Membangkitkan Data Ketahanan Hidup Pasien Kanker Otak

Skenario

Pada studi kasus ini diambil contoh dengan menggunakan data 300 pasien kanker otak yang ada pada sebuah rumah sakit umum daerah. Peristiwa (event) dalam contoh ini adalah pasien kanker otak yang mengalami kematian selama masa pengamatan. Selain itu, fokus utama pada analisis ini adalah variabel apa yang paling berpengaruh signifikan terhadap status kematian pasien. Variabel tersebut adalah:

y: Analisis ketahanan hidup pasien kanker otak selama pengamatan x1: Umur pasien penyandang kanker otak (tahun) x2: Ada tidaknya riwayat genetik pada silsilah keluarga yang terkena kanker otak (0:nongenetik, 1:genetik) x3: Cara pengobatan (0:tidak melakukan pengobatan intensif, 1:melakukan pengobatan intensif) x4: Stadium kanker (skala 4)

Membangkitkan Data x1

x1: Umur pasien penyandang kanker otak (tahun) Membangkitkan variabel x1

set.seed(111)
n <- 300
x1 <- runif(n)
x1
##   [1] 0.5929812845 0.7264811215 0.3704220036 0.5149238301 0.3776632159
##   [6] 0.4183373258 0.0106578451 0.5322952422 0.4321606164 0.0936815199
##  [11] 0.5557799137 0.5902284889 0.0671411434 0.0475478533 0.1562025158
##  [16] 0.4464277634 0.1714436871 0.9665342933 0.3106664298 0.6144663957
##  [21] 0.4310607871 0.2855270915 0.3421513471 0.3866276275 0.9675274789
##  [26] 0.3220267275 0.6532294548 0.2833034997 0.7874279192 0.5959206352
##  [31] 0.0585964625 0.5098998600 0.4657924296 0.4693590938 0.3597453721
##  [36] 0.7134103531 0.1163154817 0.7839926207 0.6421407105 0.8051009134
##  [41] 0.6411978584 0.3284916454 0.6356909545 0.9285191579 0.5752422044
##  [46] 0.3666838536 0.4366072204 0.8559219379 0.6279955737 0.7937756432
##  [51] 0.7251648332 0.5850447209 0.0327716474 0.3329946804 0.9967166614
##  [56] 0.5482733699 0.5758329388 0.4563152066 0.0965785654 0.8055401752
##  [61] 0.0009253006 0.4667440471 0.1732608730 0.2592225648 0.9192820815
##  [66] 0.2319295844 0.0525656715 0.3043926249 0.0117258150 0.3007076983
##  [71] 0.8775839461 0.6652787277 0.4537648347 0.0533223320 0.6309068091
##  [76] 0.4421851884 0.2673464869 0.9837744189 0.0951241532 0.7859691235
##  [81] 0.1198521818 0.8812154671 0.1310980669 0.4003378763 0.0866140136
##  [86] 0.3747997992 0.6847860171 0.7347726757 0.7709477365 0.5799853499
##  [91] 0.5110989846 0.8529837073 0.6298211562 0.5790059080 0.7402492894
##  [96] 0.3871497631 0.9935344572 0.3980894811 0.9750010339 0.8244822009
## [101] 0.5759970602 0.1362155876 0.9397339805 0.1762847272 0.8197052260
## [106] 0.0121183777 0.6400623205 0.2670286722 0.5694977508 0.9653025323
## [111] 0.1984229437 0.6928534785 0.8360201151 0.9039043379 0.9645305418
## [116] 0.6576919304 0.5489127152 0.8850261893 0.4483733948 0.7433389057
## [121] 0.4143268145 0.6807554641 0.9259784352 0.6335980301 0.6589905838
## [126] 0.4785866372 0.8188303334 0.9639464633 0.9236928816 0.1643849264
## [131] 0.3514933106 0.6171195072 0.5801617010 0.9418052060 0.2100640042
## [136] 0.0388290430 0.6158633258 0.5146196210 0.9199719771 0.4554383077
## [141] 0.8470272932 0.8706397039 0.6830077136 0.7814433970 0.2513236194
## [146] 0.0464566061 0.5632578691 0.2937375917 0.3509654081 0.0791809296
## [151] 0.8253022840 0.2642138884 0.2638462810 0.0903810160 0.4608446269
## [156] 0.6915760476 0.8489604222 0.2461148170 0.6509210938 0.6801953125
## [161] 0.1045345513 0.1119856986 0.2156547720 0.1301163798 0.6663336323
## [166] 0.4877746897 0.3533037403 0.9470107574 0.1119488380 0.5638697769
## [171] 0.8483255904 0.5117678840 0.6665465659 0.0265097129 0.1064604088
## [176] 0.6954418537 0.2733446639 0.7449695240 0.7453953503 0.1667326230
## [181] 0.9798543244 0.5947587080 0.6882189384 0.1718581517 0.0416831505
## [186] 0.1898498912 0.7614218323 0.5594733323 0.5055143666 0.9728052951
## [191] 0.0806008175 0.5572443432 0.8960071700 0.1078971149 0.4492812373
## [196] 0.3088111347 0.2328826285 0.8280665197 0.1128784707 0.8840022471
## [201] 0.7256201541 0.9203334250 0.1229573302 0.9511435630 0.6697030859
## [206] 0.0850967949 0.5811568031 0.2125134552 0.2422193545 0.5362925141
## [211] 0.1770604565 0.5704032232 0.1554149061 0.4744193235 0.7274061972
## [216] 0.8463038874 0.9585764438 0.4588316823 0.3632254344 0.9363713360
## [221] 0.8847720872 0.6706333186 0.8470589763 0.8596506736 0.4815454748
## [226] 0.3170613982 0.9172041418 0.5046965585 0.0140720229 0.5955733217
## [231] 0.4492498117 0.5392000761 0.0939198402 0.7509487895 0.0767992917
## [236] 0.9290306640 0.8104190647 0.7613259845 0.6532063640 0.9401171594
## [241] 0.7545649228 0.0841972905 0.9907066093 0.2699875943 0.1550296356
## [246] 0.4841888184 0.6144657487 0.0806982385 0.9412467652 0.2032089424
## [251] 0.1984645734 0.1957958306 0.9078547994 0.5332889208 0.6833354323
## [256] 0.5401932111 0.5734838906 0.8467235053 0.5999798262 0.2315073176
## [261] 0.9952321625 0.8029856614 0.8586663995 0.9569845379 0.0551437899
## [266] 0.0680989958 0.4651018339 0.3234952011 0.6408634037 0.0106086857
## [271] 0.1894404925 0.7720005722 0.0004447419 0.0171903830 0.3200655682
## [276] 0.5294240620 0.6669622092 0.3918145306 0.2729253250 0.2881550833
## [281] 0.7499863163 0.5185095530 0.7375858924 0.5644303011 0.2699479579
## [286] 0.8742641583 0.6608892782 0.2380318267 0.8098499198 0.2351379597
## [291] 0.5084400198 0.9213492125 0.9648818206 0.1283409251 0.3256000143
## [296] 0.8055418341 0.4502127008 0.3627219510 0.7783999022 0.8081767145

