Tópicos de Análise de Sobrevivência
Exemplos de Aplicação
library(rmarkdown); library(knitr); library(readxl); library(tidyverse); library(survival)
library(survminer); library(ggsurvfit); library(gtsummary); library(pacman) ; library(ggplot2)Estimador de Kaplan-Meier
Dados sem Sensura
Consideremos este dado hipotético (sem sensura)
Temp_0 = c(3, 18, 29, 54, 60, 84, 110, 112, 116, 123, 134, 145, 151, 151, 158, 173, 194, 214, 329, 331,
371, 408, 490, 514, 541, 55, 688, 780, 801, 858, 887, 998); Status_0 = rep(1, 32)Estimador Kaplan-Meier
# Tempo de sobrevivência ← Surv(Temp_0, Status_0)
E_KM_0 = survfit(Surv(Temp_0, Status_0)~1); E_KM_0; summary(E_KM_0)## Call: survfit(formula = Surv(Temp_0, Status_0) ~ 1)
##
## n events median 0.95LCL 0.95UCL
## [1,] 32 32 166 134 408## Call: survfit(formula = Surv(Temp_0, Status_0) ~ 1)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 3 32 1 0.9688 0.0308 0.91030 1.000
## 18 31 1 0.9375 0.0428 0.85727 1.000
## 29 30 1 0.9062 0.0515 0.81068 1.000
## 54 29 1 0.8750 0.0585 0.76760 0.997
## 55 28 1 0.8438 0.0642 0.72688 0.979
## 60 27 1 0.8125 0.0690 0.68792 0.960
## 84 26 1 0.7812 0.0731 0.65038 0.938
## 110 25 1 0.7500 0.0765 0.61402 0.916
## 112 24 1 0.7188 0.0795 0.57870 0.893
## 116 23 1 0.6875 0.0819 0.54428 0.868
## 123 22 1 0.6562 0.0840 0.51070 0.843
## 134 21 1 0.6250 0.0856 0.47789 0.817
## 145 20 1 0.5938 0.0868 0.44580 0.791
## 151 19 2 0.5312 0.0882 0.38367 0.736
## 158 17 1 0.5000 0.0884 0.35359 0.707
## 173 16 1 0.4688 0.0882 0.32415 0.678
## 194 15 1 0.4375 0.0877 0.29536 0.648
## 214 14 1 0.4062 0.0868 0.26723 0.618
## 329 13 1 0.3750 0.0856 0.23976 0.587
## 331 12 1 0.3438 0.0840 0.21298 0.555
## 371 11 1 0.3125 0.0819 0.18692 0.522
## 408 10 1 0.2812 0.0795 0.16164 0.489
## 490 9 1 0.2500 0.0765 0.13719 0.456
## 514 8 1 0.2188 0.0731 0.11365 0.421
## 541 7 1 0.1875 0.0690 0.09115 0.386
## 688 6 1 0.1562 0.0642 0.06985 0.350
## 780 5 1 0.1250 0.0585 0.04998 0.313
## 801 4 1 0.0938 0.0515 0.03193 0.275
## 858 3 1 0.0625 0.0428 0.01633 0.239
## 887 2 1 0.0312 0.0308 0.00454 0.215
## 998 1 1 0.0000 NaN NA NAplot(E_KM_0, conf.int = F, xlab = "Dias", ylab = "Sobrevivências", main = "Estimador de Kaplan-Meier")
Dados com Censura
Consideremos este dado hipotético (com sensura)
Temp_1 = c(16, 18, 21, 21, 22, 25, 29, 35, 37, 39, 40, 50, 52, 54, 60, 80, 80, 81, 83, 84, 85)
Status_1 = c(1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0) # 0 - Censura; 1 - Evento
Surv(Temp_1, Status_1) # ← Surv(Temp_0, Status_0) ## [1] 16 18 21+ 21 22 25+ 29 35 37 39 40 50+ 52 54 60 80+ 80 81+ 83
## [20] 84 85+Estimador Kaplan-Meier
## Call: survfit(formula = Surv(Temp_1, Status_1) ~ 1)
##
## n events median 0.95LCL 0.95UCL
## [1,] 21 15 52 37 NA## Call: survfit(formula = Surv(Temp_1, Status_1) ~ 1)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 16 21 1 0.9524 0.0465 0.8655 1.000
## 18 20 1 0.9048 0.0641 0.7875 1.000
## 21 19 1 0.8571 0.0764 0.7198 1.000
## 22 17 1 0.8067 0.0869 0.6531 0.996
## 29 15 1 0.7529 0.0963 0.5859 0.968
## 35 14 1 0.6992 0.1034 0.5232 0.934
## 37 13 1 0.6454 0.1085 0.4642 0.897
## 39 12 1 0.5916 0.1120 0.4082 0.857
## 40 11 1 0.5378 0.1140 0.3550 0.815
## 52 9 1 0.4781 0.1160 0.2972 0.769
## 54 8 1 0.4183 0.1158 0.2431 0.720
## 60 7 1 0.3585 0.1137 0.1926 0.667
## 80 6 1 0.2988 0.1093 0.1459 0.612
## 83 3 1 0.1992 0.1092 0.0680 0.583
## 84 2 1 0.0996 0.0891 0.0172 0.575plot(E_KM_1, conf.int = F, mark.time = T, xlab = "Dias", ylab = "Sobrevivências",
main = "Estimador ede Kaplan-Meier")
Exemplos Reais - Aplicação
A base de dados diabetic é um conjunto de dados clássico
amplamente utilizado em Análise de Sobrevivência, estando disponível no
pacote survival do R. O estudo investiga o
tempo até à ocorrência de perda visual grave em pacientes com
retinopatia diabética, avaliando a eficácia de um tratamento a laser em
comparação com a ausência de tratamento, com o objetivo de analisar se o
tratamento reduz o risco de progressão da doença ao longo do tempo.
Os dados são provenientes de um ensaio clínico conduzido nos Estados Unidos, no âmbito do Early Treatment Diabetic Retinopathy Study (ETDRS), um grande estudo multicêntrico desenvolvido para avaliar estratégias terapêuticas em doentes com diabetes e complicações oculares.
