homework0429
Tung-Han Wu
2020/4/29
To analyze the renal transplant patients survival and associated factors to their mortality. Data on 863 kidney transplant patients (data file: kidney1a.txt or kidney1.xlsx).
Please use the log-rank test to compare the overall survival curves between the white and black groups and plot Kaplan-Meier survival curves.
Please use the log-rank test to compare the overall survival curves between the age≥40 and age<40 groups and plot Kaplan-Meier survival curves.
Please use the multiple Cox regression to estimate the hazard ratio of death between group A (age≥40) and group B (age<40).
(Predictors: age(≥40 or < 40), sex, race)
資料匯入、檢視資料
dta <- read.table("/Users/User/Desktop/LearnR/CA/CAdata/kidney1a.txt", header=T , stringsAsFactor=F, fill=T )
dim(dta)## [1] 863 6str(dta)## 'data.frame': 863 obs. of 6 variables:
## $ id : int 1 2 3 4 5 6 7 8 9 10 ...
## $ time: int 1 5 7 9 13 13 17 20 26 26 ...
## $ dead: int 0 0 1 0 0 0 1 0 1 1 ...
## $ sex : int 1 1 1 1 1 1 1 1 1 1 ...
## $ race: int 1 1 1 1 1 1 1 1 1 1 ...
## $ age : int 46 51 55 57 45 43 47 65 55 44 ...查看data
class(dta)## [1] "data.frame"names(dta)## [1] "id" "time" "dead" "sex" "race" "age"head(dta)## id time dead sex race age
## 1 1 1 0 1 1 46
## 2 2 5 0 1 1 51
## 3 3 7 1 1 1 55
## 4 4 9 0 1 1 57
## 5 5 13 0 1 1 45
## 6 6 13 0 1 1 43View(dta)(a)
- race
library(survival)
# Create the survival data object
surv.fit<-with(dta, Surv(time, dead == 1))
surv.fit## [1] 1+ 5+ 7 9+ 13+ 13+ 17 20+ 26 26 28 32+
## [13] 32+ 43+ 43 44 51+ 51+ 51+ 56 57 59 62 66+
## [25] 66+ 67+ 68 69 79+ 79 79+ 87+ 88 91 93+ 98
## [37] 98 104+ 105+ 106 112+ 116+ 116+ 118+ 119 121+ 121+ 135
## [49] 144+ 150 150+ 162 162+ 167+ 183+ 186+ 190 198+ 198+ 200+
## [61] 211+ 215+ 223+ 224+ 228 236+ 238+ 242 243+ 248 249 251+
## [73] 252 253+ 256+ 257+ 259+ 261+ 271+ 271+ 277+ 283+ 284+ 289+
## [85] 291 311 312+ 316+ 316+ 331+ 334 338+ 340+ 340 341+ 346
## [97] 347+ 354 361+ 367+ 370+ 370+ 386+ 391 392+ 403+ 406+ 410+
## [109] 421 428+ 432+ 432+ 439 452+ 478 481 485+ 486+ 490+ 494+
## [121] 495 512+ 512+ 535+ 543+ 545+ 545+ 545+ 563+ 570+ 570 572+
## [133] 579+ 582+ 583 590+ 596+ 615 621 630+ 631+ 633+ 652 654+
## [145] 655+ 659+ 670+ 670+ 692+ 697 701+ 719+ 723+ 725+ 730 734+
## [157] 753+ 757+ 773 776 790 806 834+ 835+ 864+ 864+ 875 888+
## [169] 890+ 903+ 909+ 915+ 932+ 939 945 945 946 951+ 961+ 965+
## [181] 968+ 1016+ 1028+ 1050+ 1058+ 1058+ 1092+ 1092+ 1105 1110+ 1110+ 1114+
## [193] 1115+ 1118+ 1124+ 1124+ 1125+ 1128+ 1128+ 1145+ 1149+ 1154+ 1154+ 1165+
## [205] 