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Example high-dimensional survival data

ExampleData_highdim.Rd

A simulated survival dataset in a high-dimensional linear setting with 50 covariates (6 signals + 44 AR(1) noise), Weibull baseline hazard, and controlled censoring. Includes internal train/test sets, and an external-data–estimated coefficient vector.

Usage

data(ExampleData_highdim)

Format

A list containing the following elements:

train

A list with components:

z

Data frame of size \(n_\mathrm{train}\times 50\) with covariates Z1–Z50.

status

Vector of event indicators (1=event, 0=censored).

time

Numeric vector of observed times \(\min(T, C)\).

stratum

Vector of stratum labels (here all 1).

test

A list with the same structure as train, with size \(n_\mathrm{test}\times 50\) for z.

beta_external

Numeric vector (length 50, named Z1–Z50) of Cox coefficients estimated on an external dataset using only Z1–Z6 and expanded to length 50 (zeros for Z7–Z50).

Details

Data-generating mechanism:

  • Covariates: 50 variables with signals Z1–Z6 and noise Z7–Z50.

    • Z1, Z2 ~ bivariate normal with AR(1) correlation \(\rho=0.5\).

    • Z3, Z4 ~ independent Bernoulli(0.5).

    • Z5 ~ \(N(2,1)\), Z6 ~ \(N(-2,1)\) (group indicator fixed at 1).

    • Z7–Z50 ~ multivariate normal with AR(1) correlation \(\rho=0.5\).

  • True coefficients: \(\beta = (0.3,-0.3,0.3,-0.3,0.3,-0.3,0,\ldots,0)\) (length 50).

  • Event times: Weibull baseline hazard \(h_0(t)=\lambda\nu\, t^{\nu-1}\) with \(\lambda=1\), \(\nu=2\). Given linear predictor \(\eta = Z^\top \beta\), draw \(U\sim\mathrm{Unif}(0,1)\) and set $$T = \left(\frac{-\log U}{\lambda\, e^{\eta}}\right)^{1/\nu}.$$

  • Censoring: \(C\sim \mathrm{Unif}(0,\text{ub})\) with ub tuned iteratively to achieve the target censoring rate (internal: 0.70; external: 0.50). Observed time is \(\min(T,C)\), status is \(\mathbf{1}\{T \le C\}\).

  • External coefficients: Fit a Cox model Surv(time, status) ~ Z1 + ... + Z6 on the external data (Breslow ties), then place the estimated coefficients into a length-50 vector (zeros elsewhere).

Examples

data(ExampleData_highdim)

