analisis data survival
TRANSCRIPT
LAPORAN UTS
PRAKTIKUM ANALISIS DATA SURVIVAL
Dosen Pengampu :
Rianti Siswi Utami, S.Si.
Asisten Praktikum :
Muhamad Bayu
Djati Sampoerna
Disusun Oleh :
Adhitya Akbar
10/297716/PA/13065
LABORATARIUM KOMPUTASI MATEMATIKA DAN STATISTIKA
FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM
UNIVERSITAS GADJAH MADA2014
BAB I
PERMASALAHAN
1. Buatlah plot fungsi survival, densitas dan hazard untuk distribusi Gamma dan distribusi
Log-normal.
2. Perhatikan kembali data lama kambuh pasien leukemia pada Modul 1. Jika diasumsikan
lama kambuh berdistribusi eksponensial dengan fungsi hazard untuk AG positive adalah
0,016 dan untuk AG negative adalah 0,056, buatlah sket grafik fungsi survival untuk AG
positive maupun AG negative pada satu gambar dalam skala yang sama kemudian
interpretasikan hasilnya.
3. Pada file col.xlsx diketahui data lama hidup pasien yang menderita colon cancer, dimana:
Time : lama hidup pasien colon cancer (hari)
Status : indikator mendapatkan event (1 = meninggal, 0 = tersensor)
Sex : jenis kelamin (1 = laki - laki, 0 = perempuan)
a. Hitunglah estimasi fungsi survival untuk pasien laki – laki dan pasien perempuan
menggunakan estimasi Kaplan-Meier!
b. Berdasarkan (a), bandingkan antara pasien laki – laki dan perempuan, manakah yang
dapat bertahan hidup lebih lama? (hint: lakukan secara deskriptif dengan melihat nilai
– nilai S(t) maupun dengan grafik!)
4. Menggunakan data pada nomer 3 untuk pasien perempuan, hitunglah estimasi fungsi
hazard dan survival menggunakan estimator Nelson Aalen, kemudian bandingkan dengan
hasil pada nomor 3 (dengan menggunakan estimasi Kaplan Meier). Apakah kedua
estimasi ini menghasilkan nilai – nilai yang berbeda jauh? Estimasi apakah yang
memberikan kesimpulan bahwa pasien dapat bertahan hidup lebih lama?
BAB II
PERMBAHASAN
1.
o Distribusi Gamma (dengan α = 1, 2, 3 dan β = 10,2)
Fungsi densitas
0 5 10 15 20 25 30 350
0.020.040.060.08
0.10.120.140.160.18
Fungsi Densitas
α = 1α = 2α = 3
t
f(t)
Fungsi Survival
0 5 10 15 20 25 30 350
0.2
0.4
0.6
0.8
1
1.2
Fungsi Survival
α = 1α = 2α = 3
t
S(t)
Fungsi Hazard
0 5 10 15 20 25 30 350
0.05
0.1
0.15
0.2
0.25
Fungsi Hazard
α = 1α = 2α = 3
t
H(t)
o Distribusi Lognormal (dengan μ =1, 2, 3 dan σ = 0,5)
Fungsi Densitas
0 5 10 15 20 25 30 350
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Fungsi Densitas
μ = 1μ = 2μ = 3
t
f(t)
Fungsi Survival
0 5 10 15 20 25 30 350
0.2
0.4
0.6
0.8
1
1.2
Fungsi Survival
μ = 1μ = 2μ = 3
t
S(t)
Fungsi Hazard
0 5 10 15 20 25 30 350
0.10.20.30.40.50.60.70.8
Fungsi Hazard
μ = 1μ = 2μ = 3
t
H(t)
2.
3.
a. Estimasi fungsi survival untuk pasien laki-laki adalah :
time Y d S(t) se[S(t)] H(t)
28 281 10,99644
10,00354
60,00356
5
43 280 10,99288
30,00500
60,00714
3
45 278 10,98931
10,00613
40,01074
662 277 1 0,98574 0,00707 0,01436
3 3
80 276 10,98216
80,00789
50,01799
3
105 275 10,97859
60,00863
30,02163
6
119 274 10,97502
50,00930
90,02529
2
121 273 10,97145
30,00993
40,02896
2
127 272 10,96788
20,01051
80,03264
5
133 271 1 0,964310,01106
60,03634
2
136 270 10,96073
90,01158
50,04005
3
147 269 10,95716
70,01207
80,04377
7
154 268 10,95359
60,01254
80,04751
5
171 267 10,95002
40,01299
70,05126
8
173 266 10,94645
30,01342
80,05503
4
174 265 10,94288
10,01384
30,05881
5
176 264 1 0,939310,01424
2 0,06261
179 263 10,93573
80,01462
70,06641
9
183 262 10,93216
70,01499
90,07024
4
185 261 10,92859
50,01535
90,07408
2
191 258 30,91779
80,01638
20,08577
8
196 257 10,91422
60,01670
20,08967
7
206 256 10,91065
50,01701
30,09359
1
216 255 10,90708
40,01731
5 0,09752
219 254 10,90351
3 0,017610,10146
5
222 253 10,89994
20,01789
70,10542
5
228 252 1 0,896370,01817
70,10940
2
229 251 10,89279
90,01845
10,11339
4230 250 1 0,88922 0,01871 0,11740
8 8 2
238 249 10,88565
70,01897
90,12142
6
245 248 10,88208
60,01923
40,12546
6
246 247 10,87851
40,01948
30,12952
3
250 246 10,87494
30,01972
70,13359
6
256 245 10,87137
20,01996
60,13768
6
258 244 10,86780
10,02019
90,14179
3
262 243 1 0,864230,02042
80,14591
7
263 242 10,86065
80,02065
20,15005
8
279 241 10,85708
70,02087
10,15421
6
291 240 10,85351
60,02108
60,15839
1
303 239 10,84994
50,02129
70,16258
4
304 238 10,84637
40,02150
30,16679
4
308 237 10,84280
20,02170
60,17102
3
311 236 10,83923
10,02190
40,17526
9
324 235 1 0,835660,02209
90,17953
3
330 234 10,83208
9 0,022290,18381
6
341 233 10,82851
80,02247
70,18811
7
343 232 10,82494
6 0,022660,19243
7
348 231 10,82137
50,02284