1186 1191 1196+ 1208+ 1208+ 1210 1224+ 1224+ 1229+ 1230+ 1252+ 1256+
## [217] 1274+ 1291+ 1297+ 1297+ 1302+ 1313+ 1316+ 1350+ 1357 1383+ 1383+ 1383+
## [229] 1383+ 1386+ 1388 1395+ 1418 1428+ 1429+ 1435+ 1449+ 1449+ 1450+ 1457+
## [241] 1463+ 1470+ 1497+ 1497+ 1500+ 1509 1522+ 1527+ 1527+ 1541+ 1567+ 1571+
## [253] 1578+ 1586+ 1594+ 1610+ 1610+ 1611+ 1617+ 1624+ 1638+ 1641+ 1655+ 1668+
## [265] 1674+ 1699+ 1700+ 1700+ 1707+ 1717+ 1717+ 1718+ 1718+ 1734 1736+ 1736+
## [277] 1739+ 1739+ 1739+ 1745+ 1745+ 1746+ 1749+ 1770+ 1770+ 1795+ 1802+ 1802+
## [289] 1803+ 1808+ 1808+ 1815+ 1820 1839+ 1861+ 1861+ 1893+ 1900+ 1920+ 1937+
## [301] 1947+ 1947+ 1959+ 1959+ 1975+ 1988+ 1988+ 1995+ 1995+ 2001+ 2016+ 2025+
## [313] 2032+ 2035+ 2038+ 2041+ 2043+ 2048+ 2049+ 2056 2060+ 2090+ 2090+ 2095+
## [325] 2096+ 2096+ 2098+ 2102+ 2109+ 2135+ 2135+ 2147+ 2190+ 2211+ 2221+ 2223+
## [337] 2253+ 2253+ 2264+ 2267+ 2270+ 2291 2291+ 2313 2313+ 2313+ 2330+ 2332+
## [349] 2335+ 2356+ 2367+ 2384+ 2418+ 2421+ 2421 2430+ 2433+ 2434+ 2462+ 2462+
## [361] 2488+ 2489 2497+ 2516+ 2531+ 2533+ 2575+ 2585+ 2589+ 2601+ 2607+ 2625+
## [373] 2630+ 2646+ 2654+ 2690+ 2696+ 2700+ 2712+ 2714+ 2716+ 2716+ 2740+ 2761+
## [385] 2762+ 2765+ 2789+ 2789+ 2812+ 2815+ 2827+ 2831+ 2846+ 2867+ 2871+ 2889+
## [397] 2909+ 2922+ 2936+ 2948+ 2955+ 2957+ 2994+ 2994+ 2999+ 3007+ 3045+ 3060+
## [409] 3078+ 3078+ 3084+ 3084+ 3110+ 3130+ 3131+ 3146 3147+ 3172+ 3179+ 3187+
## [421] 3187+ 3255+ 3260+ 3287+ 3289+ 3300+ 3301+ 3319+ 3361+ 3402+ 3425+ 3434+
## [433] 37 43 57 80+ 82+ 93+ 114+ 116+ 116+ 119+ 152+ 158
## [445] 172+ 200+ 206 211+ 231+ 280+ 311 312+ 402 414+ 443+ 450
## [457] 452+ 479+ 499+ 535+ 642+ 646+ 661+ 663+ 663+ 671+ 750+ 777+
## [469] 863+ 863+ 864+ 868+ 934+ 951+ 992+ 1001 1002+ 1109+ 1122+ 1124+
## [481] 1149+ 1178+ 1230+ 1232+ 1242+ 1275 1352+ 1384 1450+ 1586+ 1624+ 1668+
## [493] 1681+ 1778+ 1795+ 1795+ 1877+ 1989+ 2049+ 2094+ 2095+ 2264+ 2291+ 2369+
## [505] 2369 2414 2425+ 2451+ 2455+ 2557 2598+ 2625+ 2659+ 2688+ 2726+ 2741+
## [517] 2750+ 2909+ 2961+ 2994+ 3019+ 3255+ 3281+ 3430+ 1+ 2 3 5+
## [529] 7 9+ 10 10 17+ 20+ 21 26+ 33+ 43+ 43+ 48+
## [541] 50 51+ 52 62 62+ 68 78 79+ 82+ 97 104 105+
## [553] 112+ 115+ 124+ 141+ 142+ 143 150+ 154 162+ 162+ 167+ 173+
## [565] 193+ 205+ 209 231+ 238+ 239+ 246+ 246+ 250+ 253+ 260+ 269+
## [577] 271+ 273 280+ 297 306+ 331+ 337+ 341+ 341+ 347+ 366 377+
## [589] 387+ 388+ 399+ 417+ 424+ 428+ 448+ 448+ 448+ 459+ 470 490
## [601] 507+ 512+ 549+ 593+ 604+ 614 642+ 652+ 654+ 660+ 670+ 675+
## [613] 678+ 693+ 715+ 