head(ExampleData_highdim$train$z)
#>           Z1         Z2 Z3 Z4       Z5        Z6          Z7         Z8
#> 1  0.8341847  1.2548397  0  1 1.230205 -1.379354  0.29715594 -0.1846824
#> 2 -0.3289623 -0.5440874  1  1 3.009319 -2.027648  0.06107997 -0.7877205
#> 3 -3.1720374 -0.4180468  1  0 2.387088 -2.780979 -0.85233051 -1.3215052
#> 4  0.1281318 -0.8776107  1  1 2.521981 -2.184659 -0.71413081  0.9238884
#> 5 -1.2284273 -0.7566494  0  1 1.762825 -2.555997 -1.87046640 -1.2583798
#> 6  0.8213465  1.4635825  1  1 1.887867 -1.232408  0.02923435 -0.5281927
#>           Z9        Z10        Z11        Z12        Z13        Z14        Z15
#> 1  1.0982052  0.4904068  0.5025818  0.9381855  0.4799360  0.3437346  0.4320523
#> 2 -1.2572372 -0.7316574 -1.2545473  0.3399338 -2.3401946 -0.6721147 -0.7741806
#> 3 -0.8917207  0.5492385  1.2280196 -0.4813451  0.4396726  0.5759964 -0.3324509
#> 4  0.2700611 -0.5746064 -0.3090879  0.2892202  1.2383940  1.4950458 -0.2552768
#> 5 -0.8879612 -1.1652591 -1.3263840  0.1811636  1.0627427  0.7584533  0.8554499
#> 6 -1.3821379  0.7588488  1.1300513 -0.3151114  0.2124996 -0.7406890 -0.6363002
#>          Z16        Z17        Z18         Z19         Z20        Z21
#> 1  0.8633326  0.7533490  1.0215138  1.51246470  0.94004928 -0.2257148
#> 2 -0.0393791 -0.5752974 -0.8462299 -0.16716546 -1.79317838 -0.5395597
#> 3 -1.3388491  0.1427682 -0.2026194  1.60425188  2.47017074  0.4935123
#> 4 -0.5982543  0.1761313 -0.9428526 -0.98955493  1.55572861  1.5238076
#> 5 -0.6517327 -1.5715401 -0.8141908 -0.03304642 -0.01628385 -1.3252785
#> 6 -1.2840411  0.1747675 -0.1237938  0.29138370  0.14430507  0.6488622
#>          Z22        Z23        Z24         Z25        Z26        Z27        Z28
#> 1  1.2631874 -0.8176610 -1.3054956 -2.59423303 -1.0819914 -1.7759045 -0.3130515
#> 2  0.2219920 -1.3828436  0.2169797  0.69637444  0.1963209  0.3101008  0.1045186
#> 3 -0.5419710 -0.5775182 -0.9108406  0.18592158  1.3871736  0.2519995  0.9655862
#> 4  0.7762024 -0.3625580 -1.6130505 -1.06893004  0.3174351  1.0103921 -0.4376606
#> 5 -0.6695136 -0.5061301  0.0331691 -0.73308691  0.2968483  0.3420247  0.3465201
#> 6  1.7856642 -0.8147424 -1.9587034 -0.05948988 -1.1346326  0.2344805 -0.5347376
#>          Z29        Z30        Z31        Z32         Z33         Z34
#> 1  0.1450573 -0.3522625  1.3583706 -1.1354976 -0.08176453  0.90301566
#> 2  0.1736015  0.1832902 -1.0431791 -1.6964999 -1.59347993 -2.33205882
#> 3 -0.3261791 -0.2129586 -1.1342233 -0.4226060  0.96752663 -0.11062591
#> 4 -1.0527535 -0.6244569 -0.3397628  1.1462418  0.45662572  0.05212241
#> 5 -0.7050586 -0.8054282 -0.8825711 -1.4828052  0.14471226  0.12423004
#> 6  0.1302796  0.4279924  0.5541080  0.5823341 -0.53471012 -0.37043642
#>           Z35         Z36        Z37        Z38        Z39        Z40
#> 1 -0.33873339  0.90547061  0.9280060 -0.1313232 -0.5279536  0.7480440
#> 2 -2.03014417 -1.01837762 -0.9425266 -0.7156324 -1.2498089  0.2309582
#> 3 -0.04469714 -0.05222202 -0.8417919 -0.5504270  0.6418680  1.4240399
#> 4 -0.21573577 -0.91514694  0.1936167  0.4127731  0.1198166  0.2578691
#> 5  1.04310306  1.31328693  0.1785853 -2.0694800 -2.3911914 -1.2461304
#> 6  0.79710530  0.36294685  0.8356093  0.3896813 -0.9716663 -0.4682918
#>            Z41         Z42          Z43        Z44         Z45         Z46
#> 1  0.626297434  0.04292509  0.612210812 -1.2068899 -1.03689495 -0.63210927
#> 2  1.043110114  0.51952039 -0.709333558  1.5400533  1.40551197  2.54570573
#> 3  0.009322651  1.00946381  0.201396249  0.7608163  0.60980799  0.07967597
#> 4  0.375786446 -0.07833188  0.004788632  1.4215175  1.26539924 -1.54623996
#> 5 -0.205232458  1.02566517  1.481439960  2.0989416  0.04201603 -0.39717619
#> 6 -0.662404892  0.11826542 -0.038936256 -1.8301693 -1.24983745 -0.61987848
#>           Z47       Z48        Z49        Z50
#> 1 -0.75296206 -1.466023 -0.6107553  0.5837428
#> 2  1.88849816  2.157199  0.6465888 -0.3936396
#> 3  0.25028165 -1.490555 -0.6696376  0.6741264
#> 4  1.26147753 -0.467992  1.0971287  1.3047671
#> 5  0.01994461 -0.493669 -0.3828498  0.5840523
#> 6  0.28317437  1.268658  1.8107407  0.1405356
table(ExampleData_highdim$train$status)
#> 
#>   0   1 
#> 144  56 
summary(ExampleData_highdim$train$time)
#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
#> 0.002357 0.118257 0.226289 0.229358 0.339145 0.575841 