10,19677
5
349 229 20,81420
20,02319
20,20554
7
352 228 10,81063
10,02336
20,20994
3
356 226 20,80345
70,02369
40,21883
2
360 225 10,79988
60,02385
50,22328
6
362 224 10,79631
50,02401
3 0,22776380 223 1 0,79274 0,02416 0,23225
4 8 5
381 222 10,78917
3 0,024320,23676
9
389 221 10,78560
20,02446
90,24130
5
406 220 10,78203
10,02461
6 0,24586
413 219 1 0,778460,02475
90,25043
7
420 218 1 0,774890,02490
10,25503
5
421 217 0 0,774890,02495
80,25503
5
422 216 10,77130
20,02509
70,25967
5
430 215 10,76771
50,02523
40,26433
7
435 214 10,76412
70,02536
90,26902
1
437 213 1 0,760540,02550
10,27372
7
438 212 10,75695
2 0,025630,27845
5
443 211 10,75336
50,02575
70,28320
6
448 210 10,74977
70,02588
10,28797
9
454 209 1 0,746190,02600
30,29277
5
462 208 10,74260
20,02612
30,29759
4
472 207 10,73901
50,02624
10,30243
7
475 206 10,73542
80,02635
60,30730
3
485 205 00,73542
8 0,026420,30730
3
489 204 10,73182
30,02653
40,31221
7
497 203 10,72821
80,02664
50,31715
6
498 202 10,72461
20,02675
50,32211
8
499 201 10,72100
70,02686
20,32710
6
510 200 10,71740
20,02696
70,33211
8
522 199 10,71379
7 0,027070,33715
6523 198 1 0,71019 0,02717 0,34221
2 1 9
527 197 10,70658
70,02726
90,34730
9
534 196 10,70298
20,02736
60,35242
4
543 195 10,69937
7 0,027460,35756
5
548 194 10,69577
20,02755
30,36273
3
553 193 10,69216
70,02764
30,36792
8
569 192 10,68856
20,02773
2 0,37315
570 191 10,68495
70,02781
80,37839
9
580 190 10,68135
20,02790
30,38367
6
582 189 10,67774
70,02798
60,38898
1
602 188 10,67414
20,02806
60,39431
5
622 187 10,67053
70,02814
50,39967
7
638 186 10,66693
20,02822
20,40506
7
641 185 10,66332
70,02829
70,41048
7
647 184 10,65972
20,02837
10,41593
7
653 183 10,65611
70,02844
20,42141
7
659 182 10,65251
20,02851
20,42692
6
668 181 10,64890
70,02857
90,43246
6
685 180 10,64530
20,02864
50,43803
7
708 179 10,64169
7 0,02871 0,44364
709 178 10,63809
20,02877
20,44927
3
712 177 10,63448
70,02883
30,45493
9
717 176 10,63088
20,02889
20,46063
7
721 175 10,62727
60,02894
90,46636
8
736 174 10,62367
10,02900
40,47213
2739 173 1 0,62006 0,02905 0,47792
6 8 9
755 172 10,61646
1 0,02911 0,48376
761 171 10,61285
60,02916
10,48962
5
772 170 10,60925
10,02920
90,49552
4
774 169 10,60564
60,02925
60,50145
9
775 168 10,60204
10,02930
20,50742
9
795 167 10,59843
60,02934
50,51343
5
797 165 20,59118
20,02942
70,52563
1
803 164 10,58757
80,02946
60,53174
7
833 163 10,58397
30,02950
30,53790
1
835 162 10,58036
80,02953
80,54409
3
855 161 10,57676
30,02957
20,55032
3
883 160 10,57315
90,02960
40,55659
3
885 159 10,56955
40,02963
40,56290
2
900 158 10,56594
90,02966
30,56925
1
905 157 10,56234
40,02969
10,57564
1
912 156 10,55873
90,02971
60,58207
2
918 155 10,55513
5 0,029740,58854
5
924 154 1 0,551530,02976
30,59505
9
931 153 10,54792
50,02978
40,60161
7
938 152 00,54792
50,02988
20,60161
7
949 151 10,54429
70,02990
10,60826
1
961 150 10,54066
80,02991
9 0,61495
968 149 10,53703
90,02993
50,62168
4
977 148 10,53341
1 0,029950,62846
4993 147 1 0,52978 0,02996 0,63529
2 3
997 146 10,52615
30,02997
50,64216
3
1013 145 10,52252
50,02998
50,64908
3
1025 144 10,51889
60,02999
30,65605
2
1026 143 10,51526
7 0,030,66306
9
1042 142 10,51163
90,03000
50,67013
7
1105 141 1 0,508010,03000
80,67725
4
1112 140 10,50438
1 0,030010,68442
2
1122 139 10,50075
30,03001
10,69164
3
1130 138 10,49712
40,03000
90,69891
6
1134 137 10,49349
50,03000
60,70624
2
1135 136 10,48986
70,03000
20,71362
2
1166 135 10,48623
80,02999
60,72105
7
1178 134 1 0,482610,02998
80,72854
7
1193 133 10,47898
10,02997
90,73609
5
1215 132 10,47535
20,02996
80,74369
9
1216 131 10,47172
40,02995
60,75136
2
1279 129 10,46806
70,03005
70,75914
4
1304 128 1 0,464410,03004
10,76698
7
1323 127 10,46075
30,03002
30,77489
2
1474 126 00,46075
30,03014
20,77489
2
1475 125 10,45706
70,03012
30,78292
5
1521 124 10,45338
10,03010
20,79102
2
1530 123 10,44969
50,03007
90,79918
5
1548 121 10,44597
90,03017
80,80748
41561 120 1 0,44226 0,03015 0,81585
2 1 2
1709 119 10,43854
60,03012
30,82429
1
1749 118 10,43482
90,03009
30,83280
2
1759 117 10,43111
30,03006
20,84138
6
1772 116 10,42739
60,03002
80,85004
4
1788 115 1 0,423680,02999
30,85877
7
1798 114 10,41996
30,02995
60,86758
8
1839 113 10,41624
70,02991
80,87647
7
1876 112 1 0,412530,02987
70,88544
6
1879 111 10,40881
40,02983
50,89449
5
1895 110 10,40509
70,02979
10,90362
8
1976 109 10,40138
10,02974
50,91284
4
2012 108 10,39766
40,02969
80,92214
7
2018 107 10,39394
80,02964
80,93153
7