731+ 750+ 753+ 757+ 759+ 762+ 772+ 772+ 777+
## [625] 777+ 793 840 852 900+ 907+ 907+ 909+ 915+ 963+ 995+ 995+
## [637] 1012+ 1013 1051+ 1072+ 1086+ 1114+ 1125+ 1164 1196+ 1229+ 1242+ 1252+
## [649] 1254+ 1254+ 1269+ 1291+ 1291+ 1299+ 1304+ 1309+ 1315+ 1326 1331 1350+
## [661] 1365+ 1368+ 1368+ 1427+ 1435+ 1449+ 1473 1497+ 1594+ 1605+ 1606+ 1611+
## [673] 1623+ 1638+ 1673+ 1681+ 1698+ 1699+ 1702+ 1702+ 1707+ 1732+ 1736+ 1746+
## [685] 1777 1778+ 1785+ 1786+ 1786+ 1791+ 1795+ 1815+ 1835 1875+ 1877 1893+
## [697] 1914+ 1939+ 1940 1942+ 1962+ 1966+ 1973+ 1980+ 2001+ 2014+ 2014+ 2025+
## [709] 2034+ 2034 2034+ 2038+ 2048+ 2060+ 2083+ 2094+ 2102+ 2108 2129+ 2193+
## [721] 2211+ 2221+ 2223+ 2233+ 2236+ 2252+ 2252+ 2271+ 2301 2312+ 2332+ 2335+
## [733] 2356+ 2392+ 2405+ 2405+ 2421+ 2433+ 2462+ 2486+ 2488+ 2504+ 2529+ 2529+
## [745] 2531+ 2556+ 2567 2632+ 2638+ 2638+ 2654+ 2659+ 2663+ 2670+ 2680+ 2700+
## [757] 2701+ 2705+ 2726+ 2750+ 2759+ 2768+ 2783+ 2795 2870+ 2871+ 2876+ 2900+
## [769] 2906+ 2918+ 2948+ 2993+ 3028+ 3042+ 3063+ 3063+ 3072+ 3077+ 3084+ 3086+
## [781] 3096+ 3102+ 3106+ 3116+ 3124+ 3142+ 3145+ 3145+ 3172+ 3173+ 3175+ 3186+
## [793] 3202+ 3215+ 3224+ 3229+ 3265+ 3300+ 3325+ 3360+ 3372+ 3379+ 3412+ 3420+
## [805] 14+ 40 45 93+ 106 116+ 116+ 121 229 250+ 259+ 261+
## [817] 306+ 312+ 344 392+ 442+ 512+ 625+ 673+ 731+ 777+ 864 879+
## [829] 887+ 899+ 899+ 903+ 920+ 929 943 953+ 953+ 1016 1151+ 1196
## [841] 1291+ 1291+ 1457+ 1508+ 1567+ 1674+ 1736+ 1739+ 1942+ 2026+ 2171 2268+
## [853] 2276 2413+ 2434+ 2463+ 2650 2680+ 2935+ 3072+ 3161+ 3211+ 3304+KM estimates
# Create KM estimates broken out by race
surv.byrace= survfit(Surv(time,dead == 1) ~ race, data = dta)
summary(surv.byrace)## Call: survfit(formula = Surv(time, dead == 1) ~ race, data = dta)
##
## race=1
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2 710 1 0.999 0.00141 0.996 1.000
## 3 709 1 0.997 0.00199 0.993 1.000
## 7 706 2 0.994 0.00281 0.989 1.000
## 10 702 2 0.992 0.00345 0.985 0.998
## 17 698 1 0.990 0.00372 0.983 0.997
## 21 694 1 0.989 0.00398 0.981 0.997
## 26 693 2 0.986 0.00445 0.977 0.995
## 28 690 1 0.984 0.00467 0.975 0.994
## 43 686 1 0.983 0.00488 0.973 0.993
## 44 682 1 0.982 0.00508 0.972 0.992
## 50 680 1 0.980 0.00527 0.970 0.990
## 52 675 1 0.979 0.00546 0.968 0.989
## 56 674 1 0.977 0.00564 0.966 0.988
## 57 673 1 0.976 0.00582 0.964 0.987
## 59 672 1 0.974 0.00599 0.963 0.986
## 62 671 2 0.971 0.00631 0.959 0.984
## 68 665 2 0.968 0.00662 0.956 0.982
## 69 663 1 0.967 0.00677 0.954 0.980
## 78 662 1 0.966 0.00692 0.952 