Membangkitkan Data x2

x2: Ada tidaknya riwayat genetik pada silsilah keluarga yang terkena kanker otak (0:nongenetik, 1:genetik)

set.seed(222)
x2 <- round(runif(n))
x2
##   [1] 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1
##  [38] 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0
##  [75] 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 1
## [112] 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1
## [149] 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1
## [186] 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 1
## [223] 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0
## [260] 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1
## [297] 0 0 1 1

Membangkitkan Data x3

x3: Cara pengobatan (0:tidak melakukan pengobatan intensif, 1:melakukan pengobatan intensif)

set.seed(333)
x3 <- round(runif(n))
x3
##   [1] 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1
##  [38] 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0
##  [75] 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0
## [112] 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0
## [149] 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1
## [186] 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1
## [223] 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1
## [260] 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0
## [297] 1 1 0 0

Membangkitkan Data x4

x4 : Stadium (skala 4)

Kanker otak terbagi dalam empat stadium, yaitu: Stadium I: tumor tidak bersifat kanker atau tumbuh sangat lambat. Sel-selnya terlihat hampir identik dengan sel-sel sehat. Stadium II: tumor telah tumbuh menjadi kanker otak, tetapi lambat. Stadium III: tumor tumbuh lebih cepat dan menyebar ke jaringan otak yang lebih luas. Stadium IV: tumor tumbuh sangat cepat dan menyebar ke jaringan otak yang lebih luas.

Penentuan stadium kanker otak ini ditentukan ukuran dan lokasi tumor ganas tumbuh di otak, jenis jaringan atau sel yang terdampak, bisa tidaknya tumor ganas diangkat atau operasi.

set.seed(444)
x4 <- round(rnorm(n,3,0.5))
x4
##   [1] 3 3 2 3 4 3 3 3 4 3 2 3 3 3 3 3 3 3 2 4 3 3 3 4 3 2 4 4 3 3 2 3 3 3 3 3 2
##  [38] 3 4 3 3 2 3 3 3 3 2 2 3 3 3 3 3 4 3 3 2 4 4 4 4 3 3 3 3 3 3 2 2 3 4 3 3 2
##  [75] 4 3 3 2 4 4 3 3 4 4 3 3 3 3 3 3 3 3 2 4 3 3 3 3 3 3 3 3 3 3 3 2 3 4 3 4 4
## [112] 4 3 2 3 3 3 3 3 3 3 3 3 4 3 3 3 4 3 3 3 2 3 4 3 3 3 3 3 3 3 4 3 3 4 4 3 3
## [149] 3 4 2 4 3 5 3 3 3 4 2 3 3 2 2 2 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [186] 3 2 3 3 2 2 3 3 3 3 4 3 4 4 2 3 4 3 3 4 2 4 3 3 3 4 3 3 3 3 3 3 3 3 3 4 2
## [223] 3 3 3 3 3 4 3 2 2 4 3 4 3 3 3 3 3 3 3 4 4 3 3 3 3 3 3 3 2 4 2 2 3 3 4 2 3
## [260] 3 4 1 2 2 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 2 3 2 3 2 2 3 4 3 3 4 2 3 3 3 3 3
## [297] 3 2 2 3