2074 106 10,39023
10,02959
70,94101
5
2085 105 10,38651
50,02954
40,95058
5
2117 104 00,38651
50,02968
60,95058
5
2184 103 00,38651
5 0,029830,95058
5
2204 102 00,38651
50,02997
60,95058
5
2231 101 10,38268
80,02991
80,96053
5
2263 100 00,38268
80,03006
70,96053
5
2267 99 00,38268
80,03021
90,96053
5
2284 98 10,37878
30,03015
80,97079
2
2288 97 10,37487
80,03009
40,98115
4
2304 96 00,37487
80,03025
10,98115
42313 95 0 0,37487 0,03041 0,98115
8 4
2318 94 00,37487
80,03057
10,98115
4
2326 93 00,37487
80,03073
50,98115
4
2343 92 00,37487
80,03090
10,98115
4
2350 91 00,37487
80,03107
10,98115
4
2351 90 10,37071
30,03099
90,99232
8
2352 88 00,37071
30,03134
90,99232
8
2356 87 00,37071
30,03152
80,99232
8
2386 86 00,37071
30,03171
10,99232
8
2423 84 00,37071
30,03208
70,99232
8
2435 83 00,37071
30,03227
90,99232
8
2444 82 00,37071
30,03247
50,99232
8
2449 81 00,37071
30,03267
50,99232
8
2456 80 00,37071
30,03287
90,99232
8
2458 79 00,37071
30,03308
60,99232
8
2472 78 00,37071
30,03329
80,99232
8
2482 77 10,36589
80,03320
4 1,0054
2484 76 00,36589
80,03342
2 1,0054
2487 75 00,36589
80,03364
4 1,0054
2488 74 00,36589
80,03387
1 1,0054
2490 73 00,36589
80,03410
2 1,0054
2495 72 00,36589
80,03433
8 1,0054
2497 71 00,36589
80,03457
9 1,0054
2509 70 00,36589
80,03482
5 1,0054
2517 68 00,36589
80,03533
3 1,00542520 67 0 0,36589 0,03559 1,0054
8 6
2525 66 00,36589
80,03586
5 1,0054
2527 64 10,36018
10,03601
31,02114
8
2538 63 00,36018
10,03629
81,02114
8
2542 62 10,35437
20,03616
21,03740
9
2547 61 00,35437
20,03645
71,03740
9
2558 59 00,35437
2 0,037071,03740
9
2568 58 00,35437
20,03738
81,03740
9
2577 57 00,35437
20,03771
51,03740
9
2592 56 00,35437
2 0,038051,03740
9
2593 55 10,34792
90,03788
41,05575
8
2600 54 00,34792
90,03823
31,05575
8
2618 52 00,34792
90,03896
21,05575
8
2628 51 00,34792
90,03934
21,05575
8
2648 50 00,34792
90,03973
31,05575
8
2656 49 00,34792
90,04013
71,05575
8
2672 48 00,34792
90,04055
21,05575
8
2679 47 00,34792
90,04098
21,05575
8
2683 46 10,34036
50,04075
81,07773
7
2695 45 10,33280
10,04052
3 1,10021
2699 44 00,33280
10,04098
1 1,10021
2716 43 00,33280
10,04145
5 1,10021
2718 42 10,32487
70,04118
91,12430
7
2720 41 00,32487
70,04168
91,12430
7
2723 39 00,32487
70,04274
41,12430
72725 38 0 0,32487 0,04330 1,12430
7 3 7
2726 36 00,32487
7 0,044491,12430
7
2730 35 00,32487
70,04512
11,12430
7
2732 34 00,32487
7 0,045781,12430
7
2737 33 00,32487
70,04646
81,12430
7
2743 32 00,32487
70,04718
81,12430
7
2754 30 00,32487
70,04873
61,12430
7
2761 28 00,32487
70,05044
71,12430
7
2764 27 00,32487
70,05137
21,12430
7
2765 24 00,32487
70,05448
91,12430
7
2772 23 00,32487
7 0,055661,12430
7
2781 22 00,32487
70,05691
11,12430
7
2789 21 00,32487
70,05825
11,12430
7
2800 20 00,32487
70,05968
91,12430
7
2862 19 00,32487
7 0,061241,12430
7
2899 18 00,32487
70,06291
81,12430
7
2901 17 00,32487
70,06474
21,12430
7
2905 16 00,32487
70,06673
51,12430
7
2910 15 10,30321
90,06535
2 1,1933
2915 14 00,30321
90,06764
6 1,1933
2916 13 00,30321
90,07019
9 1,1933
2918 12 00,30321
90,07306
6 1,1933
2941 11 00,30321
90,07631
5 1,1933
2958 10 00,30321
9 0,08004 1,1933
2969 9 00,30321
90,08436
9 1,19332985 8 0 0,30321 0,08948 1,1933
9 7
3085 7 00,30321
90,09566
6 1,1933
3087 6 00,30321
90,10333
1 1,1933
3173 5 00,30321
90,11319
3 1,1933
3185 4 00,30321
90,12655
4 1,1933
3192 3 00,30321
90,14613
2 1,1933
3214 2 00,30321
90,17897
4 1,1933
3309 1 00,30321
90,25310
7 1,1933
Estimasi fungsi survival untuk pasien perempuan adalah :
time Y d S(t) se[S(t)] H(t)23 286 0 1 0 0
36 285 10,99649122
80,00349
60,00351
5
68 284 10,99298245
60,00493
60,00704
2
72 283 10,98947368
40,00603
50,01058
2
77 282 10,98596491
20,00695
60,01413
5
79 281 1 0,982456140,00776
3 0,0177
80 280 10,97894736
80,00848
90,02127
7
86 279 10,97543859
60,00915
20,02486
8
98 277 20,96839571
90,01034
40,03211
4
101 276 10,96488703
80,01088
30,03574
4
113 275 10,96137835
80,01139
30,03938
7
118 274 10,95786967
80,01187
80,04304
4
121 273 10,95436099
8 0,012340,04671
3
127 272 10,95085231
80,01278
10,05039
7
139 271 10,94734363
80,01320
50,05409
3143 270 1 0,94383495 0,01361 0,05780
8 3 4
146 269 10,94032627
70,01400
50,06152
8
157 267 20,93328263
50,01475
30,06904
7
165 266 10,92977405
40,01510
70,07281
4
173 265 10,92626547
20,01545
10,07659
4
174 264 10,92275689
10,01578
40,08038
9
176 263 1 0,919248310,01610
80,08419
9
183 262 10,91573972
80,01642
20,08802
3
185 260 20,90869557
60,01702
90,09574
5