Estimador Kaplan-Meier
# survival::survfit - evitar conflitos com outras funções de mesmo nome em outros pacotes.
E_KM_2 = survival::survfit(Surv(time, status) ~ 1, data = diabetic); summary(E_KM_2)## Call: survfit(formula = Surv(time, status) ~ 1, data = diabetic)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.30 394 1 0.997 0.00253 0.993 1.000
## 0.60 393 1 0.995 0.00358 0.988 1.000
## 0.83 392 1 0.992 0.00438 0.984 1.000
## 1.33 391 1 0.990 0.00505 0.980 1.000
## 1.43 390 1 0.987 0.00564 0.976 0.998
## 1.50 385 2 0.982 0.00667 0.969 0.995
## 1.57 383 1 0.980 0.00713 0.966 0.994
## 1.63 382 2 0.974 0.00796 0.959 0.990
## 1.70 380 3 0.967 0.00906 0.949 0.985
## 1.73 377 1 0.964 0.00939 0.946 0.983
## 1.77 376 1 0.962 0.00971 0.943 0.981
## 1.80 375 1 0.959 0.01001 0.940 0.979
## 1.90 374 1 0.957 0.01031 0.937 0.977
## 1.97 373 1 0.954 0.01060 0.933 0.975
## 2.10 372 1 0.951 0.01087 0.930 0.973
## 2.17 371 1 0.949 0.01114 0.927 0.971
## 2.67 370 1 0.946 0.01140 0.924 0.969
## 2.70 369 1 0.944 0.01166 0.921 0.967
## 2.83 367 1 0.941 0.01191 0.918 0.965
## 2.90 366 1 0.939 0.01215 0.915 0.963
## 3.67 365 1 0.936 0.01238 0.912 0.961
## 4.10 363 1 0.933 0.01262 0.909 0.958
## 4.27 362 1 0.931 0.01284 0.906 0.956
## 4.30 361 1 0.928 0.01306 0.903 0.954
## 4.97 360 1 0.926 0.01328 0.900 0.952
## 5.33 359 1 0.923 0.01349 0.897 0.950
## 5.43 358 1 0.921 0.01370 0.894 0.948
## 5.67 357 1 0.918 0.01390 0.891 0.946
## 5.73 356 1 0.915 0.01410 0.888 0.943
## 5.77 355 1 0.913 0.01429 0.885 0.941
## 5.83 354 1 0.910 0.01448 0.882 0.939
## 5.90 353 1 0.908 0.01467 0.879 0.937
## 6.10 350 1 0.905 0.01485 0.876 0.935
## 6.13 349 1 0.902 0.01504 0.873 0.932
## 6.20 348 1 0.900 0.01521 0.871 0.930
## 6.30 347 1 0.897 0.01539 0.868 0.928
## 6.53 346 1 0.895 0.01556 0.865 0.926
## 6.57 345 2 0.889 0.01590 0.859 0.921
## 6.90 343 1 0.887 0.01606 0.856 0.919
## 7.07 342 1 0.884 0.01622 0.853 0.917
## 7.10 341 1 0.882 0.01638 0.850 0.914
## 7.60 339 1 0.879 0.01654 0.847 0.912
## 7.90 338 1 0.877 0.01669 0.844 0.910
## 8.30 335 2 0.871 0.01700 0.839 0.905
## 8.83 333 1 0.869 0.01715 0.836 0.903
## 9.40 332 1 0.866 0.01729 0.833 0.901
## 9.60 331 1 0.863 0.01744 0.830 0.898
## 9.63 330 1 0.861 0.01758 0.827 0.896
## 9.87 328 1 0.858 0.01772 0.824 0.894
## 9.90 326 3 0.850 0.01814 0.815 0.887
## 10.27 323 1 0.848 0.01827 0.813 0.884
## 10.33 322 1 0.845 0.01840 0.810 0.882
## 10.80 316 1 0.842 0.01854 0.807 0.879
## 10.97 315 1 0.840 0.01867 0.804 0.877
## 11.07 314 1 0.837 0.01880 0.801 0.875
## 11.30 313 1 0.834 0.01893 0.798 0.872
## 12.20 312 1 0.832 0.01906 0.795 0.870
## 12.73 311 1 0.829 0.01918 0.792 0.867
## 12.93 310 1 0.826 0.01931 0.789 0.865
## 13.10 309 1 0.824 0.01943 0.786 0.863
## 13.33 308 1 0.821 0.01955 0.784 0.860
## 13.37 307 1 0.818 0.01967 0.781 0.858
## 13.57 306 1 0.816 0.01978 0.778 0.855
## 13.77 305 2 0.810 0.02001 0.772 0.850
## 13.80 303 1 0.808 0.02012 0.769 0.848
## 13.83 302 4 0.797 0.02056 0.758 0.838
## 13.87 298 1 0.794 0.02066 0.755 0.836
## 13.90 297 1 0.792 0.02076 0.752 0.833
## 13.97 296 1 0.789 0.02086 0.749 0.831
## 14.00 295 1 0.786 0.02096 0.746 0.828
## 14.10 294 1 0.784 0.02106 0.743 0.826
## 14.27 293 1 0.781 0.02116 0.740 0.823
## 14.30 292 1 0.778 0.02126 0.738 0.821
## 14.37 291 1 0.775 0.02135 0.735 0.818
## 14.80 289 1 0.773 0.02144 0.732 0.816
## 15.83 288 1 0.770 0.02154 0.729 0.814
## 17.73 286 1 0.767 0.02163 0.726 0.811
## 18.03 285 2 0.762 0.02181 0.720 0.806
## 18.43 283 1 0.759 0.02190 0.718 0.804
## 18.70 282 1 0.757 0.02199 0.715 0.801
## 18.93 278 1 0.754 0.02207 0.712 0.798
## 19.00 277 1 0.751 0.02216 0.709 0.796
## 19.40 276 1 0.748 0.02225 0.706 0.793
## 20.17 274 1 0.746 0.02233 0.703 0.791
## 21.10 271 1 0.743 0.02242 0.700 0.788
## 21.57 270 1 0.740 0.02251 0.697 0.786
## 21.90 268 1 0.737 0.02259 0.695 0.783
## 21.97 267 1 0.735 0.02267 0.692 0.781
## 22.00 266 2 0.729 0.02284 0.686 0.775
## 22.13 264 1 0.726 0.02292 0.683 0.773
## 22.20 263 1 0.724 0.02300 0.680 0.770
## 22.23 262 1 0.721 0.02307 0.677 0.768
## 24.43 259 1 0.718 0.02315 0.674 0.765
## 24.73 258 1 0.715 0.02323 0.671 0.762
## 25.30 257 1 0.713 0.02331 0.668 0.760
## 25.63 256 1 0.710 0.02338 0.665 0.757
## 25.80 255 1 0.707 0.02345 0.663 0.755
## 25.93 252 1 0.704 0.02353 0.660 0.752
## 26.17 251 1 0.701 0.02360 0.657 0.749
## 26.20 250 1 0.699 0.02367 0.654 0.747
## 26.23 249 1 0.696 0.02374 0.651 0.744
## 26.37 248 1 0.693 0.02381 0.648 0.741
## 26.47 247 1 0.690 0.02388 0.645 0.739
## 27.60 244 1 0.687 0.02395 0.642 0.736
## 29.97 241 1 0.684 0.02402 0.639 0.733
## 30.20 240 1 0.682 0.02409 0.636 0.731
## 30.40 239 1 0.679 0.02416 0.633 0.728
## 30.83 238 1 0.676 0.02422 0.630 0.725
## 31.30 235 1 0.673 0.02429 0.627 0.722
## 31.63 232 1 0.670 0.02436 0.624 0.720
## 33.63 225 2 0.664 0.02450 0.618 0.714
## 33.90 223 1 0.661 0.02457 