0.979
## 79 661 1 0.964 0.00706 0.950 0.978
## 88 655 1 0.963 0.00720 0.949 0.977
## 91 654 1 0.961 0.00734 0.947 0.976
## 97 652 1 0.960 0.00747 0.945 0.974
## 98 651 2 0.957 0.00774 0.942 0.972
## 104 649 1 0.955 0.00786 0.940 0.971
## 106 645 1 0.954 0.00799 0.938 0.970
## 119 638 1 0.952 0.00812 0.936 0.968
## 135 634 1 0.951 0.00824 0.935 0.967
## 143 631 1 0.949 0.00836 0.933 0.966
## 150 629 1 0.948 0.00849 0.931 0.965
## 154 626 1 0.946 0.00861 0.929 0.963
## 162 625 1 0.945 0.00872 0.928 0.962
## 190 616 1 0.943 0.00884 0.926 0.961
## 209 610 1 0.942 0.00896 0.924 0.959
## 228 605 1 0.940 0.00908 0.922 0.958
## 242 599 1 0.938 0.00920 0.921 0.957
## 248 595 1 0.937 0.00932 0.919 0.955
## 249 594 1 0.935 0.00944 0.917 0.954
## 252 591 1 0.934 0.00955 0.915 0.953
## 273 579 1 0.932 0.00967 0.913 0.951
## 291 573 1 0.931 0.00979 0.912 0.950
## 297 572 1 0.929 0.00991 0.910 0.949
## 311 570 1 0.927 0.01002 0.908 0.947
## 334 564 1 0.926 0.01014 0.906 0.946
## 340 561 1 0.924 0.01026 0.904 0.944
## 346 556 1 0.922 0.01037 0.902 0.943
## 354 553 1 0.921 0.01049 0.900 0.941
## 366 551 1 0.919 0.01060 0.898 0.940
## 391 543 1 0.917 0.01071 0.897 0.939
## 421 536 1 0.916 0.01083 0.895 0.937
## 439 530 1 0.914 0.01095 0.893 0.936
## 470 524 1 0.912 0.01106 0.891 0.934
## 478 523 1 0.910 0.01118 0.889 0.933
## 481 522 1 0.909 0.01129 0.887 0.931
## 490 519 1 0.907 0.01141 0.885 0.929
## 495 516 1 0.905 0.01152 0.883 0.928
## 570 504 1 0.903 0.01163 0.881 0.926
## 583 499 1 0.901 0.01175 0.879 0.925
## 614 494 1 0.900 0.01187 0.877 0.923
## 615 493 1 0.898 0.01198 0.875 0.922
## 621 492 1 0.896 0.01210 0.873 0.920
## 652 487 1 0.894 0.01221 0.871 0.918
## 697 473 1 0.892 0.01233 0.868 0.917
## 730 467 1 0.890 0.01245 0.866 0.915
## 773 455 1 0.888 0.01258 0.864 0.913
## 776 454 1 0.886 0.01270 0.862 0.912
## 790 451 1 0.884 0.01282 0.860 0.910
## 793 450 1 0.883 0.01294 0.858 0.908
## 806 449 1 0.881 0.01306 0.855 0.907
## 840 446 1 0.879 0.01318 0.853 0.905
## 852 445 1 0.877 0.01330 0.851 0.903
## 875 442 1 0.875 0.01342 0.849 0.901
## 939 430 1 0.873 0.01354 0.846 0.900
## 945 429 2 0.869 0.01378 0.842 0.896
## 946 427 1 0.866 0.01390 0.840 0.894
## 1013 418 1 0.864 0.01402 0.837 0.892
## 1105 407 1 0.862 0.01414 0.835 0.890
## 1164 390 1 0.860 0.01428 0.833 0.889
## 1186 388 1 0.858 0.01441 0.830 0.887
## 1191 387 1 0.856 0.01454 0.828 0.885
## 1210 382 1 0.853 0.01468 0.825 0.883
## 1326 356 1 0.851 0.01483 0.822 0.881
## 1331 355 1 0.849 0.01498 0.820 0.878
## 1357 352 1 0.846 0.01513 0.817 0.876
## 1388 