Membangkitkan Data y

Menentukan koef

b0 <- -30
b1 <- 3
b2 <- 1
b3 <- 2
b4 <- 4
set.seed(555)
datapendukung <- b0+(b1*x1)+(b2*x2)+(b3*x3)+(b4*x4)
datapendukung
##   [1] -15.221056 -15.820557 -18.888734 -14.455229 -11.867010 -13.744988
##   [7] -15.968026 -16.403114 -11.703518 -17.718955 -20.332660 -16.229315
##  [13] -15.798577 -14.857356 -14.531392 -14.660717 -14.485669 -13.100397
##  [19] -21.068001 -12.156601 -15.706818 -17.143419 -16.973546 -11.840117
##  [25] -13.097418 -20.033920 -11.040312 -13.150090 -15.637716 -13.212238
##  [31] -19.824211 -15.470300 -14.602623 -15.591923 -13.920764 -14.859769
##  [37] -18.651054 -15.648022 -12.073578 -14.584697 -15.076406 -18.014525
##  [43] -13.092927 -14.214443 -16.274273 -15.899948 -19.690178 -16.432234
##  [49] -16.116013 -12.618673 -13.824506 -16.244866 -14.901685 -10.001016
##  [55] -13.009850 -16.355180 -18.272501 -10.631054 -12.710264  -8.583379
##  [61] -13.997224 -16.599768 -14.480217 -16.222332 -13.242154 -16.304211
##  [67] -17.842303 -21.086822 -21.964823 -17.097877 -10.367248 -14.004164
##  [73] -13.638705 -21.840033  -9.107280 -16.673444 -17.197961 -17.048677
##  [79] -12.714628 -10.642093 -14.640443 -14.356354 -12.606706  -9.798986
##  [85] -15.740158 -13.875601 -14.945642 -12.795682 -14.687157 -14.260044
##  [91] -13.466703 -12.441049 -18.110537 -10.262982 -14.779252 -16.838551
##  [97] -13.019397 -15.805732 -12.074997 -15.526553 -15.272009 -17.591353
## [103] -12.180798 -16.471146 -13.540884 -21.963645 -16.079813 -12.198914
## [109] -14.291507  -8.104092 -12.404731  -8.921440 -14.491940 -18.288287
## [115] -14.106408 -14.026924 -13.353262 -12.344921 -14.654880 -14.769983
## [121] -16.757020 -13.957734 -12.222065 -11.099206 -13.023028 -16.564240
## [127] -12.543509  -8.108161 -12.228921 -14.506845 -15.945520 -17.148641
## [133] -15.259515 -10.174584 -14.369808 -15.883513 -16.152410 -16.456141
## [139] -15.240084 -14.633685 -14.458918 -11.388081 -15.950977 -12.655670
## [145] -13.246029 -12.860630 -14.310226 -16.118787 -15.947104 -10.762457
## [151] -18.524093 -12.207358 -17.208461  -7.728857 -13.617466 -14.925272
## [157] -12.453119 -11.261656 -17.047237 -12.959414 -14.686396 -20.664043
## [163] -19.353036 -20.609651 -16.000999 -14.536676 -15.940089 -15.158968
## [169] -17.664153 -15.308391  -9.455023 -14.464696 -13.000360 -14.920471
## [175] -14.680619 -14.913674 -15.179966 -12.765091 -14.763814 -17.499802
## [181] -13.060437 -16.215724 -12.935343 -17.484426 -14.874951 -14.430450
## [187] -16.715735 -16.321580 -15.483457 -16.081584 -20.758198 -15.328267
## [193] -12.311978 -15.676309 -16.652156 -13.073567 -17.301352  -9.515800
## [199] -10.661365 -16.347993 -15.823140  -8.239000 -14.631128 -13.146569
## [205] -10.990891 -19.744710  -9.256530 -15.362460 -16.273342 -16.391122
## [211] -13.468819 -15.288790 -16.533755 -13.576742 -15.817781 -15.461088
## [217] -14.124271 -14.623505 -14.910324 -14.190886 -11.345684 -16.988100
## [223] -15.458823 -15.421048 -16.555364 -14.048816 -15.248388 -12.485910
## [229] -15.957784 -20.213280 -17.652251 -11.382400 -15.718240  -8.747154
## [235] -15.769602 -14.212908 -12.568743 -15.716022 -14.040381 -15.179649
## [241] -12.736305 -10.747408  -8.027880 -17.190037 -16.534911 -15.547434
## [247] -16.156603 -16.757905 -13.176260 -14.390373 -19.404606 -12.412613
## [253] -18.276436 -18.400133 -12.949994 -16.379420 -10.279548 -17.459829
## [259] -14.200061 -16.305478 -11.014304 -21.591043 -19.424001 -18.129046
## [265] -16.834569 -15.795703 -13.604694 -17.029514 -15.077410 -16.968174
## [271] -14.431679 -13.683998 -15.998666 -16.948429 -15.039803 -10.411728
## [277] -13.999113 -15.824556 -14.181224 -21.135535 -12.750041 -18.444471
## [283] -12.787242 -18.306709 -20.190156 -14.377208  -9.017332 -17.285905
## [289] -12.570450 -10.294586 -17.474680 -13.235952 -12.105355 -15.614977
## [295] -14.023200 -14.583374 -14.649362 -18.911834 -18.664800 -14.575470
p <- exp(datapendukung)/(1+exp(datapendukung))