0.615 0.711
## 34.37 220 1 0.658 0.02464 0.612 0.708
## 34.57 219 1 0.655 0.02471 0.609 0.705
## 35.53 218 1 0.652 0.02478 0.605 0.703
## 38.40 207 1 0.649 0.02486 0.602 0.700
## 38.47 206 1 0.646 0.02494 0.599 0.697
## 38.57 205 2 0.640 0.02509 0.592 0.691
## 38.87 195 1 0.636 0.02518 0.589 0.688
## 41.40 185 1 0.633 0.02527 0.585 0.684
## 42.17 177 2 0.626 0.02549 0.578 0.678
## 42.33 167 1 0.622 0.02561 0.574 0.674
## 42.43 166 1 0.618 0.02573 0.570 0.671
## 43.03 161 1 0.614 0.02585 0.566 0.667
## 43.33 158 1 0.611 0.02598 0.562 0.664
## 43.70 155 1 0.607 0.02611 0.557 0.660
## 46.20 145 1 0.602 0.02626 0.553 0.656
## 46.27 140 1 0.598 0.02643 0.548 0.652
## 46.43 136 1 0.594 0.02660 0.544 0.648
## 46.63 133 1 0.589 0.02677 0.539 0.644
## 48.30 128 1 0.585 0.02695 0.534 0.640
## 48.43 127 1 0.580 0.02713 0.529 0.636
## 48.87 125 1 0.575 0.02731 0.524 0.631
## 54.10 104 1 0.570 0.02760 0.518 0.627
## 54.27 99 1 0.564 0.02791 0.512 0.622
## 59.80 56 1 0.554 0.02918 0.500 0.614
## 61.83 51 1 0.543 0.03056 0.486 0.606
## 63.33 43 1 0.531 0.03235 0.471 0.598Curva de Sobrevivência
ggsurvfit(E_KM_2, color = "cadetblue") +
add_censor_mark(color = "cadetblue") +
add_confidence_interval(fill = "cadetblue") +
add_quantile(y_value = 0.5, linetype = "dashed", color = "grey30") +
labs(x = "Tempo (dias)", y = "Probabilidade de sobrevivência") +
scale_ggsurvfit(x_scales = list(breaks = seq(0, 2250, by = 250))) +
add_risktable(stats_label = c("Em risco", "Eventos")) +
theme(axis.title = element_text(size = 11),
axis.title.x = element_text(margin = margin(5,5,15,5)))
Comparação entre os grupos
## Call: survfit(formula = Surv(time, status) ~ trt, data = diabetic)
##
## trt=0
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.30 197 1 0.995 0.00506 0.985 1.000
## 0.60 196 1 0.990 0.00714 0.976 1.000
## 0.83 195 1 0.985 0.00872 0.968 1.000
## 1.33 194 1 0.980 0.01005 0.960 1.000
## 1.43 193 1 0.975 0.01121 0.953 0.997
## 1.50 190 1 0.969 0.01226 0.946 0.994
## 1.57 189 1 0.964 0.01323 0.939 0.991
## 1.63 188 2 0.954 0.01495 0.925 0.984
## 1.70 186 2 0.944 0.01645 0.912 0.977
## 1.80 184 1 0.939 0.01714 0.906 0.973
## 1.97 183 1 0.934 0.01780 0.899 0.969
## 2.17 182 1 0.928 0.01843 0.893 0.965
## 2.67 181 1 0.923 0.01903 0.887 0.961
## 2.83 179 1 0.918 0.01961 0.881 0.957
## 2.90 178 1 0.913 0.02016 0.874 0.953
## 3.67 177 1 0.908 0.02070 0.868 0.949
## 4.27 176 1 0.903 0.02121 0.862 0.945
## 4.30 175 1 0.898 0.02171 0.856 0.941
## 4.97 174 1 0.892 0.02219 0.850 0.937
## 5.33 173 1 0.887 0.02265 0.844 0.933
## 5.43 172 1 0.882 0.02310 0.838 0.929
## 5.83 171 1 0.877 0.02354 0.832 0.924
## 6.20 169 1 0.872 0.02396 0.826 0.920
## 6.53 168 1 0.867 0.02437 0.820 0.916
## 6.57 167 1 0.861 0.02477 0.814 0.911
## 6.90 166 1 0.856 0.02516 0.808 0.907
## 7.10 165 1 0.851 0.02554 0.802 0.903
## 7.60 164 1 0.846 0.02591 0.796 0.898
## 7.90 163 1 0.841 0.02626 0.791 0.894
## 8.30 161 1 0.835 0.02661 0.785 0.889
## 8.83 160 1 0.830 0.02695 0.779 0.885
## 9.40 159 1 0.825 0.02728 0.773 0.880
## 9.60 158 1 0.820 0.02761 0.767 0.876
## 9.63 157 1 0.814 0.02792 0.762 0.871
## 9.87 156 1 0.809 0.02822 0.756 0.867
## 9.90 155 2 0.799 0.02881 0.744 0.857
## 10.80 151 1 0.794 0.02910 0.738 0.853
## 10.97 150 1 0.788 0.02938 0.733 0.848
## 11.30 149 1 0.783 0.02966 0.727 0.843
## 12.20 148 1 0.778 0.02993 0.721 0.839
## 12.73 147 1 0.772 0.03019 0.715 0.834
## 13.37 146 1 0.767 0.03044 0.710 0.829
## 13.77 145 1 0.762 0.03069 0.704 0.824
## 13.83 144 3 0.746 0.03139 0.687 0.810
## 13.87 141 1 0.741 0.03161 0.681 0.805
## 13.90 140 1 0.735 0.03182 0.676 0.800
## 14.00 139 1 0.730 0.03203 0.670 0.796
## 14.10 138 1 0.725 0.03223 0.664 0.791
## 14.37 137 1 0.719 0.03243 0.659 0.786
## 14.80 135 1 0.714 0.03262 0.653 0.781
## 15.83 134 1 0.709 0.03281 0.647 0.776
## 18.03 133 2 0.698 0.03317 0.636 0.766
## 18.43 131 1 0.693 0.03334 0.630 0.761
## 18.93 129 1 0.687 0.03351 0.625 0.756
## 19.00 128 1 0.682 0.03368 0.619 0.751
## 19.40 127 1 0.677 0.03384 0.614 0.746
## 21.10 125 1 0.671 0.03400 0.608 0.741
## 21.90 124 1 0.666 0.03415 0.602 0.736
## 21.97 123 1 0.660 0.03430 0.597 0.731
## 22.00 122 2 0.650 0.03458 0.585 0.721
## 22.13 120 1 0.644 0.03472 0.580 0.716
## 22.20 119 1 0.639 0.03484 0.574 0.711
## 22.23 118 1 0.633 0.03497 0.568 0.706
## 24.73 116 1 0.628 0.03509 0.563 0.701
## 25.30 115 1 0.622 0.03521 0.557 0.695
## 25.93 113 1 0.617 0.03532 0.551 0.690
## 26.17 112 1 0.611 0.03543 0.546 0.685
## 26.37 111 1 0.606 0.03554 0.540 0.680
## 26.47 110 1 0.600 0.03564 0.534 0.675
## 27.60 108 1 0.595 0.03574 0.529 0.669
## 29.97 106 1 0.589 0.03584 0.523 0.664
## 30.40 105 1 0.584 0.03594 0.517 0.659
## 31.30 103 1 0.578 0.03603 0.512 0.653
## 31.63 101 1 0.572 0.03613 0.506 0.648
## 33.63 98 1 0.566 0.03623 0.500 0.642
## 35.53 96 1 0.561 0.03633 0.494 0.636
## 38.40 91 1 0.554 0.03645 0.487 