343 1 0.844 0.01529 0.814 0.874
## 1418 341 1 0.841 0.01544 0.812 0.872
## 1473 328 1 0.839 0.01561 0.809 0.870
## 1509 323 1 0.836 0.01577 0.806 0.868
## 1734 281 1 0.833 0.01599 0.802 0.865
## 1777 267 1 0.830 0.01624 0.799 0.862
## 1820 252 1 0.827 0.01650 0.795 0.860
## 1835 251 1 0.823 0.01676 0.791 0.857
## 1877 246 1 0.820 0.01702 0.787 0.854
## 1940 238 1 0.817 0.01730 0.783 0.851
## 2034 215 1 0.813 0.01763 0.779 0.848
## 2056 204 1 0.809 0.01799 0.774 0.845
## 2108 191 1 0.805 0.01839 0.769 0.841
## 2291 167 1 0.800 0.01890 0.764 0.838
## 2301 165 1 0.795 0.01939 0.758 0.834
## 2313 163 1 0.790 0.01988 0.752 0.830
## 2421 147 1 0.785 0.02046 0.746 0.826
## 2489 134 1 0.779 0.02113 0.739 0.821
## 2567 124 1 0.773 0.02187 0.731 0.817
## 2795 85 1 0.763 0.02342 0.719 0.811
## 3146 33 1 0.740 0.03217 0.680 0.806
##
## race=2
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 37 150 1 0.993 0.00664 0.980 1.000
## 40 149 1 0.987 0.00937 0.968 1.000
## 43 148 1 0.980 0.01143 0.958 1.000
## 45 147 1 0.973 0.01315 0.948 0.999
## 57 146 1 0.967 0.01466 0.938 0.996
## 106 141 1 0.960 0.01608 0.929 0.992
## 121 134 1 0.953 0.01748 0.919 0.988
## 158 132 1 0.945 0.01878 0.909 0.983
## 206 129 1 0.938 0.02001 0.900 0.978
## 229 127 1 0.931 0.02117 0.890 0.973
## 311 120 1 0.923 0.02237 0.880 0.968
## 344 117 1 0.915 0.02353 0.870 0.962
## 402 115 1 0.907 0.02463 0.860 0.957
## 450 111 1 0.899 0.02573 0.850 0.951
## 864 91 1 0.889 0.02728 0.837 0.944
## 929 82 1 0.878 0.02902 0.823 0.937
## 943 80 1 0.867 0.03067 0.809 0.929
## 1001 75 1 0.856 0.03236 0.795 0.922
## 1016 73 1 0.844 0.03398 0.780 0.913
## 1196 66 1 0.831 0.03579 0.764 0.904
## 1275 62 1 0.818 0.03764 0.747 0.895
## 1384 58 1 0.804 0.03954 0.730 0.885
## 2171 36 1 0.781 0.04430 0.699 0.873
## 2276 33 1 0.758 0.04888 0.668 0.860
## 2369 31 1 0.733 0.05306 0.636 0.845
## 2414 28 1 0.707 0.05726 0.603 0.829
## 2557 22 1 0.675 0.06304 0.562 0.810
## 2650 19 1 0.639 0.06901 0.517 0.790plot(surv.byrace)
plot(surv.byrace, ylab="survival rate", xlab="time", col=c("red", "black"), lty= 1:2 , mark.time=T)
#lty=c(1,2) -> 2為虛線(Dashed line)
legend(800, 0.3, c("white", "black"),
lty=c(1, 2), lwd=2, col=c("red", "black"))
Logranktest for difference in survival by race
surv.diff.race= survdiff(Surv(time,dead == 1) ~ race, data = dta)
surv.diff.race## Call:
## survdiff(formula = Surv(time, dead == 1) ~ race, data = dta)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## race=1 712 112 116.6 0.185 1.11
## race=2 151 28 23.4 0.925 1.11
##
## Chisq= 1.1 on 1 degrees of freedom, p= 0.3- p=0.3
(b)