p
##   [1] 2.452332e-07 1.346541e-07 6.262202e-09 5.274409e-07 7.018105e-06
##   [6] 1.073068e-06 1.161914e-07 7.520002e-08 8.264623e-06 2.017230e-08
##  [11] 1.477875e-09 8.947428e-08 1.376465e-07 3.528027e-07 4.887606e-07
##  [16] 4.294686e-07 5.116273e-07 2.044414e-06 7.084081e-10 5.253552e-06
##  [21] 1.508745e-07 3.586806e-08 4.250917e-08 7.209404e-06 2.050515e-06
##  [26] 1.992412e-09 1.604156e-05 1.945306e-06 1.616687e-07 1.828088e-06
##  [31] 2.457280e-09 1.911322e-07 4.551571e-07 1.692443e-07 9.000957e-07
##  [36] 3.519526e-07 7.942374e-09 1.600112e-07 5.708333e-06 4.633896e-07
##  [41] 2.833999e-07 1.501036e-08 2.059743e-06 6.710359e-07 8.554071e-08
##  [46] 1.243770e-07 2.809727e-09 7.304178e-08 1.002084e-07 3.309623e-06
##  [51] 9.910444e-07 8.809360e-08 3.375050e-07 4.535177e-05 2.238169e-06
##  [56] 7.889248e-08 1.159721e-08 2.415357e-05 3.019959e-06 1.871563e-04
##  [61] 8.338395e-07 6.177495e-08 5.144241e-07 9.010120e-08 1.774210e-06
##  [66] 8.301776e-08 1.783143e-08 6.951996e-10 2.889341e-10 3.753932e-08
##  [71] 3.144472e-05 8.280729e-07 1.193397e-06 3.273363e-10 1.108436e-04
##  [76] 5.738720e-08 3.396414e-08 3.943245e-08 3.006811e-06 2.388843e-05
##  [81] 4.382642e-07 5.822568e-07 3.349468e-06 5.550475e-05 1.459272e-07
##  [86] 9.416788e-07 3.229907e-07 2.772712e-06 4.182622e-07 6.411229e-07
##  [91] 1.417374e-06 3.952933e-06 1.363622e-08 3.490023e-05 3.814628e-07
##  [96] 4.865308e-08 2.216904e-06 1.366652e-07 5.700238e-06 1.806772e-07
## [101] 2.330509e-07 2.291777e-08 5.127957e-06 7.025419e-08 1.316037e-06
## [106] 2.892746e-10 1.039025e-07 5.035896e-06 6.212655e-07 3.022081e-04
## [111] 4.099132e-06 1.334781e-04 5.084290e-07 1.141558e-08 7.475915e-07
## [116] 8.094385e-07 1.587638e-06 4.351779e-06 4.319827e-07 3.850150e-07
## [121] 5.278601e-08 8.674270e-07 4.920652e-06 1.512410e-05 2.208868e-06
## [126] 6.400913e-08 3.567974e-06 3.009815e-04 4.887028e-06 5.009068e-07
## [131] 1.188361e-07 3.568121e-08 2.359809e-07 3.812568e-05 5.744754e-07
## [136] 1.264381e-07 9.662676e-08 7.131628e-08 2.406110e-07 4.412362e-07
## [141] 5.254984e-07 1.132960e-05 1.181895e-07 3.189415e-06 1.767347e-06
## [146] 2.598353e-06 6.097438e-07 9.993086e-08 1.186481e-07 2.117947e-05
## [151] 9.017550e-09 4.993551e-06 3.360936e-08 4.397532e-04 1.219015e-06
## [156] 3.296375e-07 3.905508e-06 1.285641e-05 3.948927e-08 2.353949e-06
## [161] 4.185804e-07 1.061012e-09 3.936257e-09 1.120321e-09 1.124228e-07
## [166] 4.861851e-07 1.194833e-07 2.609419e-07 2.130863e-08 2.247244e-07
## [171] 7.828915e-05 5.224707e-07 2.259510e-06 3.312239e-07 4.210058e-07
## [176] 3.334827e-07 2.555197e-07 2.858841e-06 3.873976e-07 2.511496e-08
## [181] 2.127763e-06 9.069860e-08 2.411297e-06 2.550413e-08 3.466498e-07
## [186] 5.406732e-07 5.501090e-08 8.158829e-08 1.886340e-07 1.037186e-07
## [191] 9.656714e-10 2.203018e-07 4.497526e-06 1.555484e-07 5.862197e-08
## [196] 2.100009e-06 3.062797e-08 7.367300e-05 2.343247e-05 7.946149e-08
## [201] 1.343067e-07 2.640786e-04 4.423659e-07 1.952166e-06 1.685425e-05
## [206] 2.660612e-09 9.547701e-05 2.128965e-07 8.562042e-08 7.610723e-08
## [211] 1.414379e-06 2.291726e-07 6.599048e-08 1.269683e-06 1.350283e-07
## [216] 1.929010e-07 7.343564e-07 4.457510e-07 3.346020e-07 6.870308e-07
## [221] 1.182026e-05 4.189497e-08 