0.631
## 38.57 90 2 0.542 0.03666 0.475 0.619
## 41.40 80 1 0.535 0.03683 0.468 0.613
## 42.17 76 1 0.528 0.03701 0.460 0.606
## 42.33 70 1 0.521 0.03724 0.453 0.599
## 43.03 68 1 0.513 0.03747 0.445 0.592
## 43.33 66 1 0.505 0.03770 0.437 0.585
## 43.70 65 1 0.497 0.03792 0.428 0.578
## 46.20 61 1 0.489 0.03816 0.420 0.570
## 46.27 58 1 0.481 0.03842 0.411 0.562
## 46.63 55 1 0.472 0.03871 0.402 0.554
## 48.30 53 1 0.463 0.03899 0.393 0.546
## 48.43 52 1 0.454 0.03924 0.384 0.538
## 54.10 42 1 0.444 0.03977 0.372 0.529
## 54.27 40 1 0.432 0.04029 0.360 0.519
## 59.80 23 1 0.414 0.04270 0.338 0.506
## 61.83 21 1 0.394 0.04498 0.315 0.493
##
## trt=1
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 1.50 195 1 0.995 0.00512 0.985 1.000
## 1.70 194 1 0.990 0.00722 0.976 1.000
## 1.73 193 1 0.985 0.00881 0.967 1.000
## 1.77 192 1 0.979 0.01015 0.960 1.000
## 1.90 191 1 0.974 0.01132 0.952 0.997
## 2.10 190 1 0.969 0.01237 0.945 0.994
## 2.70 189 1 0.964 0.01332 0.938 0.991
## 4.10 187 1 0.959 0.01421 0.931 0.987
## 5.67 186 1 0.954 0.01504 0.925 0.984
## 5.73 185 1 0.949 0.01582 0.918 0.980
## 5.77 184 1 0.943 0.01655 0.912 0.976
## 5.90 183 1 0.938 0.01725 0.905 0.973
## 6.10 181 1 0.933 0.01791 0.899 0.969
## 6.13 180 1 0.928 0.01855 0.892 0.965
## 6.30 179 1 0.923 0.01916 0.886 0.961
## 6.57 178 1 0.918 0.01974 0.880 0.957
## 7.07 177 1 0.912 0.02030 0.873 0.953
## 8.30 174 1 0.907 0.02085 0.867 0.949
## 9.90 171 1 0.902 0.02139 0.861 0.945
## 10.27 170 1 0.897 0.02191 0.855 0.941
## 10.33 169 1 0.891 0.02241 0.848 0.936
## 11.07 165 1 0.886 0.02292 0.842 0.932
## 12.93 164 1 0.880 0.02341 0.836 0.928
## 13.10 163 1 0.875 0.02388 0.829 0.923
## 13.33 162 1 0.870 0.02433 0.823 0.919
## 13.57 161 1 0.864 0.02478 0.817 0.914
## 13.77 160 1 0.859 0.02520 0.811 0.910
## 13.80 159 1 0.853 0.02562 0.805 0.905
## 13.83 158 1 0.848 0.02602 0.799 0.901
## 13.97 157 1 0.843 0.02641 0.792 0.896
## 14.27 156 1 0.837 0.02678 0.786 0.891
## 14.30 155 1 0.832 0.02715 0.780 0.887
## 17.73 153 1 0.826 0.02751 0.774 0.882
## 18.70 152 1 0.821 0.02786 0.768 0.877
## 20.17 148 1 0.815 0.02822 0.762 0.873
## 21.57 146 1 0.810 0.02858 0.756 0.868
## 24.43 143 1 0.804 0.02893 0.749 0.863
## 25.63 142 1 0.798 0.02928 0.743 0.858
## 25.80 141 1 0.793 0.02961 0.737 0.853
## 26.20 139 1 0.787 0.02994 0.731 0.848
## 26.23 138 1 0.781 0.03026 0.724 0.843
## 30.20 135 1 0.776 0.03059 0.718 0.838
## 30.83 134 1 0.770 0.03090 0.712 0.833
## 33.63 127 1 0.764 0.03125 0.705 0.828
## 33.90 126 1 0.758 0.03158 0.698 0.822
## 34.37 124 1 0.752 0.03191 0.692 0.817
## 34.57 123 1 0.746 0.03223 0.685 0.811
## 38.47 116 1 0.739 0.03259 0.678 0.806
## 38.87 110 1 0.732 0.03298 0.670 0.800
## 42.17 101 1 0.725 0.03344 0.662 0.794
## 42.43 97 1 0.718 0.03392 0.654 0.787
## 46.43 80 1 0.709 0.03466 0.644 0.780
## 48.87 75 1 0.699 0.03547 0.633 0.772
## 63.33 25 1 0.671 0.04371 0.591 0.763## Call: survfit(formula = Surv(time, status) ~ trt, data = diabetic)
##
## trt=0
## time n.risk n.event survival
##
## trt=1
## time n.risk n.event survival## Call:
## survdiff(formula = Surv(time, status) ~ trt, data = diabetic)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## trt=0 197 101 71.8 11.9 22.2
## trt=1 197 54 83.2 10.3 22.2
##
## Chisq= 22.2 on 1 degrees of freedom, p= 2e-06Curva de Sobrevivência
ggsurvfit(E_KM_3) + add_censor_mark() +
add_confidence_interval() +
add_quantile(y_value = 0.5, linetype = "dashed", color = "grey30") +
labs(x = "Tempo (dias)", y = "Probabilidade de sobrevivência") +
scale_ggsurvfit(x_scales = list(breaks = seq(0, 90, by = 10))) +
add_risktable(stats_label = c("Em risco", "Eventos")) +
theme(
legend.position = "inside",
legend.position.inside = c(0.05, 0.05), # Canto inferior esquerdo
legend.justification = c(0, 0), # Ancora o canto no ponto escolhido
legend.background = element_rect(fill = "white", colour = "grey70", linewidth = 0.4),
legend.text = element_text(size = 10),
legend.direction = "vertical", # Orientação da Legenda
legend.box = "vertical", # garante a Orientação
legend.margin = margin(4, 6, 4, 6),
axis.title = element_text(size = 11),
axis.title.x = element_text(margin = margin(5,5,15,5)) # Adiciona margem em baixo do eixo x
)
Exemplo Real - Cancro
O conjunto de dados lung resulta de um
estudo clínico conduzido pelo North Central Cancer Treatment
Group (NCCTG, EUA), cujo objetivo foi analisar a
sobrevivência de pacientes com cancro de pulmão
avançado. O problema central consistiu em avaliar o
tempo até ao óbito e identificar fatores clínicos e
demográficos que influenciam o risco de morte. O estudo envolveu
228 pacientes, acompanhados ao longo do tempo, com
presença de censura à direita. Nele encontramos
10 variáveis, incluindo variáveis de sobrevivência,
demográficas e clínicas. A seguir descrevem-se as variáveis, a sua
natureza e respetiva codificação.