head(ExampleData_highdim$test$z)
#>           Z1          Z2 Z3 Z4        Z5        Z6         Z7          Z8
#> 1 -0.8755157 -0.19970306  1  0 2.4542939 -3.280559 0.13764707 -0.29951270
#> 2  0.8236265  0.07930611  1  0 1.4890025 -3.938458 0.22951537 -0.27756548
#> 3  0.9263612 -0.01997836  1  1 0.6358499 -3.195342 0.52670452  0.05328195
#> 4  0.1850598 -0.70337717  0  1 2.2810817 -4.434547 0.79721336 -0.31697608
#> 5  0.3474487 -0.42614590  0  0 0.7145202 -2.830799 0.07278411 -1.42828452
#> 6 -0.8803044 -0.91163905  0  0 2.4224220 -2.329654 1.28874933 -0.30053293
#>           Z9        Z10         Z11        Z12        Z13        Z14        Z15
#> 1 -1.8593895 -0.1736244 -0.03612483  1.7472408  1.7360144  1.6572400  0.7806403
#> 2  0.2713486  0.2236954 -1.35911106 -0.3897491 -0.3989989  0.1117077 -0.2587745
#> 3  0.2293453 -0.5221144 -0.41978900 -0.6275746 -1.0680740  0.5019976  0.9790618
#> 4 -1.0048234 -1.1459370  0.26200422  0.4194908  2.3126135  0.6683572  0.6028322
#> 5 -0.4451788  0.4631919  1.05744097  1.3881108  1.2026630 -1.8938359 -1.0292716
#> 6 -0.7162089  1.0104155 -0.38368599  0.4486694 -0.6833364 -1.1513100 -0.1524856
#>          Z16        Z17         Z18         Z19         Z20        Z21
#> 1  1.0419634  1.0014758  0.87853402  1.20154893  0.70993166  0.6926842
#> 2  2.5036764  1.0563505  0.49304476  0.83883757  0.53522160  1.7725695
#> 3  1.9456876  0.2410226  0.93140905 -0.50013494 -0.24039917 -1.3943652
#> 4  0.6518553  0.5833234  0.56267706 -0.68226000 -0.49821852  0.4635016
#> 5 -1.1394870 -0.6498890 -0.63055354 -0.67106393 -1.36795205  0.7937763
#> 6 -2.1706700 -0.6895768 -0.09568807  0.01370934  0.07330939  1.4275766
#>          Z22         Z23         Z24         Z25         Z26        Z27
#> 1  0.1522400  0.72886816  0.96106634  0.75738274 -0.24679473  0.3333615
#> 2  0.1914927 -0.24217057 -1.69998202 -0.83921306 -0.83895440  0.2525735
#> 3  0.2215496 -3.38045379 -1.67431365 -0.08341914 -1.07549132 -0.9306513
#> 4  0.8072025 -0.06383284  1.40726238  0.61687798  0.42779651  0.3411079
#> 5 -0.8177690 -0.07890665  1.10520120  0.75595253  2.58006781  1.6626002
#> 6  1.1219039  2.08552715 -0.01395411 -0.58492795  0.05189429  0.3238361
#>          Z28        Z29          Z30         Z31          Z32         Z33
#> 1  1.8533162  1.1413543  0.006618972 -0.31956804  0.221347062  0.01912242
#> 2 -0.3164956 -1.3575425  0.098572849  0.53449844 -0.008900405 -1.03863804
#> 3 -1.4797537 -0.3794754 -0.995543024 -1.07427224  0.071562637 -1.64276895
#> 4 -0.1274482 -0.4986956 -1.922319725 -0.84184222 -0.806627329  0.19492516
#> 5  1.3229320  0.9924067 -0.181815965  0.04308887  1.322061805  0.33903185
#> 6 -0.9531971 -0.7657889  0.221706398 -0.39189299 -0.107754578  0.14435895
#>           Z34         Z35         Z36         Z37         Z38        Z39
#> 1  0.02259753 -0.03638311  1.31072107  0.63267465  0.70821261 -0.9644446
#> 2 -0.83534512 -1.02532257  1.42087476  1.59472721  0.99560368  0.8583339
#> 3 -1.88285945 -1.23116307 -0.74063599 -0.07947944  0.84127101  0.6270051
#> 4 -0.57991673 -0.05609040 -0.03119781 -0.18212746 -0.03795407  1.4248389
#> 5  0.96870265  0.25522277  0.44204637  0.61391922  1.20862465  0.8528802
#> 6 -0.27541315  1.29134035  2.20868594  1.90517098  2.78024828  1.5704774
#>           Z40          Z41        Z42         Z43        Z44        Z45
#> 1  0.22510720  0.007031161  0.7480677 -0.33153709 -0.1101352 -0.4382325
#> 2 -0.18666426 -0.453598905  0.3280036 -0.07132729 -0.2260509 -1.3126325
#> 3  0.41890927 -0.893598361 -2.9933830 -0.48448676 -0.1082089 -0.6425374
#> 4  2.43427290 -0.059044636 -0.2373969  1.03315480  0.6519150  0.4775821
#> 5  0.07008611 -0.466548212 -1.4381315 -1.17389378 -0.8892987 -1.9979700
#> 6  1.82803873  0.190203105  0.5919327 -0.88877615 -0.4811745  0.6985946
#>           Z46        Z47        Z48          Z49        Z50
#> 1 -0.80117966  0.3576286 -1.0226513  0.301427228  1.5643462
#> 2 -0.06452281  0.2829715  1.0356304  0.984220152 -0.4857993
#> 3 -1.16150511 -0.4833850 -0.3193366 -0.001306896  0.0298568
#> 4 -0.41523841 -0.1098118  1.3527896  1.375761270  2.1009230
#> 5 -0.71063502  1.2419492  1.5455219 -0.117504888 -0.3591661
#> 6  0.82786996 -0.3889966 -1.9303816 -1.512722570 -1.8478961
table(ExampleData_highdim$test$status)
#> 
#>    0    1 
#> 1376  624 
summary(ExampleData_highdim$test$time)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> 0.0003132 0.1309088 0.2467850 0.2605349 0.3766332 0.6122603