186 259 10,90518709
90,01731
90,09961
4
189 258 10,90167862
20,01760
20,10349
7
204 257 10,89817014
50,01787
80,10739
6
215 256 10,89466166
80,01814
8 0,11131
218 254 20,88761708
80,01867
10,11921
5
221 253 1 0,884108720,01892
20,12317
5
226 252 10,88060035
20,01916
80,12715
1
229 251 10,87709198
40,01940
90,13114
3
230 250 10,87358361
60,01964
40,13515
1
232 249 10,87007524
80,01987
50,13917
6
245 248 1 0,866566880,02010
10,14321
6
260 247 10,86305851
20,02032
20,14727
3
261 246 10,85955014
40,02053
80,15134
6
264 245 10,85604177
60,02075
10,15543
6
279 244 10,85253340
90,02095
90,15954
3
283 243 10,84902504
10,02116
30,16366
7286 242 1 0,84551667 0,02136 0,16780
3 3 7
289 241 10,84200830
50,02155
90,17196
5
290 239 2 0,834962210,02194
10,18036
9
293 238 10,83145396
60,02212
60,18457
9
315 236 20,82440774
50,02248
7 0,19309
322 235 10,82089962
70,02266
20,19735
4
325 234 10,81739150
90,02283
40,20163
7
326 233 00,81739150
90,02288
30,20163
7
335 232 1 0,813868270,02305
30,20595
7
348 231 10,81034503
10,02321
90,21029
5
363 230 10,80682179
20,02338
30,21465
2
365 229 10,80329855
20,02354
30,21902
9
370 228 10,79977531
30,02370
10,22342
4
382 227 10,79625207
40,02385
50,22783
9
384 225 20,78917427
80,02415
70,23676
8
392 224 10,78565117
80,02430
30,24124
2
400 223 10,78212807
90,02444
70,24573
7
402 222 10,77860497
90,02458
80,25025
1
411 221 1 0,775081880,02472
70,25478
7
431 220 1 0,771558780,02486
30,25934
2
433 219 10,76803568
10,02499
60,26391
9
437 218 10,76451258
10,02512
70,26851
7
440 217 10,76098948
20,02525
60,27313
6
443 216 10,75746638
20,02538
20,27777
6
459 215 10,75394328
30,02550
60,28243
8461 214 1 0,75042018 0,02562 0,28712
4 7 2
464 213 10,74689708
40,02574
70,29182
8
474 212 10,74337398
50,02586
40,29655
6
480 211 10,73985088
50,02597
90,30130
7
484 210 10,73632778
60,02609
1 0,30608
490 209 10,73280468
60,02620
20,31087
6
496 208 10,72928158
7 0,026310,31569
5
498 207 10,72575848
70,02641
60,32053
8
505 206 10,72223538
80,02652
10,32540
4
526 205 10,71871228
80,02662
30,33029
4
528 204 10,71518918
90,02672
30,33520
8
542 203 1 0,711666090,02682
10,34014
6
547 202 1 0,708142990,02691
70,34510
9
559 201 10,70461989
10,02701
10,35009
7
561 200 10,70109679
10,02710
40,35510
9
578 199 10,69757369
20,02719
40,36014
7
580 198 10,69405059
20,02728
2 0,36521
581 197 10,69052749
30,02736
90,37029
9
593 195 2 0,683445160,02753
70,38060
9
595 194 10,67992224
60,02761
80,38577
7
599 193 00,67992224
60,02768
90,38577
7
604 192 10,67638098
50,02776
90,39099
9
614 191 10,67283972
30,02784
70,39624
8
632 190 10,66929846
10,02792
30,40152
5
643 189 1 0,66575720,02799
7 0,40683649 188 1 0,66221593 0,02807 0,41216
8 4
654 187 10,65867467
60,02814
10,41752
6
657 186 10,65513341
5 0,028210,42291
6
670 185 10,65159215
30,02827
70,42833
6
673 184 10,64805089
10,02834
30,43378
6
697 183 10,64450962
90,02840
70,43926
6
700 182 10,64096836
80,02846
90,44477
5
702 181 10,63742710
60,02852
90,45031
5
706 180 10,63388584
40,02858
80,45588
6
709 179 10,63034458
30,02864
50,46148
9
711 178 10,62680332
10,02870
10,46712
2
726 177 10,62326205
90,02875
40,47278
8
735 176 10,61972079
80,02880
70,47848
6
743 175 10,61617953
60,02885
70,48421
7
770 174 10,61263827
40,02890
60,48998
1
802 172 20,60551457
30,02899
90,50167
7
805 171 10,60197355
20,02904
30,50754
2
806 169 20,59484960
50,02912
50,51944
7
833 168 10,59130883
40,02916
50,52541
7
840 167 10,58776806
20,02920
20,53142
3
853 166 10,58422729
10,02923
90,53746
5
874 165 10,58068651
90,02927
30,54354
4
887 164 10,57714574
80,02930
6 0,54966
891 163 10,57360497
60,02933
80,55581
4
904 162 10,57006420
50,02936
80,56200
6911 161 1 0,56652343 0,02939 0,56823
3 6 7
940 160 10,56298266
20,02942
30,57450
6
944 159 1 0,559441890,02944
80,58081
6
952 158 10,55590111
90,02947
20,58716
5
961 157 10,55236034
70,02949
40,59355
5
963 156 10,54881957
60,02951
50,59998
6
968 155 10,54527880
50,02953
40,60645
8
1020 154 10,54173803
30,02955
20,61297
3
1021 153 10,53819726
20,02956
8 0,61953
1024 152 1 0,534656490,02958
30,62613
1
1037 151 10,53111571
90,02959
60,63277
5
1057 150 10,52757494
70,02960
80,63946
4
1092 149 10,52403417
60,02961
80,64619
8
1117 148 10,52049340
40,02962
70,65297
8
1133 147 10,51695263
30,02963
40,65980
4
1136 146 10,51341186
10,02963
90,66667
7
1142 145 1 0,509871090,02964
40,67359
7
1211 144 10,50633031
90,02964
60,68056
6
1219 143 10,50278954
70,02964
80,68758
4
1230 142 10,49924877
60,02964
70,69465