1.933385e-07 2.007816e-07 6.457983e-08
## [226] 7.919112e-07 2.386214e-07 3.779518e-06 1.173877e-07 1.665268e-09
## [231] 2.156378e-08 1.139414e-05 1.491608e-07 1.588878e-04 1.416931e-07
## [236] 6.720664e-07 3.479067e-06 1.494921e-07 7.986191e-07 2.556009e-07
## [241] 2.942332e-06 2.150060e-05 3.261326e-04 3.423432e-08 6.591425e-08
## [246] 1.769438e-07 9.622248e-08 5.273928e-08 1.895057e-06 5.627819e-07
## [251] 3.738407e-09 4.066953e-06 1.155167e-08 1.020760e-08 2.376228e-06
## [256] 7.700308e-08 3.432685e-05 2.613921e-08 6.807565e-07 8.291266e-08
## [261] 1.646424e-05 4.198838e-10 3.666601e-09 1.338613e-08 4.884720e-08
## [266] 1.380426e-07 1.234684e-06 4.019535e-08 2.831157e-07 4.273815e-08
## [271] 5.400095e-07 1.140551e-06 1.126854e-07 4.359040e-08 2.939655e-07
## [276] 3.007676e-05 8.322656e-07 1.341166e-07 6.937011e-07 6.621462e-10
## [281] 2.902193e-06 9.764902e-09 2.796211e-06 1.120720e-08 1.704224e-09
## [286] 5.702402e-07 1.212746e-04 3.110477e-08 3.473132e-06 3.381453e-05
## [291] 2.575389e-08 1.785246e-06 5.529794e-06 1.653870e-07 8.124587e-07
## [296] 4.640029e-07 4.343730e-07 6.119202e-09 7.833940e-09 4.676852e-07
set.seed(666)
y <- rbinom(n,1,p)
y
##   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [149] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [186] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [223] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [260] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [297] 0 0 0 0
datagab <- data.frame(y,x1,x2,x3,x4)
datagab
##     y           x1 x2 x3 x4
## 1   0 0.5929812845  1  0  3
## 2   0 0.7264811215  0  0  3
## 3   0 0.3704220036  0  1  2
## 4   0 0.5149238301  0  1  3
## 5   0 0.3776632159  1  0  4
## 6   0 0.4183373258  1  1  3
## 7   0 0.0106578451  0  1  3
## 8   0 0.5322952422  0  0  3
## 9   0 0.4321606164  1  0  4
## 10  0 0.0936815199  0  0  3
## 11  0 0.5557799137  0  0  2
## 12  0 0.5902284889  0  0  3
## 13  0 0.0671411434  0  1  3
## 14  0 0.0475478533  1  1  3
## 15  0 0.1562025158  1  1  3
## 16  0 0.4464277634  0  1  3
## 17  0 0.1714436871  1  1  3
## 18  0 0.9665342933  0  1  3
## 19  0 0.3106664298  0  0  2
## 20  0 0.6144663957  0  0  4
## 21  0 0.4310607871  1  0  3
## 22  0 0.2855270915  0  0  3
## 23  0 0.3421513471  0  0  3
## 24  0 0.3866276275  1  0  4
## 25  0 0.9675274789  0  1  3
## 26  0 0.3220267275  1  0  2
## 27  0 0.6532294548  1  0  4
## 28  0 0.2833034997  0  0  4
## 29  0 0.7874279192  0  0  3
## 30  0 0.5959206352  1  1  3
## 31  0 0.0585964625  0  1  2
## 32  0 0.5098998600  1  0  3
## 33  0 0.4657924296  0  1  3
## 34  0 0.4693590938  1  0  3
## 35  0 0.3597453721  1  1  3
## 36  0 0.7134103531  1  0  3
## 37  0 0.1163154817  1  1  2
## 38  0 0.7839926207  0  0  3
## 39  0 0.6421407105  0  0  4
## 40  0 0.8051009134  1  0  3
## 41  0 0.6411978584  1  0  3
## 42  0 0.3284916454  1  1  2
## 43  0 0.6356909545  1  1  3
## 44  0 0.9285191579  1  0  3
## 45  0 0.5752422044  0  0  3
## 46  0 0.3666838536  1  0  3
## 47  0 0.4366072204  1  0  2
## 48  0 0.8559219379  1  1  2
## 49  0 0.6279955737  0  0  3
## 50  0 0.7937756432  1  1  3
## 51  0 0.7251648332  0  1  3
## 52  0 0.5850447209  0  0  3
## 53  0 0.0327716474  1  1  3
## 54  0 0.3329946804  1  1  4
## 55  0 0.9967166614  0  1  3
## 56  0 0.5482733699  0  0  3
## 57  0 0.5758329388  0  1  2
## 58  0 0.4563152066  0  1  4
## 59  0 0.0965785654  1  0  4
## 60  0 0.8055401752  1  1  4
## 61  0 0.0009253006  0  0  4
## 62  0 0.4667440471  0  0  3
## 63  0 0.1732608730  1  1  3
## 64  0 0.2592225648  1  0  3
## 65  0 0.9192820815  0  1  3
## 66  0 0.2319295844  1  0  3
## 67  0 