Recodificar algumas variáveis (Sexo e Status)
lung =
lung %>%
mutate (
status = recode(status, "1" = 0, "2" = 1),
sex = recode(sex, "1" = "Masculino", "2" = "Feminino"),
)Kaplan-Meier (Simples)
## Call: survfit(formula = Surv(time, status) ~ 1, data = lung)
##
## n events median 0.95LCL 0.95UCL
## [1,] 228 165 310 285 363## Call: survfit(formula = Surv(time, status) ~ 1, data = lung)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 5 228 1 0.9956 0.00438 0.9871 1.000
## 11 227 3 0.9825 0.00869 0.9656 1.000
## 12 224 1 0.9781 0.00970 0.9592 0.997
## 13 223 2 0.9693 0.01142 0.9472 0.992
## 15 221 1 0.9649 0.01219 0.9413 0.989
## 26 220 1 0.9605 0.01290 0.9356 0.986
## 30 219 1 0.9561 0.01356 0.9299 0.983
## 31 218 1 0.9518 0.01419 0.9243 0.980
## 53 217 2 0.9430 0.01536 0.9134 0.974
## 54 215 1 0.9386 0.01590 0.9079 0.970
## 59 214 1 0.9342 0.01642 0.9026 0.967
## 60 213 2 0.9254 0.01740 0.8920 0.960
## 61 211 1 0.9211 0.01786 0.8867 0.957
## 62 210 1 0.9167 0.01830 0.8815 0.953
## 65 209 2 0.9079 0.01915 0.8711 0.946
## 71 207 1 0.9035 0.01955 0.8660 0.943
## 79 206 1 0.8991 0.01995 0.8609 0.939
## 81 205 2 0.8904 0.02069 0.8507 0.932
## 88 203 2 0.8816 0.02140 0.8406 0.925
## 92 201 1 0.8772 0.02174 0.8356 0.921
## 93 199 1 0.8728 0.02207 0.8306 0.917
## 95 198 2 0.8640 0.02271 0.8206 0.910
## 105 196 1 0.8596 0.02302 0.8156 0.906
## 107 194 2 0.8507 0.02362 0.8056 0.898
## 110 192 1 0.8463 0.02391 0.8007 0.894
## 116 191 1 0.8418 0.02419 0.7957 0.891
## 118 190 1 0.8374 0.02446 0.7908 0.887
## 122 189 1 0.8330 0.02473 0.7859 0.883
## 131 188 1 0.8285 0.02500 0.7810 0.879
## 132 187 2 0.8197 0.02550 0.7712 0.871
## 135 185 1 0.8153 0.02575 0.7663 0.867
## 142 184 1 0.8108 0.02598 0.7615 0.863
## 144 183 1 0.8064 0.02622 0.7566 0.859
## 145 182 2 0.7975 0.02667 0.7469 0.852
## 147 180 1 0.7931 0.02688 0.7421 0.848
## 153 179 1 0.7887 0.02710 0.7373 0.844
## 156 178 2 0.7798 0.02751 0.7277 0.836
## 163 176 3 0.7665 0.02809 0.7134 0.824
## 166 173 2 0.7577 0.02845 0.7039 0.816
## 167 171 1 0.7532 0.02863 0.6991 0.811
## 170 170 1 0.7488 0.02880 0.6944 0.807
## 175 167 1 0.7443 0.02898 0.6896 0.803
## 176 165 1 0.7398 0.02915 0.6848 0.799
## 177 164 1 0.7353 0.02932 0.6800 0.795
## 179 162 2 0.7262 0.02965 0.6704 0.787
## 180 160 1 0.7217 0.02981 0.6655 0.783
## 181 159 2 0.7126 0.03012 0.6559 0.774
## 182 157 1 0.7081 0.03027 0.6511 0.770
## 183 156 1 0.7035 0.03041 0.6464 0.766
## 186 154 1 0.6989 0.03056 0.6416 0.761
## 189 152 1 0.6943 0.03070 0.6367 0.757
## 194 149 1 0.6897 0.03085 0.6318 0.753
## 197 147 1 0.6850 0.03099 0.6269 0.749
## 199 145 1 0.6803 0.03113 0.6219 0.744
## 201 144 2 0.6708 0.03141 0.6120 0.735
## 202 142 1 0.6661 0.03154 0.6071 0.731
## 207 139 1 0.6613 0.03168 0.6020 0.726
## 208 138 1 0.6565 0.03181 0.5970 0.722
## 210 137 1 0.6517 0.03194 0.5920 0.717
## 212 135 1 0.6469 0.03206 0.5870 0.713
## 218 134 1 0.6421 0.03218 0.5820 0.708
## 222 132 1 0.6372 0.03231 0.5769 0.704
## 223 130 1 0.6323 0.03243 0.5718 0.699
## 226 126 1 0.6273 0.03256 0.5666 0.694
## 229 125 1 0.6223 0.03268 0.5614 0.690
## 230 124 1 0.6172 0.03280 0.5562 0.685
## 239 121 2 0.6070 0.03304 0.5456 0.675
## 245 117 1 0.6019 0.03316 0.5402 0.670
## 246 116 1 0.5967 0.03328 0.5349 0.666
## 267 112 1 0.5913 0.03341 0.5294 0.661
## 268 111 1 0.5860 0.03353 0.5239 0.656
## 269 110 1 0.5807 0.03364 0.5184 0.651
## 270 108 1 0.5753 0.03376 0.5128 0.645
## 283 104 1 0.5698 0.03388 0.5071 0.640
## 284 103 1 0.5642 0.03400 0.5014 0.635
## 285 101 2 0.5531 0.03424 0.4899 0.624
## 286 99 1 0.5475 0.03434 0.4841 0.619
## 288 98 1 0.5419 0.03444 0.4784 0.614
## 291 97 1 0.5363 0.03454 0.4727 0.608
## 293 94 1 0.5306 0.03464 0.4669 0.603
## 301 91 1 0.5248 0.03475 0.4609 0.597
## 303 89 1 0.5189 0.03485 0.4549 0.592
## 305 87 1 0.5129 0.03496 