1
1233 141 10,49570800
40,02964
50,70176
8
1236 140 10,49216723
30,02964
20,70893
7
1237 139 10,48862646
10,02963
70,71615
7
1246 138 1 0,485085690,02963
1 0,72343
1272 137 10,48154491
80,02962
30,73075
61274 136 1 0,47800414 0,02961 0,73813
7 4 6
1276 135 10,47446337
50,02960
30,74557
1
1290 134 10,47092260
40,02959
10,75306
2
1295 133 10,46738183
20,02957
70,76060
9
1327 132 10,46384106
10,02956
20,76821
3
1387 131 1 0,460300290,02954
50,77587
6
1439 130 10,45675951
80,02952
70,78359
8
1446 128 20,44962265
10,02948
30,79934
7
1471 127 10,44608231
5 0,029460,80725
2
1488 126 10,44254197
90,02943
6 0,81522
1511 125 10,43900164
3 0,029410,82325
2
1550 124 00,43900164
30,02952
80,82325
2
1607 123 00,43900164
30,02964
80,82325
2
1620 122 10,43540326
9 0,029620,83148
3
1637 121 10,43180489
5 0,029590,83978
1
1668 120 10,42820652
10,02955
8 0,84815
1679 119 10,42460814
70,02952
50,85658
9
1745 118 10,42100977
30,02949
10,86509
9
1767 117 10,41741139
80,02945
50,87368
3
1786 116 10,41381302
40,02941
70,88234
1
1851 115 1 0,410214650,02937
70,89107
5
1885 114 10,40661627
60,02933
60,89988
5
1981 113 10,40301790
20,02929
30,90877
4
1995 112 10,39941952
80,02924
90,91774
3
2021 111 10,39582115
40,02920
30,92679
32035 110 1 0,39222278 0,02915 0,93592
5 5
2077 109 10,38862440
50,02910
50,94514
2
2083 108 10,38502603
10,02905
40,95444
4
2127 107 10,38142765
70,02900
10,96383
4
2133 106 10,37782928
30,02894
70,97331
3
2152 105 10,37423090
9 0,028890,98288
2
2219 103 00,37423090
90,02916
90,98288
2
2237 102 00,37423090
90,02931
20,98288
2
2257 101 00,37423090
90,02945
70,98288
2
2280 100 00,37423090
90,02960
40,98288
2
2287 99 10,37045079
90,02954
10,99303
5
2324 98 00,37045079
90,02969
20,99303
5
2349 97 00,37045079
90,02984
40,99303
5
2353 96 00,37045079
90,02999
90,99303
5
2362 95 00,37045079
90,03015
70,99303
5
2393 94 00,37045079
90,03031
70,99303
5
2413 93 00,37045079
90,03047
90,99303
5
2442 92 00,37045079
90,03064
40,99303
5
2445 91 00,37045079
90,03081
20,99303
5
2450 90 00,37045079
90,03098
30,99303
5
2458 89 00,37045079
90,03115
70,99303
5
2461 88 00,37045079
90,03133
30,99303
5
2467 87 00,37045079
90,03151
30,99303
5
2474 86 00,37045079
90,03169
50,99303
5
2486 85 00,37045079
90,03188
10,99303
52488 84 0 0,37045079 0,03207 0,99303
9 1 5
2496 83 00,37045079
90,03226
30,99303
5
2497 82 00,37045079
90,03245
90,99303
5
2501 81 00,37045079
90,03265
90,99303
5
2503 80 00,37045079
90,03286
20,99303
5
2506 79 00,37045079
9 0,033070,99303
5
2507 78 00,37045079
90,03328
10,99303
5
2513 77 00,37045079
90,03349
70,99303
5
2527 76 00,37045079
90,03371
60,99303
5
2541 75 00,37045079
9 0,033940,99303
5
2545 74 00,37045079
90,03416
90,99303
5
2548 73 00,37045079
90,03440
20,99303
5
2552 72 10,36530564
90,03429
81,00702
1
2562 71 00,36530564
90,03453
91,00702
1
2580 70 00,36530564
90,03478
51,00702
1
2588 69 00,36530564
90,03503
61,00702
1
2592 68 00,36530564
90,03529
31,00702
1
2598 67 00,36530564
90,03555
51,00702
1
2613 66 00,36530564
90,03582
31,00702
1
2621 65 00,36530564
90,03609
81,00702
1
2628 64 00,36530564
90,03637
91,00702
1
2630 63 00,36530564
90,03666
61,00702
1
2631 62 00,36530564
90,03696
11,00702
1
2651 61 00,36530564
90,03726
31,00702
1
2653 60 00,36530564
90,03757
21,00702
12656 59 0 0,36530564 0,03788 1,00702
9 9 1
2663 58 00,36530564
90,03821
41,00702
1
2674 57 00,36530564
90,03854
81,00702
1
2676 56 00,36530564
90,03889
11,00702
1
2678 55 00,36530564
90,03924
31,00702
1
2679 54 00,36530564
90,03960
41,00702
1
2688 53 00,36530564
90,03997
61,00702
1
2697 52 00,36530564
90,04035
91,00702
1
2703 51 00,36530564
90,04075
21,00702
1
2706 50 00,36530564
90,04115
81,00702
1
2708 49 00,36530564
90,04157
61,00702
1
2709 48 00,36530564
90,04200
71,00702
1
2711 47 00,36530564
90,04245
11,00702
1
2713 46 00,36530564
9 0,042911,00702
1
2724 45 00,36530564
90,04338
41,00702
1
2730 44 00,36530564
90,04387
51,00702
1
2731 43 00,36530564
90,04438
21,00702
1
2739 42 00,36530564
90,04490
71,00702
1
2740 41 00,36530564
90,04545
11,00702
1
2747 39 00,36530564
90,04660
21,00702
1
2760 38 00,36530564
90,04721
11,00702
1
2775 37 00,36530564
90,04784
51,00702
1
2779 36 00,36530564
90,04850
51,00702
1
2789 35 00,36530564
90,04919
31,00702
1
2794 34 00,36530564
90,04991
11,00702
12802 33 0 0,36530564 0,05066 1,00702
9 2 1
2815 31 00,36530564
90,05227
11,00702
1
2820 30 00,36530564
90,05313
51,00702
1
2821 29 00,36530564
90,05404
31,00702
1
2826 28 00,36530564
9 0,0551,00702