- age變項分組
dta$age_gp<-ifelse(dta$age>= 40, 2, 1) #年齡分為大於等於40(=2),小於40(=1)View(dta)Logranktest for difference in survival by age_gp
surv.diff.age_gp= survdiff(Surv(time , dead == 1) ~ age_gp, data = dta)
surv.diff.age_gp## Call:
## survdiff(formula = Surv(time, dead == 1) ~ age_gp, data = dta)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## age_gp=1 333 22 62.4 26.2 47.7
## age_gp=2 530 118 77.6 21.0 47.7
##
## Chisq= 47.7 on 1 degrees of freedom, p= 5e-12- p=<.0001
KM estimates
surv.byagegp= survfit(Surv(time , dead ==1 ) ~ age_gp, data = dta)
summary(surv.byagegp)## Call: survfit(formula = Surv(time, dead == 1) ~ age_gp, data = dta)
##
## age_gp=1
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 3 333 1 0.997 0.00300 0.991 1.000
## 7 332 1 0.994 0.00423 0.986 1.000
## 62 323 1 0.991 0.00522 0.981 1.000
## 135 311 1 0.988 0.00610 0.976 1.000
## 143 310 1 0.985 0.00686 0.971 0.998
## 209 302 1 0.981 0.00757 0.967 0.996
## 229 300 1 0.978 0.00822 0.962 0.994
## 242 297 1 0.975 0.00883 0.958 0.992
## 311 288 1 0.971 0.00943 0.953 0.990
## 366 283 1 0.968 0.01000 0.949 0.988
## 450 278 1 0.964 0.01055 0.944 0.985
## 570 271 1 0.961 0.01110 0.939 0.983
## 621 269 1 0.957 0.01162 0.935 0.980
## 773 256 1 0.954 0.01216 0.930 0.978
## 793 253 1 0.950 0.01268 0.925 0.975
## 852 251 1 0.946 0.01318 0.921 0.972
## 1001 237 1 0.942 0.01372 0.916 0.969
## 1186 222 1 0.938 0.01430 0.910 0.966
## 1196 221 1 0.934 0.01485 0.905 0.963
## 1877 148 1 0.927 0.01603 0.896 0.959
## 2108 119 1 0.919 0.01769 0.885 0.955
## 3146 21 1 0.876 0.04593 0.790 0.970
##
## age_gp=2
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2 528 1 0.998 0.00189 0.994 1.000
## 7 525 1 0.996 0.00268 0.991 1.000
## 10 522 2 0.992 0.00379 0.985 1.000
## 17 518 1 0.990 0.00424 0.982 0.999
## 21 515 1 0.989 0.00465 0.979 0.998
## 26 514 2 0.985 0.00537 0.974 0.995
## 28 512 1 0.983 0.00569 0.972 0.994
## 37 509 1 0.981 0.00600 0.969 0.993
## 40 508 1 0.979 0.00629 0.967 0.991
## 43 507 2 0.975 0.00683 0.962 0.989
## 44 503 1 0.973 0.00709 0.959 0.987
## 45 502 1 0.971 0.00733 0.957 0.986
## 50 501 1 0.969 0.00757 0.955 0.984
## 52 498 1 0.967 0.00780 0.952 0.983
## 56 497 1 0.965 0.00803 0.950 0.981
## 57 496 2 0.961 0.00845 0.945 0.978
## 59 494 1 0.960 0.00866 0.943 0.977
## 62 493 1 0.958 0.00885 0.940 0.975
## 68 488 2 0.954 0.00924 0.936 0.972
## 69 486 1 0.952 0.00943 0.933 0.970
## 78 485 1 0.950 0.00961 0.931 0.969
## 79 484 1 0.948 0.00979 0.929 0.967
## 88 479 1 0.946 0.00997 0.926 0.966
## 91 478 