R version 4.4.0 beta (2024-04-12 r86413 ucrt) -- "Puppy Cup" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # 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 > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > # I don't match their answers, and I think that I'm right > 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$id, sum) > temp2 <- log(rr/1 +1) > aeq(temp1$coef, kfit1$coef, tolerance=.005) [1] TRUE > aeq(temp2, kfit1$frail, tolerance=.005) [1] TRUE > > > > kfit Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id), data = kidney) coef se(coef) se2 Chisq DF p age 3.18e-03 1.11e-02 1.11e-02 8.14e-02 1 0.775 sex -1.48e+00 3.58e-01 3.58e-01 1.71e+01 1 3.5e-05 diseaseGN 8.80e-02 4.06e-01 4.06e-01 4.68e-02 1 0.829 diseaseAN 3.51e-01 4.00e-01 4.00e-01 7.70e-01 1 0.380 diseasePKD -1.43e+00 6.31e-01 6.31e-01 5.14e+00 1 0.023 frailty(id) 2.71e-05 0 0.933 Iterations: 6 outer, 35 Newton-Raphson Variance of random effect= 5e-07 I-likelihood = -179.1 Degrees of freedom for terms= 1 1 3 0 Likelihood ratio test=17.6 on 5 df, p=0.003 n= 76, number of events= 58 > kfit1 Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, theta = 1), data = kidney, iter = 20) coef se(coef) se2 Chisq DF p age 0.00389 0.01959 0.00943 0.03933 1.0 0.84280 sex -2.00764 0.59104 0.41061 11.53834 1.0 0.00068 diseaseGN 0.35335 0.71653 0.38015 0.24319 1.0 0.62191 diseaseAN 0.52341 0.72298 0.40463 0.52413 1.0 0.46909 diseasePKD -0.45938 1.08977 0.66088 0.17770 1.0 0.67336 frailty(id, theta = 1) 28.50571 18.8 0.06909 Iterations: 1 outer, 14 Newton-Raphson Variance of random effect= 1 I-likelihood = -182.5 Degrees of freedom for terms= 0.2 0.5 1.1 18.8 Likelihood ratio test=63.8 on 20.6 df, p=3e-06 n= 76, number of events= 58 > kfit0 Call: coxph(formula = Surv(time, status) ~ age + sex + disease, data = kidney) coef exp(coef) se(coef) z p age 0.003181 1.003186 0.011146 0.285 0.7754 sex -1.483137 0.226925 0.358230 -4.140 3.47e-05 diseaseGN 0.087957 1.091941 0.406369 0.216 0.8286 diseaseAN 0.350794 1.420195 0.399717 0.878 0.3802 diseasePKD -1.431108 0.239044 0.631109 -2.268 0.0234 Likelihood ratio test=17.65 on 5 df, p=0.003423 n= 76, number of events= 58 > 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 0.01865 0.01120 0.04342 1.0 0.83494 sex -2.00763 0.57624 0.40799 12.13849 1.0 0.00049 diseaseGN 0.35335 0.67865 0.43154 0.27109 1.0 0.60260 diseaseAN 0.52340 0.68910 0.44038 0.57690 1.0 0.44753 diseasePKD -0.45934 1.01394 0.71297 0.20523 1.0 0.65053 frailty(id, theta = 1, sp 26.23016 18.7 0.11573 Iterations: 1 outer, 5 Newton-Raphson Variance of random effect= 1 I-likelihood = -182.5 Degrees of freedom for terms= 0.4 0.5 1.4 18.7 Likelihood ratio test=63.8 on 21 df, p=3e-06 n= 76, number of events= 58 > > # > # 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 0.01497 0.01059 0.10678 1.0 0.74384 sex -1.69728 0.46101 0.36170 13.55454 1.0 0.00023 diseaseGN 0.17986 0.54485 0.39273 0.10897 1.0 0.74131 diseaseAN 0.39294 0.54482 0.39816 0.52016 1.0 0.47077 diseasePKD -1.13631 0.82519 0.61728 1.89621 1.0 0.16850 frailty(id, dist = "gauss 17.89195 12.1 0.12376 Iterations: 7 outer, 42 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 14.9 df, p=3e-05 n= 76, number of events= 58 > summary(kfitm2) Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, dist = "gauss", sparse = F), data = kidney) n= 76, number of events= 58 coef se(coef) se2 Chisq DF p age 0.004924 0.0149 0.01084 0.11 1.00 0.74000 sex -1.702037 0.4631 0.36134 13.51 1.00 0.00024 diseaseGN 0.181733 0.5413 0.40169 0.11 1.00 0.74000 diseaseAN 0.394416 0.5428 0.40520 0.53 1.00 0.47000 diseasePKD -1.131602 0.8175 0.62981 1.92 1.00 0.17000 frailty(id, dist = "gauss 18.13 12.27 0.12000 exp(coef) exp(-coef) lower .95 upper .95 age 1.0049 0.9951 0.97601 1.0347 sex 0.1823 5.4851 0.07355 0.4519 diseaseGN 1.1993 0.8338 0.41515 