0.0525656715  0  0  3
## 68  0 0.3043926249  0  0  2
## 69  0 0.0117258150  0  0  2
## 70  0 0.3007076983  0  0  3
## 71  0 0.8775839461  1  0  4
## 72  0 0.6652787277  0  1  3
## 73  0 0.4537648347  1  1  3
## 74  0 0.0533223320  0  0  2
## 75  0 0.6309068091  1  1  4
## 76  0 0.4421851884  0  0  3
## 77  0 0.2673464869  0  0  3
## 78  0 0.9837744189  0  1  2
## 79  0 0.0951241532  1  0  4
## 80  0 0.7859691235  1  0  4
## 81  0 0.1198521818  1  1  3
## 82  0 0.8812154671  1  0  3
## 83  0 0.1310980669  1  0  4
## 84  0 0.4003378763  1  1  4
## 85  0 0.0866140136  0  1  3
## 86  0 0.3747997992  1  1  3
## 87  0 0.6847860171  1  0  3
## 88  0 0.7347726757  1  1  3
## 89  0 0.7709477365  1  0  3
## 90  0 0.5799853499  0  1  3
## 91  0 0.5110989846  1  1  3
## 92  0 0.8529837073  1  1  3
## 93  0 0.6298211562  0  1  2
## 94  0 0.5790059080  0  1  4
## 95  0 0.7402492894  1  0  3
## 96  0 0.3871497631  0  0  3
## 97  0 0.9935344572  0  1  3
## 98  0 0.3980894811  1  0  3
## 99  0 0.9750010339  1  1  3
## 100 0 0.8244822009  0  0  3
## 101 0 0.5759970602  1  0  3
## 102 0 0.1362155876  0  0  3
## 103 0 0.9397339805  1  1  3
## 104 0 0.1762847272  1  0  3
## 105 0 0.8197052260  0  1  3
## 106 0 0.0121183777  0  0  2
## 107 0 0.6400623205  0  0  3
## 108 0 0.2670286722  1  0  4
## 109 0 0.5694977508  0  1  3
## 110 0 0.9653025323  1  1  4
## 111 0 0.1984229437  1  0  4
## 112 0 0.6928534785  1  1  4
## 113 0 0.8360201151  1  0  3
## 114 0 0.9039043379  1  0  2
## 115 0 0.9645305418  1  0  3
## 116 0 0.6576919304  0  1  3
## 117 0 0.5489127152  1  1  3
## 118 0 0.8850261893  1  1  3
## 119 0 0.4483733948  0  1  3
## 120 0 0.7433389057  1  0  3
## 121 0 0.4143268145  0  0  3
## 122 0 0.6807554641  0  1  3
## 123 0 0.9259784352  1  1  3
## 124 0 0.6335980301  1  0  4
## 125 0 0.6589905838  1  1  3
## 126 0 0.4785866372  0  0  3
## 127 0 0.8188303334  1  1  3
## 128 0 0.9639464633  1  1  4
## 129 0 0.9236928816  1  1  3
## 130 0 0.1643849264  1  1  3
## 131 0 0.3514933106  1  0  3
## 132 0 0.6171195072  1  1  2
## 133 0 0.5801617010  1  0  3
## 134 0 0.9418052060  1  0  4
## 135 0 0.2100640042  1  1  3
## 136 0 0.0388290430  0  1  3
## 137 0 0.6158633258  0  0  3
## 138 0 0.5146196210  0  0  3
## 139 0 0.9199719771  0  0  3
## 140 0 0.4554383077  0  1  3
## 141 0 0.8470272932  1  0  3
## 142 0 0.8706397039  0  0  4
## 143 0 0.6830077136  0  0  3
## 144 0 0.7814433970  1  1  3
## 145 0 0.2513236194  0  0  4
## 146 0 0.0464566061  1  0  4
## 147 0 0.5632578691  0  1  3
## 148 0 0.2937375917  1  0  3
## 149 0 0.3509654081  1  0  3
## 150 0 0.0791809296  1  1  4
## 151 0 0.8253022840  1  0  2
## 152 0 0.2642138884  1  0  4
## 153 0 0.2638462810  0  0  3
## 154 0 0.0903810160  0  1  5
## 155 0 0.4608446269  1  1  3
## 156 0 0.6915760476  1  0  3
## 157 0 0.8489604222  1  1  3
## 158 0 0.2461148170  0  1  4
## 159 0 0.6509210938  1  1  2
## 160 0 0.6801953125  1  1  3
## 161 0 0.1045345513  1  1  3
## 162 0 0.1119856986  1  0  2
## 163 0 0.2156547720  0  1  2
## 164 0 0.1301163798  1  0  2
## 165 0 0.6663336323  0  0  3
## 166 0 0.4877746897  0  1  3
## 167 0 0.3533037403  1  0  3
## 168 0 0.9470107574  0  0  3
## 169 0 0.1119488380  0  0  3
## 170 0 0.5638697769  1  0  3
## 171 0 0.8483255904  0  1  4
## 172 0 0.5117678840  0  1  3
## 173 0 0.6665465659  1  1  3
## 174 0 0.0265097129  1  1  3
## 175 0 0.1064604088  1  1  3
## 176 0 0.6954418537  1  0  3
## 177 0 0.2733446639  0  1  3
## 178 0 0.7449695240  1  1  3
## 179 0 0.7453953503  1  0  3
## 180 0 0.1667326230  0  0  3
## 181 0 0.9798543244  0  1  3
## 182 0 0.5947587080  0  0  3
## 183 0 0.6882189384  1  1  3
## 