1
2828 27 00,36530564
90,05600
91,00702
1
2835 26 00,36530564
90,05707
61,00702
1
2840 25 00,36530564
90,05820
61,00702
1
2842 24 00,36530564
90,05940
61,00702
1
2849 23 00,36530564
90,06068
41,00702
1
2869 22 00,36530564
90,06204
81,00702
1
2871 21 00,36530564
90,06350
81,00702
1
2883 20 00,36530564
90,06507
61,00702
1
2889 19 00,36530564
90,06676
71,00702
1
2899 18 00,36530564
90,06859
71,00702
1
2908 17 00,36530564
90,07058
51,00702
1
2913 16 00,36530564
90,07275
81,00702
1
2925 15 00,36530564
90,07514
41,00702
1
2927 14 00,36530564
90,07778
11,00702
1
2950 13 00,36530564
90,08071
71,00702
1
2951 12 00,36530564
90,08401
31,00702
1
2969 11 00,36530564
90,08774
91,00702
1
3000 10 00,36530564
90,09203
21,00702
1
3017 9 00,36530564
9 0,097011,00702
1
3019 8 00,36530564
90,10289
51,00702
13024 7 0 0,36530564 0,10999 1,00702
9 9 1
3030 6 00,36530564
90,11881
31,00702
1
3078 5 00,36530564
90,13015
31,00702
1
3238 4 00,36530564
90,14551
51,00702
1
3308 3 00,36530564
90,16802
71,00702
1
3325 2 00,36530564
9 0,205791,00702
1
3329 1 00,36530564
90,29103
11,00702
1
Berdasarkan hasil (a) kemampuan bertahan hidup pasien laki-laki pada t = 28 adalah
0,996441 atau 99,6441% sedangkan kemampuan bertahan hidup pasien perempuan
pada titik t = 23 sebesar 1 atau 100%. Ini menunjukkan sedikit
perbedaan(kemampuan bertahan hidup pasien laki-laki sedikit lebih rendah dibanding
kemampuan bertahan hidup pasien perempuan).
b.
0 500 1000 1500 2000 2500 3000 35000
0.2
0.4
0.6
0.8
1
1.2
Perempuan
S(t)
t
S(t)
0 500 1000 1500 2000 2500 3000 35000
0.2
0.4
0.6
0.8
1
1.2
Laki-laki
S(t)
t
S(t)
Ditinjau dari sisi grafik, kemampuan bertahan hidup pasien laki-laki sedikit lebih
rendah dibanding kemampuan bertahan hidup pasien perempuan.
4. Estimasi fungsi hazard dan survival Nelson-Aalen dari kelompok pasien perempuan.
time Y d H(t) se[H(t)] S(t)23 286 0 0 0 1
36 285 10,00350
91,23115E-
050,99649
7
68 284 1 0,007032,47098E-
050,99299
5
72 283 10,01056
33,71959E-
050,98949
2
77 282 1 0,014114,97707E-
05 0,98599
79 281 10,01766
86,24352E-
050,98248
7
80 280 1 0,021247,51903E-
050,97898
4
86 279 10,02482
4 8,8037E-050,97548
2
98 277 20,03204
40,00011410
30,96846
4
101 276 10,03566
7 0,000127230,96496
1
113 275 10,03930
40,00014045
30,96145
9
118 274 10,04295
30,00015377
30,95795
6
121 273 10,04661
60,00016719
10,95445
4127 272 1 0,05029 0,00018070 0,95095
3 7 1
139 271 10,05398
30,00019432
40,94744
8
143 270 10,05768
70,00020804
10,94394
6
146 269 10,06140
40,00022186
10,94044
3
157 267 20,06889
50,00024991
60,93342
5
165 266 10,07265
40,00026404
90,92992
2
173 265 10,07642
80,00027828
9 0,92642
174 264 10,08021
60,00029263
70,92291
7
176 263 10,08401
80,00030709
40,91941
5
183 262 10,08783
50,00032166
20,91591
2
185 260 20,09552
70,00035124
80,90889
4
186 259 10,09938
80,00036615
50,90539
1
189 258 10,10326
40,00038117
80,90188
9
204 257 10,10715
50,00039631
80,89838
6
215 256 10,11106
10,00041157
70,89488
4
218 254 20,11893
50,00044257
70,88786
5
221 253 10,12288
8 0,00045820,88436
3
226 252 10,12685
60,00047394
7 0,88086
229 251 1 0,13084 0,000489820,87735
8
230 250 1 0,13484 0,000505820,87385
6
232 249 10,13885
60,00052194
90,87035
3
245 248 10,14288
80,00053820
80,86685
1
260 247 10,14693
70,00055459
90,86334
8
261 246 10,15100
20,00057112
30,85984
6
264 245 10,15508
40,00058778
30,85634
4279 244 1 0,15918 0,00060458 0,85284
2 1
283 243 10,16329
70,00062151
50,84933
9
286 242 10,16742
9 0,000638590,84583
6
289 241 10,17157
90,00065580
70,84233
4
290 239 20,17994
70,00069082
10,83531
4
293 238 10,18414
90,00070847
50,83181
2
315 236 20,19262
30,00074438
40,82479
3
322 235 10,19687
90,00076249
2 0,82129
325 234 10,20115
20,00078075
50,81778
8
326 233 00,20115
20,00078075
50,81778
8
335 232 10,20546
20,00079933
40,81427
1
348 231 10,20979
10,00081807
40,81075
3
363 230 10,21413
90,00083697
80,80723
6
365 229 10,21850
60,00085604
70,80371
9
370 228 10,22289
20,00087528
30,80020
1
382 227 10,22729
7 0,000894690,79668
4
384 225 20,23618
60,00093419
60,78963
4
392 224 10,24065
10,00095412
60,78611
6
400 223 10,24513
50,00097423
50,78259
9
402 222 10,24963
90,00099452
50,77908
2
411 221 10,25416
4 0,0010150,77556
4
431 220 1 0,258710,00103566
10,77204
7
433 219 10,26327
60,00105651
1 0,76853
437 218 10,26786
30,00107755
30,76501
3
440 217 10,27247
1 0,001098790,76149
5443 216 1 0,27710 0,00112022 0,75797
1 3 8
459 215 10,28175
20,00114185
70,75446
1
461 214 10,28642
50,00116369