0.4488 0.586
## 306 86 1 0.5070 0.03506 0.4427 0.581
## 310 85 2 0.4950 0.03523 0.4306 0.569
## 320 82 1 0.4890 0.03532 0.4244 0.563
## 329 81 1 0.4830 0.03539 0.4183 0.558
## 337 79 1 0.4768 0.03547 0.4121 0.552
## 340 78 1 0.4707 0.03554 0.4060 0.546
## 345 77 1 0.4646 0.03560 0.3998 0.540
## 348 76 1 0.4585 0.03565 0.3937 0.534
## 350 75 1 0.4524 0.03569 0.3876 0.528
## 351 74 1 0.4463 0.03573 0.3815 0.522
## 353 73 2 0.4340 0.03578 0.3693 0.510
## 361 70 1 0.4278 0.03581 0.3631 0.504
## 363 69 2 0.4154 0.03583 0.3508 0.492
## 364 67 1 0.4092 0.03582 0.3447 0.486
## 371 65 2 0.3966 0.03581 0.3323 0.473
## 387 60 1 0.3900 0.03582 0.3258 0.467
## 390 59 1 0.3834 0.03582 0.3193 0.460
## 394 58 1 0.3768 0.03580 0.3128 0.454
## 426 55 1 0.3700 0.03580 0.3060 0.447
## 428 54 1 0.3631 0.03579 0.2993 0.440
## 429 53 1 0.3563 0.03576 0.2926 0.434
## 433 52 1 0.3494 0.03573 0.2860 0.427
## 442 51 1 0.3426 0.03568 0.2793 0.420
## 444 50 1 0.3357 0.03561 0.2727 0.413
## 450 48 1 0.3287 0.03555 0.2659 0.406
## 455 47 1 0.3217 0.03548 0.2592 0.399
## 457 46 1 0.3147 0.03539 0.2525 0.392
## 460 44 1 0.3076 0.03530 0.2456 0.385
## 473 43 1 0.3004 0.03520 0.2388 0.378
## 477 42 1 0.2933 0.03508 0.2320 0.371
## 519 39 1 0.2857 0.03498 0.2248 0.363
## 520 38 1 0.2782 0.03485 0.2177 0.356
## 524 37 2 0.2632 0.03455 0.2035 0.340
## 533 34 1 0.2554 0.03439 0.1962 0.333
## 550 32 1 0.2475 0.03423 0.1887 0.325
## 558 30 1 0.2392 0.03407 0.1810 0.316
## 567 28 1 0.2307 0.03391 0.1729 0.308
## 574 27 1 0.2221 0.03371 0.1650 0.299
## 583 26 1 0.2136 0.03348 0.1571 0.290
## 613 24 1 0.2047 0.03325 0.1489 0.281
## 624 23 1 0.1958 0.03297 0.1407 0.272
## 641 22 1 0.1869 0.03265 0.1327 0.263
## 643 21 1 0.1780 0.03229 0.1247 0.254
## 654 20 1 0.1691 0.03188 0.1169 0.245
## 655 19 1 0.1602 0.03142 0.1091 0.235
## 687 18 1 0.1513 0.03090 0.1014 0.226
## 689 17 1 0.1424 0.03034 0.0938 0.216
## 705 16 1 0.1335 0.02972 0.0863 0.207
## 707 15 1 0.1246 0.02904 0.0789 0.197
## 728 14 1 0.1157 0.02830 0.0716 0.187
## 731 13 1 0.1068 0.02749 0.0645 0.177
## 735 12 1 0.0979 0.02660 0.0575 0.167
## 765 10 1 0.0881 0.02568 0.0498 0.156
## 791 9 1 0.0783 0.02462 0.0423 0.145
## 814 7 1 0.0671 0.02351 0.0338 0.133
## 883 4 1 0.0503 0.02285 0.0207 0.123plot(E_KM_4, conf.int = F, mark.time = T, xlab = "Dias", ylab = "Sobrevivências",
main = "Estimador ede Kaplan-Meier")
survfit(Surv(time, status)~1, data = lung) %>%
ggsurvfit() +
labs(
x = "Dias",
y = "probabilidade de Sobrevivência"
)
Adicionando o intevalo de confiança
survfit(Surv(time, status)~1, data = lung) %>%
ggsurvfit() +
labs(
x = "Dias",
y = "probabilidade de Sobrevivência"
) +
add_confidence_interval()
Adicionando tabela com o número de observações em risco
survfit(Surv(time, status)~1, data = lung) %>%
ggsurvfit() +
labs(
x = "Dias",
y = "probabilidade de Sobrevivência"
) +
add_confidence_interval() +
add_risktable()
Estimando a probabilidade de sobreviver até um certo tempo
## Call: survfit(formula = Surv(time, status) ~ 1, data = lung)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 200 144 72 0.68 0.0311 0.622 0.744Adicionando tabela de estimativas de probabilidades até um certo tempo
survfit(Surv(time, status)~1, data = lung) %>%
tbl_survfit( # do pacote - gtsummary
times = 200,
label_header = "** Sobrevivência até 1 Ano - I.C 95% **"
)| Characteristic | ** Sobrevivência até 1 Ano - I.C 95% ** |
|---|---|
| Overall | 68% (62%, 74%) |
Adicionando o tempo mediado de sobrevivência
survfit(Surv(time, status)~1, data = lung) %>%
ggsurvfit() +
labs(
x = "Dias",
y = "probabilidade de Sobrevivência"
) +
add_confidence_interval() +
add_risktable() +
add_quantile()
O que aconteceria com o tempo mediano se excluíssimos as censuras
lung2 =
lung %>%
filter (status == 1) %>%
summarise( median_surv = median(time))