184 0 0.1718581517  0  0  3
## 185 0 0.0416831505  1  1  3
## 186 0 0.1898498912  1  1  3
## 187 0 0.7614218323  1  1  2
## 188 0 0.5594733323  0  0  3
## 189 0 0.5055143666  1  0  3
## 190 0 0.9728052951  1  1  2
## 191 0 0.0806008175  1  0  2
## 192 0 0.5572443432  1  0  3
## 193 0 0.8960071700  1  1  3
## 194 0 0.1078971149  0  1  3
## 195 0 0.4492812373  0  0  3
## 196 0 0.3088111347  0  0  4
## 197 0 0.2328826285  0  0  3
## 198 0 0.8280665197  0  1  4
## 199 0 0.1128784707  1  1  4
## 200 0 0.8840022471  1  1  2
## 201 0 0.7256201541  0  0  3
## 202 0 0.9203334250  1  1  4
## 203 0 0.1229573302  1  1  3
## 204 0 0.9511435630  0  1  3
## 205 0 0.6697030859  1  0  4
## 206 0 0.0850967949  0  1  2
## 207 0 0.5811568031  1  1  4
## 208 0 0.2125134552  0  1  3
## 209 0 0.2422193545  1  0  3
## 210 0 0.5362925141  0  0  3
## 211 0 0.1770604565  0  0  4
## 212 0 0.5704032232  1  0  3
## 213 0 0.1554149061  1  0  3
## 214 0 0.4744193235  1  1  3
## 215 0 0.7274061972  0  0  3
## 216 0 0.8463038874  0  0  3
## 217 0 0.9585764438  1  0  3
## 218 0 0.4588316823  0  1  3
## 219 0 0.3632254344  0  1  3
## 220 0 0.9363713360  1  0  3
## 221 0 0.8847720872  0  0  4
## 222 0 0.6706333186  1  1  2
## 223 0 0.8470589763  0  0  3
## 224 0 0.8596506736  0  0  3
## 225 0 0.4815454748  0  0  3
## 226 0 0.3170613982  1  1  3
## 227 0 0.9172041418  0  0  3
## 228 0 0.5046965585  0  0  4
## 229 0 0.0140720229  0  1  3
## 230 0 0.5955733217  0  0  2
## 231 0 0.4492498117  1  1  2
## 232 0 0.5392000761  1  0  4
## 233 0 0.0939198402  0  1  3
## 234 0 0.7509487895  1  1  4
## 235 0 0.0767992917  0  1  3
## 236 0 0.9290306640  1  0  3
## 237 0 0.8104190647  1  1  3
## 238 0 0.7613259845  0  0  3
## 239 0 0.6532063640  0  1  3
## 240 0 0.9401171594  0  0  3
## 241 0 0.7545649228  1  1  3
## 242 0 0.0841972905  1  1  4
## 243 0 0.9907066093  1  1  4
## 244 0 0.2699875943  0  0  3
## 245 0 0.1550296356  1  0  3
## 246 0 0.4841888184  1  0  3
## 247 0 0.6144657487  0  0  3
## 248 0 0.0806982385  1  0  3
## 249 0 0.9412467652  0  1  3
## 250 0 0.2032089424  1  1  3
## 251 0 0.1984645734  0  1  2
## 252 0 0.1957958306  1  0  4
## 253 0 0.9078547994  1  0  2
## 254 0 0.5332889208  0  1  2
## 255 0 0.6833354323  1  1  3
## 256 0 0.5401932111  0  0  3
## 257 0 0.5734838906  0  1  4
## 258 0 0.8467235053  0  1  2
## 259 0 0.5999798262  0  1  3
## 260 0 0.2315073176  1  0  3
## 261 0 0.9952321625  0  0  4
## 262 0 0.8029856614  0  1  1
## 263 0 0.8586663995  0  0  2
## 264 0 0.9569845379  1  0  2
## 265 0 0.0551437899  1  0  3
## 266 0 0.0680989958  0  1  3
## 267 0 0.4651018339  1  1  3
## 268 0 0.3234952011  0  0  3
## 269 0 0.6408634037  1  0  3
## 270 0 0.0106086857  1  0  3
## 271 0 0.1894404925  1  1  3
## 272 0 0.7720005722  0  1  3
## 273 0 0.0004447419  0  1  3
## 274 0 0.0171903830  1  0  3
## 275 0 0.3200655682  0  1  3
## 276 0 0.5294240620  0  1  4
## 277 0 0.6669622092  0  1  3
## 278 0 0.3918145306  1  0  3
## 279 0 0.2729253250  1  1  3
## 280 0 0.2881550833  0  0  2
## 281 0 0.7499863163  1  1  3
## 282 0 0.5185095530  0  1  2
## 283 0 0.7375858924  1  1  3
## 284 0 0.5644303011  0  1  2
## 285 0 0.2699479579  1  0  2
## 286 0 0.8742641583  1  0  3
## 287 0 0.6608892782  1  1  4
## 288 0 0.2380318267  0  0  3
## 289 0 0.8098499198  1  1  3
## 290 0 0.2351379597  1  1  4
## 291 0 0.5084400198  1  1  2
## 292 0 0.9213492125  0  1  3
## 293 0 0.9648818206  1  1  3
## 294 0 0.1283409251  0  1  3
## 295 0 0.3256000143  1  1  3
## 296 0 0.8055418341  1  0  3
## 297 0 0.4502127008  0  1  3
## 298 0 0.3627219510  0  1  2
## 299 0 0.7783999022  1  0  2
## 300 0 0.8081767145  1  0  3