30,75094
3
464 213 1 0,291120,00118573
40,74742
6
474 212 10,29583
70,00120798
40,74390
9
480 211 10,30057
60,00123044
50,74039
1
484 210 10,30533
80,00125312
10,73687
4
490 209 10,31012
30,00127601
40,73335
7
496 208 10,31493
10,00129912
8 0,72984
498 207 10,31976
10,00132246
60,72632
2
505 206 10,32461
60,00134603
10,72280
5
526 205 10,32949
40,00136982
60,71928
8
528 204 10,33439
60,00139385
5 0,71577
542 203 10,33932
20,00141812
20,71225
3
547 202 10,34427
20,00144262
90,70873
6
559 201 10,34924
80,00146738
10,70521
9
561 200 10,35424
80,00149238
10,70170
1
578 199 10,35927
30,00151763
30,69818
4
580 198 10,36432
30,00154314
10,69466
7
581 197 10,36939
90,00156890
80,69114
9
593 195 20,37965
60,00162150
50,68409
7
595 194 1 0,384810,00164807
5 0,68058
599 193 0 0,384810,00164807
5 0,68058
604 192 10,39001
90,00167520
20,67704
4
614 191 10,39525
40,00170261
40,67350
9632 190 1 0,40051 0,00173031 0,66997
7 4 3
643 189 10,40580
80,00175830
90,66643
8
649 188 10,41112
80,00178660
20,66290
2
654 187 10,41647
50,00181519
90,65936
7
657 186 10,42185
20,00184410
40,65583
1
670 185 10,42725
70,00187332
30,65229
6
673 184 10,43269
2 0,00190286 0,64876
697 183 10,43815
6 0,001932720,64522
5
700 182 10,44365
1 0,00196291 0,64169
702 181 10,44917
60,00199343
40,63815
4
706 180 10,45473
10,00202429
80,63461
9
709 179 10,46031
80,00205550
80,63108
3
711 178 10,46593
6 0,002087070,62754
8
726 177 10,47158
50,00211898
90,62401
2
735 176 10,47726
70,00215127
20,62047
7
743 175 10,48298
20,00218392
50,61694
1
770 174 10,48872
90,00221695
50,61340
6
802 172 20,50035
70,00228455
90,60631
4
805 171 10,50620
50,00231875
70,60277
9
806 169 20,51803
90,00238878
30,59568
8
833 168 10,52399
10,00242421
40,59215
2
840 167 10,52997
9 0,002460070,58861
7
853 166 10,53600
3 0,002496360,58508
2
874 165 10,54206
40,00253309
10,58154
7
887 164 10,54816
10,00257027
10,57801
2891 163 1 0,55429 0,00260790 0,57447
6 9 6
904 162 10,56046
90,00264601
30,57094
1
911 161 1 0,566680,00268459
20,56740
6
940 160 1 0,572930,00272365
40,56387
1
944 159 1 0,579220,00276320
90,56033
5
952 158 10,58554
90,00280326
7 0,5568
961 157 10,59191
80,00284383
70,55326
5
963 156 10,59832
90,00288492
8 0,54973
968 155 1 0,604780,00292655
10,54619
4
1020 154 10,61127
40,00296871
70,54265
9
1021 153 1 0,617810,00301143
60,53912
4
1024 152 10,62438
90,00305471
80,53558
9
1037 151 10,63101
10,00309857
60,53205
4
1057 150 10,63767
8 0,003143020,52851
8
1092 149 10,64438
90,00318806
30,52498
3
1117 148 10,65114
60,00323371
70,52144
8
1133 147 10,65794
90,00327999
40,51791
3
1136 146 10,66479
80,00332690
70,51437
7
1142 145 10,67169
5 0,003374470,51084
2
1211 144 10,67863
90,00342269
50,50730
7
1219 143 10,68563
20,00347159
70,50377
2
1230 142 10,69267
4 0,003521190,50023
7
1233 141 10,69976
6 0,003571490,49670
1
1236 140 10,70690
9 0,003622510,49316
6
1237 139 10,71410
40,00367426
70,48963
11246 138 1 0,72135 0,00372677 0,48609
7 6
1272 137 10,72864
90,00378005
7 0,48256
1274 136 10,73600
20,00383412
20,47902
5
1276 135 1 0,743410,00388899
2 0,47549
1290 134 10,75087
20,00394468
40,47195
5
1295 133 10,75839
10,00400121
60,46841
9
1327 132 10,76596
70,00405860
80,46488
4
1387 131 1 0,7736 0,004116880,46134
9
1439 130 10,78129
30,00417605
10,45781
4
1446 128 20,79691
80,00429812
20,45071
6
1471 127 10,80479
20,00436012
20,44718
1
1488 126 10,81272
8 0,004423110,44364
6
1511 125 10,82072
8 0,004487110,44011
1
1550 124 00,82072
8 0,004487110,44011
1
1607 123 00,82072
8 0,004487110,44011
1
1620 122 10,82892
50,00455429
60,43651
8
1637 121 10,83718
90,00462259
80,43292
6
1668 120 10,84552
30,00469204
20,42933
3
1679 119 10,85392
60,00476265
9 0,42574
1745 118 10,86240
10,00483447
70,42214
7
1767 117 10,87094
80,00490752
80,41855
5
1786 116 10,87956
80,00498184
50,41496
2
1851 115 10,88826
40,00505745
90,41136
9
1885 114 10,89703
60,00513440
60,40777
7
1981 113 10,90588
5 0,005212720,40418
41995 112 1 0,91481 0,00529244 0,40059
4 1
2021 111 10,92382
30,00537360
20,39699
8
2035 110 10,93291
40,00545624
70,39340
6
2077 109 10,94208
80,00554041
50,38981
3
2083 108 10,95134
80,00562614
9 0,38622
2127 107 10,96069
30,00571349
20,38262
8
2133 106 10,97012
70,00580249
20,37903
5
2152 105 10,97965
10,00589319
50,37544
2
2219 103 00,97965
10,00589319
50,37544
2
2237 102 00,97965
10,00589319
50,37544
2
2257 101 00,97965
10,00589319
50,37544
2
2280 100 00,97965
10,00589319
50,37544
2
2287 99 10,98975
20,00599522
50,37166
9