lung2 # Visualizando a alteração## median_surv
## 1 226Isso faz com que subestimamos a estimativa do tempo mediano de sobrevivência.
Kaplan-Meier (Comparação)
## Call: survfit(formula = Surv(time, status) ~ sex, data = lung)
##
## n events median 0.95LCL 0.95UCL
## sex=Feminino 90 53 426 348 550
## sex=Masculino 138 112 270 212 310## Call: survfit(formula = Surv(time, status) ~ sex, data = lung)
##
## sex=Feminino
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 5 90 1 0.9889 0.0110 0.9675 1.000
## 60 89 1 0.9778 0.0155 0.9478 1.000
## 61 88 1 0.9667 0.0189 0.9303 1.000
## 62 87 1 0.9556 0.0217 0.9139 0.999
## 79 86 1 0.9444 0.0241 0.8983 0.993
## 81 85 1 0.9333 0.0263 0.8832 0.986
## 95 83 1 0.9221 0.0283 0.8683 0.979
## 107 81 1 0.9107 0.0301 0.8535 0.972
## 122 80 1 0.8993 0.0318 0.8390 0.964
## 145 79 2 0.8766 0.0349 0.8108 0.948
## 153 77 1 0.8652 0.0362 0.7970 0.939
## 166 76 1 0.8538 0.0375 0.7834 0.931
## 167 75 1 0.8424 0.0387 0.7699 0.922
## 182 71 1 0.8305 0.0399 0.7559 0.913
## 186 70 1 0.8187 0.0411 0.7420 0.903
## 194 68 1 0.8066 0.0422 0.7280 0.894
## 199 67 1 0.7946 0.0432 0.7142 0.884
## 201 66 2 0.7705 0.0452 0.6869 0.864
## 208 62 1 0.7581 0.0461 0.6729 0.854
## 226 59 1 0.7452 0.0471 0.6584 0.843
## 239 57 1 0.7322 0.0480 0.6438 0.833
## 245 54 1 0.7186 0.0490 0.6287 0.821
## 268 51 1 0.7045 0.0501 0.6129 0.810
## 285 47 1 0.6895 0.0512 0.5962 0.798
## 293 45 1 0.6742 0.0523 0.5791 0.785
## 305 43 1 0.6585 0.0534 0.5618 0.772
## 310 42 1 0.6428 0.0544 0.5447 0.759
## 340 39 1 0.6264 0.0554 0.5267 0.745
## 345 38 1 0.6099 0.0563 0.5089 0.731
## 348 37 1 0.5934 0.0572 0.4913 0.717
## 350 36 1 0.5769 0.0579 0.4739 0.702
## 351 35 1 0.5604 0.0586 0.4566 0.688
## 361 33 1 0.5434 0.0592 0.4390 0.673
## 363 32 1 0.5265 0.0597 0.4215 0.658
## 371 30 1 0.5089 0.0603 0.4035 0.642
## 426 26 1 0.4893 0.0610 0.3832 0.625
## 433 25 1 0.4698 0.0617 0.3632 0.608
## 444 24 1 0.4502 0.0621 0.3435 0.590
## 450 23 1 0.4306 0.0624 0.3241 0.572
## 473 22 1 0.4110 0.0626 0.3050 0.554
## 520 19 1 0.3894 0.0629 0.2837 0.534
## 524 18 1 0.3678 0.0630 0.2628 0.515
## 550 15 1 0.3433 0.0634 0.2390 0.493
## 641 11 1 0.3121 0.0649 0.2076 0.469
## 654 10 1 0.2808 0.0655 0.1778 0.443
## 687 9 1 0.2496 0.0652 0.1496 0.417
## 705 8 1 0.2184 0.0641 0.1229 0.388
## 728 7 1 0.1872 0.0621 0.0978 0.359
## 731 6 1 0.1560 0.0590 0.0743 0.328
## 735 5 1 0.1248 0.0549 0.0527 0.295
## 765 3 1 0.0832 0.0499 0.0257 0.270
##
## sex=Masculino
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 11 138 3 0.9783 0.0124 0.9542 1.000
## 12 135 1 0.9710 0.0143 0.9434 0.999
## 13 134 2 0.9565 0.0174 0.9231 0.991
## 15 132 1 0.9493 0.0187 0.9134 0.987
## 26 131 1 0.9420 0.0199 0.9038 0.982
## 30 130 1 0.9348 0.0210 0.8945 0.977
## 31 129 1 0.9275 0.0221 0.8853 0.972
## 53 128 2 0.9130 0.0240 0.8672 0.961
## 54 126 1 0.9058 0.0249 0.8583 0.956
## 59 125 1 0.8986 0.0257 0.8496 0.950
## 60 124 1 0.8913 0.0265 0.8409 0.945
## 65 123 2 0.8768 0.0280 0.8237 0.933
## 71 121 1 0.8696 0.0287 0.8152 0.928
## 81 120 1 0.8623 0.0293 0.8067 0.922
## 88 119 2 0.8478 0.0306 0.7900 0.910
## 92 117 1 0.8406 0.0312 0.7817 0.904
## 93 116 1 0.8333 0.0317 0.7734 0.898
## 95 115 1 0.8261 0.0323 0.7652 0.892
## 105 114 1 0.8188 0.0328 0.7570 0.886
## 107 113 1 0.8116 0.0333 0.7489 0.880
## 110 112 1 0.8043 0.0338 0.7408 0.873
## 116 111 1 0.7971 0.0342 0.7328 0.867
## 118 110 1 0.7899 0.0347 0.7247 0.861
## 131 109 1 0.7826 0.0351 0.7167 0.855
## 132 108 2 0.7681 0.0359 0.7008 0.842
## 135 106 1 0.7609 0.0363 0.6929 0.835
## 142 105 1 0.7536 0.0367 0.6851 0.829
## 144 104 1 0.7464 0.0370 0.6772 0.823
## 147 103 1 0.7391 0.0374 0.6694 0.816
## 156 102 2 0.7246 0.0380 0.6538 0.803
## 163 100 3 0.7029 0.0389 0.6306 0.783
## 166 97 1 0.6957 0.0392 0.6230 0.777
## 170 96 1 0.6884 0.0394 0.6153 0.770
## 175 94 1 0.6811 0.0397 0.6076 0.763
## 176 93 1 0.6738 0.0399 0.5999 0.757
## 177 92 1 0.6664 0.0402 0.5922 0.750
## 179 91 2 0.6518 0.0406 0.5769 0.736
## 180 89 1 0.6445 0.0408 0.5693 0.730
## 181 88 2 0.6298 0.0412 0.5541 0.716
## 183 86 1 0.6225 0.0413 0.5466 0.709
## 189 83 1 0.6150 0.0415 0.5388 0.702
## 197 80 1 0.6073 0.0417 0.5309 0.695
## 202 78 1 0.5995 0.0419 0.5228 0.687
## 207 77 1 0.5917 0.0420 0.5148 0.680
## 210 76 1 0.5839 0.0422 0.5068 0.673
## 212 75 1 0.5762 0.0424 0.4988 0.665
## 218 74 1 0.5684 0.0425 0.4909 0.658
## 222 72 1 0.5605 0.0426 0.4829 0.651
## 223 70 1 0.5525 0.0428 0.4747 0.643
## 229 67 1 0.5442 0.0429 0.4663 0.635
## 230 66 1 0.5360 0.0431 0.4579 0.627
## 239 64 1 0.5276 0.0432 0.4494 0.619
## 246 63 1 0.5192 0.0433 0.4409 0.611
## 267 61 1 0.5107 0.0434 