1 0.944 0.01014 0.924 0.964
## 97 475 1 0.942 0.01031 0.922 0.962
## 98 474 2 0.938 0.01065 0.917 0.959
## 104 472 1 0.936 0.01081 0.915 0.957
## 106 469 2 0.932 0.01112 0.910 0.954
## 119 460 1 0.930 0.01128 0.908 0.952
## 121 459 1 0.928 0.01144 0.906 0.950
## 150 453 1 0.926 0.01159 0.903 0.949
## 154 450 1 0.924 0.01175 0.901 0.947
## 158 449 1 0.922 0.01190 0.899 0.945
## 162 448 1 0.920 0.01205 0.896 0.944
## 190 441 1 0.917 0.01220 0.894 0.942
## 206 437 1 0.915 0.01236 0.892 0.940
## 228 432 1 0.913 0.01251 0.889 0.938
## 248 426 1 0.911 0.01266 0.887 0.936
## 249 425 1 0.909 0.01281 0.884 0.934
## 252 422 1 0.907 0.01296 0.882 0.933
## 273 411 1 0.905 0.01312 0.879 0.931
## 291 406 1 0.902 0.01327 0.877 0.929
## 297 405 1 0.900 0.01342 0.874 0.927
## 311 402 1 0.898 0.01358 0.872 0.925
## 334 395 1 0.896 0.01373 0.869 0.923
## 340 394 1 0.893 0.01388 0.867 0.921
## 344 390 1 0.891 0.01403 0.864 0.919
## 346 389 1 0.889 0.01418 0.861 0.917
## 354 386 1 0.887 0.01433 0.859 0.915
## 391 378 1 0.884 0.01449 0.856 0.913
## 402 375 1 0.882 0.01464 0.854 0.911
## 421 370 1 0.879 0.01479 0.851 0.909
## 439 365 1 0.877 0.01495 0.848 0.907
## 470 357 1 0.875 0.01510 0.845 0.905
## 478 356 1 0.872 0.01526 0.843 0.903
## 481 354 1 0.870 0.01541 0.840 0.900
## 490 352 1 0.867 0.01557 0.837 0.898
## 495 350 1 0.865 0.01572 0.834 0.896
## 583 335 1 0.862 0.01588 0.832 0.894
## 614 330 1 0.859 0.01605 0.829 0.892
## 615 329 1 0.857 0.01621 0.826 0.889
## 652 323 1 0.854 0.01638 0.823 0.887
## 697 308 1 0.851 0.01656 0.820 0.885
## 730 304 1 0.849 0.01674 0.816 0.882
## 776 294 1 0.846 0.01693 0.813 0.880
## 790 291 1 0.843 0.01712 0.810 0.877
## 806 290 1 0.840 0.01730 0.807 0.875
## 840 288 1 0.837 0.01749 0.803 0.872
## 864 285 1 0.834 0.01767 0.800 0.869
## 875 281 1 0.831 0.01785 0.797 0.867
## 929 269 1 0.828 0.01805 0.793 0.864
## 939 268 1 0.825 0.01825 0.790 0.862
## 943 267 1 0.822 0.01844 0.787 0.859
## 945 266 2 0.816 0.01881 0.780 0.853
## 946 264 1 0.813 0.01899 0.776 0.851
## 1013 257 1 0.809 0.01918 0.773 0.848
## 1016 256 1 0.806 0.01936 0.769 0.845
## 1105 247 1 0.803 0.01956 0.766 0.842
## 1164 235 1 0.800 0.01977 0.762 0.839
## 1191 232 1 0.796 0.01998 0.758 0.836
## 1210 230 1 0.793 0.02020 0.754 0.833
## 1275 217 1 0.789 0.02043 0.750 0.830
## 1326 211 1 0.785 0.02067 0.746 0.827
## 1331 210 1 0.782 0.02091 0.742 0.824
## 1357 206 1 0.778 0.02115 0.737 0.820
## 1384 201 1 0.774 0.02140 0.733 0.817
## 1388 199 1 0.770 0.02164 0.729 0.814
## 1418 198 1 0.766 0.02188 0.724 0.810
## 1473 190 1 0.762 