 0.5606017 0.4994076 0.4994076 0.4830103 0.4830103 0.5450207 0.5450207 [57] 0.6054682 0.6054682 0.5207580 0.5207580 0.5374623 0.5374623 0.5908553 [64] 0.5908553 0.5063650 0.5063650 0.5288166 0.5288166 0.5366511 0.5366511 [71] 0.5992889 0.5992889 0.5760201 0.5760201 0.5780104 0.5780104 > kfit1 Call: coxph(formula = Surv(time, status) ~ frailty(id, dist = "gauss"), data = kidney ) coef se(coef) se2 Chisq DF p frailty(id, dist = "gauss 23 13.8 0.057 Iterations: 6 outer, 28 Newton-Raphson Variance of random effect= 0.457 Degrees of freedom for terms= 13.8 Likelihood ratio test=33.4 on 13.83 df, p=0.00234 n= 76 > > > # From Gail, Sautner and Brown, Biometrics 36, 255-66, 1980 > > # 48 rats were injected with a carcinogen, and then randomized to either > # drug or placebo. The number of tumors ranges from 0 to 13; all rats were > # censored at 6 months after randomization. > > # Variables: rat, treatment (1=drug, 0=control), o > # observation # within rat, > # (start, stop] status > # The raw data has some intervals of zero length, i.e., start==stop. > # We add .1 to these times as an approximate solution > # > rat2 <- read.table("data.rat2", col.names=c("id", "rx", "enum", "start", + "stop", "status")) > temp1 <- rat2$start > temp2 <- rat2$stop > for (i in 1:nrow(rat2)) { + if (temp1[i] == temp2[i]) { + temp2[i] <- temp2[i] + .1;+ if (i < nrow(rat2) && rat2$id[i] == rat2$id[i+1]) { + temp1[i+1] <- temp1[i+1] + .1;+ if (temp2[i+1] <= temp1[i+1]) temp2[i+1] _ temp1[i+1];+ };+ };+ } > rat2$start <- temp1 > rat2$stop <- temp2 > > r2fit0 <- coxph(Surv(start, stop, status) ~ rx + cluster(id), rat2) > > r2fitg <- coxph(Surv(start, stop, status) ~ rx + frailty(id), rat2) > r2fitm <- coxph(Surv(start, stop, status) ~ rx + frailty.gaussian(id), rat2) > > r2fit0 Call: coxph(formula = Surv(start, stop, status) ~ rx + cluster(id), data = rat2) coef exp(coef) se(coef) robust se z p rx -0.826 0.438 0.151 0.204 -4.04 5.3e-05 Likelihood ratio test=32.9 on 1 df, p=9.89e-09 n= 253 > r2fitg Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id), data = rat2) coef se(coef) se2 Chisq DF p rx -0.838 0.219 0.152 14.6 1.0 0.00013 frailty(id) 57.3 26.4 0.00045 Iterations: 7 outer, 21 Newton-Raphson Variance of random effect= 0.317 EM likelihood = -779.1 Degrees of freedom for terms= 0.5 26.3 Likelihood ratio test=120 on 26.83 df, p=8.43e-14 n= 253 > r2fitm Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty.gaussian(id), data = rat2) coef se(coef) se2 Chisq DF p rx -0.79 0.22 0.154 12.9 1.0 3.3e-04 frailty.gaussian(id) 61.0 24.9 7.3e-05 Iterations: 5 outer, 17 Newton-Raphson Variance of random effect= 0.303 Degrees of freedom for terms= 0.5 24.9 Likelihood ratio test=118 on 25.37 df, p=6.99e-14 n= 253 > > #This example is unusual: the frailties variances end up about the same, > # but the effect on rx differs. Double check it > # Because of different iteration paths, the coef won't be exactly the > # same, but darn close. > > temp <- coxph(Surv(start, stop, status) ~ rx + offset(r2fitm$frail[id]), rat2) > all.equal(temp$coef, r2fitm$coef[1]) [1] "Mean relative difference: 0.0005510633" > > temp <- coxph(Surv(start, stop, status) ~ rx + offset(r2fitg$frail[id]), rat2) > all.equal(temp$coef, r2fitg$coef[1]) [1] "Mean relative difference: 0.0005360911" > > # > # What do I get with AIC > # > r2fita1 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, method="aic"), + rat2) > r2fita2 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, method="aic", + dist="gauss"), rat2) > r2fita3 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, dist="t"), + rat2) > > r2fita1 Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id, method = "aic"), data = rat2) coef se(coef) se2 Chisq DF p rx -0.838 0.23 0.151 13.3 1.0 0.00026 frailty(id, method = "aic 60.4 28.2 0.00039 Iterations: 10 outer, 25 Newton-Raphson Variance of random effect= 0.375 EM likelihood = -779.2 Degrees of freedom for terms= 0.4 28.2 Likelihood ratio test=124 on 28.62 df, p=7.92e-14 n= 253 > r2fita2 Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id, method = "aic", dist = "gauss"), data = rat2) coef se(coef) se2 Chisq DF p rx -0.784 0.255 0.154 9.48 1.0 2.1e-03 frailty(id, method = "aic 73.40 29.7 1.4e-05 Iterations: 6 outer, 18 Newton-Raphson Variance of random effect= 0.493 Degrees of freedom for terms= 0.4 29.7 Likelihood ratio test=127 on 30.03 df, p=6.02e-14 n= 253 > r2fita3 Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id, dist = "t"), data = rat2) coef se(coef) se2 Chisq DF p rx -0.789 0.254 0.157 9.67 1 0.00190 frailty(id, dist = "t") 64.70 30 0.00024 Iterations: 7 outer, 23 Newton-Raphson Variance of random effect= 0.779 Degrees of freedom for terms= 0.4 30.0 Likelihood ratio test=126 on 30.37 df, p=1.39e-13 n= 253 > q()