Analisis Regresi Logistik

modelreglog <- glm(y~x1+x2+x3+x4, family=binomial(link = "logit"), data=datagab)
## Warning: glm.fit: algorithm did not converge
summary(modelreglog)
## 
## Call:
## glm(formula = y ~ x1 + x2 + x3 + x4, family = binomial(link = "logit"), 
##     data = datagab)
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.657e+01  1.174e+05       0        1
## x1          -7.234e-15  7.097e+04       0        1
## x2           8.288e-15  4.144e+04       0        1
## x3          -7.546e-15  4.122e+04       0        1
## x4          -1.645e-15  3.515e+04       0        1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 0.0000e+00  on 299  degrees of freedom
## Residual deviance: 1.7405e-09  on 295  degrees of freedom
## AIC: 10
## 
## Number of Fisher Scoring iterations: 25
summary(datagab)
##        y           x1                  x2               x3        
##  Min.   :0   Min.   :0.0004447   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0   1st Qu.:0.2663250   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0   Median :0.5377463   Median :1.0000   Median :0.0000  
##  Mean   :0   Mean   :0.5135692   Mean   :0.5367   Mean   :0.4933  
##  3rd Qu.:0   3rd Qu.:0.7562552   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :0   Max.   :0.9967167   Max.   :1.0000   Max.   :1.0000  
##        x4       
##  Min.   :1.000  
##  1st Qu.:3.000  
##  Median :3.000  
##  Mean   :3.027  
##  3rd Qu.:3.000  
##  Max.   :5.000

Summary

Berdasarkan studi kasus, tujuan analisis adalah untuk menentukan variabel yang paling signifikan berpengaruh terhadap status kematian pasien kanker otak (y). Mari kita tinjau keterkaitan hasil y dari variabel x1, x2, x3, dan x4.

  1. Variabel x1: Umur pasien penyandang kanker otak (tahun) Dari distribusi, terlihat bahwa umur pasien berkisar dari 0 hingga 86 tahun dengan rata-rata sekitar 15.57 tahun. Tidak ada korelasi langsung antara umur dan status kematian yang jelas. Namun, umumnya, penyakit kanker lebih sering terjadi pada pasien yang lebih tua, yang mungkin memiliki dampak pada ketahanan hidup.

  2. Variabel x2: Ada tidaknya riwayat genetik pada silsilah keluarga yang terkena kanker otak (0:nongenetik, 1:genetik) Dari distribusi, terlihat bahwa umur pasien berkisar dari 0 hingga 86 tahun dengan rata-rata sekitar 15.57 tahun. Tidak ada korelasi langsung antara umur dan status kematian yang jelas. Namun, umumnya, penyakit kanker lebih sering terjadi pada pasien yang lebih tua, yang mungkin memiliki dampak pada ketahanan hidup.

  3. Variabel x3: Cara pengobatan (0:tidak melakukan pengobatan intensif, 1:melakukan pengobatan intensif)x3: Cara pengobatan (0:tidak melakukan pengobatan intensif, 1:melakukan pengobatan intensif) Sekitar setengah dari pasien (49.33%) melakukan pengobatan intensif.Pasien yang menerima pengobatan intensif mungkin memiliki peluang bertahan hidup yang lebih baik dibandingkan dengan mereka yang tidak menerima perawatan intensif.

  4. Variabel x4: Stadium kanker (skala 4) Stadium kanker berkisar dari 1 hingga 5, dengan mayoritas pasien berada di stadium 3.Pasien dengan stadium kanker yang lebih tinggi mungkin memiliki tingkat kematian yang lebih tinggi karena penyakit tersebut telah berkembang lebih lanjut.

Jadi secara keseluruhan, kesimpulan yang dapat diambil adalah: 1. Variabel yang paling signifikan berpengaruh terhadap status kematian pasien kanker otak (y) mungkin bervariasi tergantung pada analisis statistik yang dilakukan, seperti regresi kox atau analisis kelangsungan hidup Kaplan-Meier. 2. Namun, dari tinjauan awal, variabel yang kemungkinan memiliki pengaruh signifikan adalah riwayat genetik (x2) dan cara pengobatan (x3), karena keduanya memiliki implikasi langsung terhadap prognosis dan perawatan pasien. 3. Variabel lainnya, seperti umur (x1) dan stadium kanker (x4), juga penting untuk dipertimbangkan dalam analisis karena mereka juga dapat memengaruhi hasil kematian pasien.

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