0.02213 0.720 0.807
## 1509 188 1 0.758 0.02238 0.715 0.803
## 1734 166 1 0.753 0.02271 0.710 0.799
## 1777 156 1 0.749 0.02307 0.705 0.795
## 1820 144 1 0.743 0.02349 0.699 0.791
## 1835 143 1 0.738 0.02389 0.693 0.787
## 1940 137 1 0.733 0.02432 0.687 0.782
## 2034 122 1 0.727 0.02485 0.680 0.777
## 2056 116 1 0.721 0.02541 0.672 0.772
## 2171 106 1 0.714 0.02607 0.664 0.767
## 2276 95 1 0.706 0.02685 0.656 0.761
## 2291 94 1 0.699 0.02760 0.647 0.755
## 2301 92 1 0.691 0.02832 0.638 0.749
## 2313 90 1 0.683 0.02903 0.629 0.743
## 2369 86 1 0.676 0.02976 0.620 0.736
## 2414 83 1 0.667 0.03050 0.610 0.730
## 2421 82 1 0.659 0.03119 0.601 0.723
## 2489 74 1 0.650 0.03202 0.591 0.716
## 2557 69 1 0.641 0.03291 0.580 0.709
## 2567 68 1 0.631 0.03375 0.569 0.701
## 2650 61 1 0.621 0.03475 0.557 0.693
## 2795 45 1 0.607 0.03661 0.540 0.684plot(surv.byagegp, ylab="survival rate", xlab="time", col=c("gray", "blue"), lty= 1:2 ,mark.time=T)
#lty=c(1,2) -> 2為虛線(Dashed line)
legend(800, 0.3, c("age>= 40", "age<40"),
lty=c(1, 2), lwd=2, col=c("gray", "blue"))
(c)
- age->group 變項分組
dta$group<-ifelse(dta$age>= 40, "A", "B") View(dta)
str(dta)## 'data.frame': 863 obs. of 8 variables:
## $ id : int 1 2 3 4 5 6 7 8 9 10 ...
## $ time : int 1 5 7 9 13 13 17 20 26 26 ...
## $ dead : int 0 0 1 0 0 0 1 0 1 1 ...
## $ sex : int 1 1 1 1 1 1 1 1 1 1 ...
## $ race : int 1 1 1 1 1 1 1 1 1 1 ...
## $ age : int 46 51 55 57 45 43 47 65 55 44 ...
## $ age_gp: num 2 2 2 2 2 2 2 2 2 2 ...
## $ group : chr "A" "A" "A" "A" ...Cox proportional hazards regression
# First, let’s look at the cox model of survival in the melanomdata set where the predictor variable is sex (male/female)
coxph.group= coxph(Surv(time , dead == 1 ) ~ group + sex + race, data = dta)
summary(coxph.group)## Call:
## coxph(formula = Surv(time, dead == 1) ~ group + sex + race, data = dta)
##
## n= 863, number of events= 140
##
## coef exp(coef) se(coef) z Pr(>|z|)
## groupB -1.46687 0.23065 0.23385 -6.273 3.55e-10 ***
## sex -0.02812 0.97227 0.17451 -0.161 0.872
## race 0.05238 1.05377 0.21212 0.247 0.805
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## groupB 0.2306 4.336 0.1458 0.3648
## sex 0.9723 1.029 0.6906 1.3688
## race 1.0538 0.949 0.6953 1.5970
##
## Concordance= 0.64 (se = 0.022 )
## Likelihood ratio test= 53.6 on 3 df, p=1e-11
## Wald test = 40.13 on 3 df, p=1e-08
## Score (logrank) test = 47.76 on 3 df, p=2e-10group： HR=0.2306 (=A (age>=40) 當對照組)，如果對照組顛倒 HR=4.336 sex ： HR=0.9723 (=1 當對照組) ，如果對照組顛倒 HR=1.029 race ： HR=1.0538 (=1 當對照組) ，如果對照組顛倒 HR=0.949