3.4646 diseaseAN 1.4835 0.6741 0.51196 4.2988 diseasePKD 0.3225 3.1006 0.06497 1.6010 gauss:1 1.7011 0.5879 0.51805 5.5856 gauss:2 1.4241 0.7022 0.38513 5.2662 gauss:3 1.1593 0.8626 0.38282 3.5108 gauss:4 0.6226 1.6063 0.23397 1.6566 gauss:5 1.2543 0.7972 0.39806 3.9526 gauss:6 1.1350 0.8811 0.38339 3.3599 gauss:7 1.9726 0.5069 0.56938 6.8342 gauss:8 0.6196 1.6140 0.21662 1.7721 gauss:9 0.8231 1.2149 0.28884 2.3456 gauss:10 0.5030 1.9882 0.17468 1.4482 gauss:11 0.7565 1.3218 0.27081 2.1134 gauss:12 1.1048 0.9052 0.33430 3.6510 gauss:13 1.3022 0.7679 0.42746 3.9673 gauss:14 0.5912 1.6915 0.18537 1.8855 gauss:15 0.5449 1.8352 0.18580 1.5980 gauss:16 1.0443 0.9576 0.31424 3.4702 gauss:17 0.9136 1.0945 0.30004 2.7820 gauss:18 0.9184 1.0889 0.32476 2.5970 gauss:19 0.6426 1.5562 0.19509 2.1166 gauss:20 1.1698 0.8549 0.34528 3.9631 gauss:21 0.3336 2.9974 0.10202 1.0910 gauss:22 0.6871 1.4554 0.23531 2.0064 gauss:23 1.4778 0.6767 0.47560 4.5918 gauss:24 1.0170 0.9832 0.31555 3.2779 gauss:25 0.8096 1.2352 0.27491 2.3843 gauss:26 0.6145 1.6274 0.21491 1.7570 gauss:27 1.0885 0.9187 0.32819 3.6101 gauss:28 1.5419 0.6485 0.49231 4.8292 gauss:29 1.3785 0.7254 0.43766 4.3421 gauss:30 1.3748 0.7274 0.44444 4.2530 gauss:31 1.4447 0.6922 0.47031 4.4380 gauss:32 1.1993 0.8339 0.35207 4.0850 gauss:33 1.9449 0.5142 0.55229 6.8491 gauss:34 0.8617 1.1605 0.27685 2.6820 gauss:35 1.7031 0.5872 0.52657 5.5084 gauss:36 0.8275 1.2085 0.22811 3.0015 gauss:37 1.4707 0.6800 0.38936 5.5549 gauss:38 1.0479 0.9543 0.30685 3.5789 Iterations: 6 outer, 21 Newton-Raphson Variance of random effect= 0.5090956 Degrees of freedom for terms= 0.5 0.6 1.7 12.3 Concordance= 0.796 (se = 0.032 ) Likelihood ratio test= 117.9 on 15.14 df, p=<2e-16 > # > # 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 0.01048 0.00891 0.12053 1.00 0.72846 sex -1.31953 0.39556 0.32497 11.12781 1.00 0.00085 frailty(id, method = "aic 13.55258 7.81 0.08692 Iterations: 9 outer, 63 Newton-Raphson Variance of random effect= 0.203 I-likelihood = -182.1 Degrees of freedom for terms= 0.7 0.7 7.8 Likelihood ratio test=33.3 on 9.21 df, p=1e-04 n= 76, number of events= 58 > > 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 0.00561 0.01203 0.00872 0.21774 1.0 0.64077 sex -1.65487 0.48294 0.38527 11.74180 1.0 0.00061 frailty(id, dist = "t") 20.33462 13.9 0.11752 Iterations: 8 outer, 58 Newton-Raphson Variance of random effect= 0.825 Degrees of freedom for terms= 0.5 0.6 13.9 Likelihood ratio test=48.6 on 15.1 df, p=2e-05 n= 76, number of events= 58 > 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 0.01031 0.00895 0.08646 1.00 0.7687 sex -1.15152 0.36368 0.30556 10.02558 1.00 0.0015 frailty(id, dist = "gauss 12.35238 6.76 0.0800 Iterations: 7 outer, 41 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=5e-04 n= 76, number of events= 58 > > > # 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 0.00785 0.01503 0.00823 0.27284 1.0 0.60143 sex -1.88990 0.56114 0.39941 11.34311 1.0 0.00076 frailty(id, method = "aic 37.45897 19.7 0.00918 Iterations: 8 outer, 87 Newton-Raphson Variance of random effect= 0.886 I-likelihood = -182.8 Degrees of freedom for terms= 0.3 0.5 19.7 Likelihood ratio test=61.2 on 20.5 df, p=6e-06 n= 76, number of events= 58 Warning message: In coxpenal.fit(X, Y, istrat, offset, init = init, control, weights = weights, : Inner loop failed to coverge for iterations 4 > > 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 0.00561 0.01203 0.00872 0.21774 1.0 0.64077 sex -1.65487 0.48294 0.38527 11.74180 1.0 0.00061 frailty(id, dist = "t", c 20.33462 13.9 0.11752 Iterations: 8 outer, 58 Newton-Raphson Variance of random effect= 0.825 Degrees of freedom for terms= 0.5 0.6 13.9 Likelihood ratio test=48.6 on 15.1 df, p=2e-05 n= 76, number of events= 58 > > proc.time() user system elapsed 0.92 0.09 1.00