0.4323 0.603
## 269 60 1 0.5022 0.0435 0.4238 0.595
## 270 59 1 0.4937 0.0436 0.4152 0.587
## 283 57 1 0.4850 0.0437 0.4065 0.579
## 284 56 1 0.4764 0.0438 0.3979 0.570
## 285 54 1 0.4676 0.0438 0.3891 0.562
## 286 53 1 0.4587 0.0439 0.3803 0.553
## 288 52 1 0.4499 0.0439 0.3716 0.545
## 291 51 1 0.4411 0.0439 0.3629 0.536
## 301 48 1 0.4319 0.0440 0.3538 0.527
## 303 46 1 0.4225 0.0440 0.3445 0.518
## 306 44 1 0.4129 0.0440 0.3350 0.509
## 310 43 1 0.4033 0.0441 0.3256 0.500
## 320 42 1 0.3937 0.0440 0.3162 0.490
## 329 41 1 0.3841 0.0440 0.3069 0.481
## 337 40 1 0.3745 0.0439 0.2976 0.471
## 353 39 2 0.3553 0.0437 0.2791 0.452
## 363 37 1 0.3457 0.0436 0.2700 0.443
## 364 36 1 0.3361 0.0434 0.2609 0.433
## 371 35 1 0.3265 0.0432 0.2519 0.423
## 387 34 1 0.3169 0.0430 0.2429 0.413
## 390 33 1 0.3073 0.0428 0.2339 0.404
## 394 32 1 0.2977 0.0425 0.2250 0.394
## 428 29 1 0.2874 0.0423 0.2155 0.383
## 429 28 1 0.2771 0.0420 0.2060 0.373
## 442 27 1 0.2669 0.0417 0.1965 0.362
## 455 25 1 0.2562 0.0413 0.1868 0.351
## 457 24 1 0.2455 0.0410 0.1770 0.341
## 460 22 1 0.2344 0.0406 0.1669 0.329
## 477 21 1 0.2232 0.0402 0.1569 0.318
## 519 20 1 0.2121 0.0397 0.1469 0.306
## 524 19 1 0.2009 0.0391 0.1371 0.294
## 533 18 1 0.1897 0.0385 0.1275 0.282
## 558 17 1 0.1786 0.0378 0.1179 0.270
## 567 16 1 0.1674 0.0371 0.1085 0.258
## 574 15 1 0.1562 0.0362 0.0992 0.246
## 583 14 1 0.1451 0.0353 0.0900 0.234
## 613 13 1 0.1339 0.0343 0.0810 0.221
## 624 12 1 0.1228 0.0332 0.0722 0.209
## 643 11 1 0.1116 0.0320 0.0636 0.196
## 655 10 1 0.1004 0.0307 0.0552 0.183
## 689 9 1 0.0893 0.0293 0.0470 0.170
## 707 8 1 0.0781 0.0276 0.0390 0.156
## 791 7 1 0.0670 0.0259 0.0314 0.143
## 814 5 1 0.0536 0.0239 0.0223 0.128
## 883 3 1 0.0357 0.0216 0.0109 0.117Adicionando tabela com o número de observações em risco
survfit(Surv(time, status)~sex, data = lung) %>%
ggsurvfit() +
labs(
x = "Dias",
y = "probabilidade de Sobrevivência"
) +
add_confidence_interval() +
add_risktable()
Testes de Comparação
Realizando os Testes de Comparações (Exemplo de Diabete)
## Call:
## survdiff(formula = Surv(time, status) ~ trt, data = diabetic)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## trt=0 197 101 71.8 11.9 22.2
## trt=1 197 54 83.2 10.3 22.2
##
## Chisq= 22.2 on 1 degrees of freedom, p= 2e-06## Call:
## survdiff(formula = Surv(time, status) ~ trt, data = diabetic)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## trt=0 197 101 71.8 11.9 22.2
## trt=1 197 54 83.2 10.3 22.2
##
## Chisq= 22.2 on 1 degrees of freedom, p= 2e-06survdiff(Surv(time, status) ~ trt, data = diabetic, rho = 1) # Wilcoxon (Breslow) ← Peto-Prent. Aproximado## Call:
## survdiff(formula = Surv(time, status) ~ trt, data = diabetic,
## rho = 1)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## trt=0 197 80.3 57.6 8.95 20.7
## trt=1 197 43.1 65.8 7.84 20.7
##
## Chisq= 20.7 on 1 degrees of freedom, p= 6e-06## Call:
## survdiff(formula = Surv(time, status) ~ trt, data = diabetic,
## rho = 0.5)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## trt=0 197 89.7 64.1 10.28 21.5
## trt=1 197 48.1 73.7 8.93 21.5
##
## Chisq= 21.5 on 1 degrees of freedom, p= 3e-06## Call:
## survdiff(formula = Surv(time, status) ~ trt, data = diabetic,
## rho = c(0, 1))
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## trt=0 197 101 71.8 11.9 22.2
## trt=1 197 54 83.2 10.3 22.2
##
## Chisq= 22.2 on 1 degrees of freedom, p= 2e-06Realizando os Testes de Comparações (Exemplo de Cancro)
## Call:
## survdiff(formula = Surv(time, status) ~ sex, data = lung)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## sex=Feminino 90 53 73.4 5.68 10.3
## sex=Masculino 138 112 91.6 4.55 10.3
##
## Chisq= 10.3 on 1 degrees of freedom, p= 0.001survdiff(Surv(time, status) ~ sex, data = lung, rho = 1) # Wilcoxon (Breslow) ← Peto-Prent. Aproximado ## Call:
## survdiff(formula = Surv(time, status) ~ sex, data = lung, rho = 1)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## sex=Feminino 90 28.7 43.5 5.04 12.7
## sex=Masculino 138 70.4 55.6 3.95 12.7
##
## Chisq= 12.7 on 1 degrees of freedom, p= 4e-04## Call:
## survdiff(formula = Surv(time, status) ~ sex, data = lung, rho = 0.5)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## sex=Feminino 90 37.7 54.9 5.41 12.3
## sex=Masculino 138 86.4 69.1 4.30 12.3
##
## Chisq= 12.3 on 1 degrees of freedom, p= 5e-04## Call:
## survdiff(formula = Surv(time, status) ~ sex, data = lung, rho = c(0,
## 1))
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## sex=Feminino 90 53 73.4 5.68 10.3
## sex=Masculino 138 112 91.6 4.55 10.3
##
## Chisq= 10.3 on 1 degrees of freedom, p= 0.001