2324 98 00,98975
20,00599522
50,37166
9
2349 97 00,98975
20,00599522
50,37166
9
2353 96 00,98975
20,00599522
50,37166
9
2362 95 00,98975
20,00599522
50,37166
9
2393 94 00,98975
20,00599522
50,37166
9
2413 93 00,98975
20,00599522
50,37166
9
2442 92 00,98975
20,00599522
50,37166
9
2445 91 00,98975
20,00599522
50,37166
9
2450 90 00,98975
20,00599522
50,37166
9
2458 89 00,98975
20,00599522
50,37166
9
2461 88 00,98975
20,00599522
50,37166
9
2467 87 00,98975
20,00599522
50,37166
92474 86 0 0,98975 0,00599522 0,37166
2 5 9
2486 85 00,98975
20,00599522
50,37166
9
2488 84 00,98975
20,00599522
50,37166
9
2496 83 00,98975
20,00599522
50,37166
9
2497 82 00,98975
20,00599522
50,37166
9
2501 81 00,98975
20,00599522
50,37166
9
2503 80 00,98975
20,00599522
50,37166
9
2506 79 00,98975
20,00599522
50,37166
9
2507 78 00,98975
20,00599522
50,37166
9
2513 77 00,98975
20,00599522
50,37166
9
2527 76 00,98975
20,00599522
50,37166
9
2541 75 00,98975
20,00599522
50,37166
9
2545 74 00,98975
20,00599522
50,37166
9
2548 73 00,98975
20,00599522
50,37166
9
2552 72 11,00364
10,00618812
70,36654
2
2562 71 01,00364
10,00618812
70,36654
2
2580 70 01,00364
10,00618812
70,36654
2
2588 69 01,00364
10,00618812
70,36654
2
2592 68 01,00364
10,00618812
70,36654
2
2598 67 01,00364
10,00618812
70,36654
2
2613 66 01,00364
10,00618812
70,36654
2
2621 65 01,00364
10,00618812
70,36654
2
2628 64 01,00364
10,00618812
70,36654
2
2630 63 01,00364
10,00618812
70,36654
2
2631 62 01,00364
10,00618812
70,36654
22651 61 0 1,00364 0,00618812 0,36654
1 7 2
2653 60 01,00364
10,00618812
70,36654
2
2656 59 01,00364
10,00618812
70,36654
2
2663 58 01,00364
10,00618812
70,36654
2
2674 57 01,00364
10,00618812
70,36654
2
2676 56 01,00364
10,00618812
70,36654
2
2678 55 01,00364
10,00618812
70,36654
2
2679 54 01,00364
10,00618812
70,36654
2
2688 53 01,00364
10,00618812
70,36654
2
2697 52 01,00364
10,00618812
70,36654
2
2703 51 01,00364
10,00618812
70,36654
2
2706 50 01,00364
10,00618812
70,36654
2
2708 49 01,00364
10,00618812
70,36654
2
2709 48 01,00364
10,00618812
70,36654
2
2711 47 01,00364
10,00618812
70,36654
2
2713 46 01,00364
10,00618812
70,36654
2
2724 45 01,00364
10,00618812
70,36654
2
2730 44 01,00364
10,00618812
70,36654
2
2731 43 01,00364
10,00618812
70,36654
2
2739 42 01,00364
10,00618812
70,36654
2
2740 41 01,00364
10,00618812
70,36654
2
2747 39 01,00364
10,00618812
70,36654
2
2760 38 01,00364
10,00618812
70,36654
2
2775 37 01,00364
10,00618812
70,36654
2
2779 36 01,00364
10,00618812
70,36654
22789 35 0 1,00364 0,00618812 0,36654
1 7 2
2794 34 01,00364
10,00618812
70,36654
2
2802 33 01,00364
10,00618812
70,36654
2
2815 31 01,00364
10,00618812
70,36654
2
2820 30 01,00364
10,00618812
70,36654
2
2821 29 01,00364
10,00618812
70,36654
2
2826 28 01,00364
10,00618812
70,36654
2
2828 27 01,00364
10,00618812
70,36654
2
2835 26 01,00364
10,00618812
70,36654
2
2840 25 01,00364
10,00618812
70,36654
2
2842 24 01,00364
10,00618812
70,36654
2
2849 23 01,00364
10,00618812
70,36654
2
2869 22 01,00364
10,00618812
70,36654
2
2871 21 01,00364
10,00618812
70,36654
2
2883 20 01,00364
10,00618812
70,36654
2
2889 19 01,00364
10,00618812
70,36654
2
2899 18 01,00364
10,00618812
70,36654
2
2908 17 01,00364
10,00618812
70,36654
2
2913 16 01,00364
10,00618812
70,36654
2
2925 15 01,00364
10,00618812
70,36654
2
2927 14 01,00364
10,00618812
70,36654
2
2950 13 01,00364
10,00618812
70,36654
2
2951 12 01,00364
10,00618812
70,36654
2
2969 11 01,00364
10,00618812
70,36654
2
3000 10 01,00364
10,00618812
70,36654
23017 9 0 1,00364 0,00618812 0,36654
1 7 2
3019 8 01,00364
10,00618812
70,36654
2
3024 7 01,00364
10,00618812
70,36654
2
3030 6 01,00364
10,00618812
70,36654
2
3078 5 01,00364
10,00618812
70,36654
2
3238 4 01,00364
10,00618812
70,36654
2
3308 3 01,00364
10,00618812
70,36654
2
3325 2 01,00364
10,00618812
70,36654
2
3329 1 01,00364
10,00618812
70,36654
2
Pada t = 23 daya tahan hidup pasien perempuan adalah 1, dan pada saat t = 36
kemampuan daya tahan hidup pasien perempuan sebesar 0,996497. Ini tidak berbeda
jauh dengan nilai yang ditunjukkan oleh estimasi fungsi survival Kaplan-Meier.
Dari kedua tabel estimasi fungsi survival ketahanan hidup dengan metode Kaplan-Meier
dan Nelson-Aalen, terlihat metode Kaplan-Meier menunjukkan nilai ketahanan hidup
yang lebih kecil dibandingkan dengan estimasi fungsi survival Nelson-Aalen. Jadi
estimasi yang memberikan kesimpulan bahwa pasien dapat bertahan hidup lebih lama
adalah estimasi Nelson-Aalen.