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Example low-dimensional survival data

ExampleData_lowdim.Rd

A simulated survival dataset in a low-dimensional linear setting with 6 covariates (2 correlated continuous, 2 binary, 2 mean-shifted normals), Weibull baseline hazard, and controlled censoring. Includes internal train/test sets, and three external-quality coefficient vectors.

Usage

data(ExampleData_lowdim)

Format

A list containing the following elements:

train

A list with components:

z

Data frame of size \(n_\mathrm{train}\times 6\) with covariates Z1–Z6.

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 \(n_\mathrm{test}\times 6\) for z.

beta_external_good

Numeric vector (length 6; named Z1–Z6) of Cox coefficients estimated on a "Good" external dataset using all Z1–Z6.

beta_external_fair

Numeric vector (length 6; names Z1–Z6) of Cox coefficients estimated on a "Fair" external dataset using a reduced subset Z1, Z3, Z5, Z6; coefficients for variables not used are 0.

beta_external_poor

Numeric vector (length 6; names Z1–Z6) of Cox coefficients estimated on a "Poor" external dataset using Z1 and Z5 only; remaining entries are 0.

Details

Data-generating mechanism:

  • Covariates: 6 variables Z1–Z6.

    • 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 for internal train/test).

  • True coefficients: \(\beta = (0.3,-0.3,0.3,-0.3,0.3,-0.3)\) (length 6).

  • 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: For each quality level ("Good", "Fair", "Poor"), fit a Cox model Surv(time, status) ~ Z1 + ... on the corresponding external data (Breslow ties) using the specified covariate subset; place estimates into a length-6 vector named Z1–Z6 with zeros for variables not included.

Examples

data(ExampleData_lowdim)

head(ExampleData_lowdim$train$z)
#>           Z1          Z2 Z3 Z4       Z5         Z6
#> 1 -3.3155831 -1.89064873  1  0 2.317864 -1.5746080
#> 2 -1.2930025  1.22289522  0  0 4.586152 -2.6807152
#> 3 -1.1529450 -0.15452519  0  1 2.887956 -2.3298936
#> 4 -0.3027544 -0.70427194  1  1 1.946349 -1.4054008
#> 5 -0.2513522  0.06933996  1  1 1.665034 -2.9357721
#> 6  2.6636660  1.27748351  0  0 1.450750 -0.6265481
table(ExampleData_lowdim$train$status)
#> 
#>  0  1 
#> 71 29 
summary(ExampleData_lowdim$train$time)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> 7.290e-06 1.125e-01 2.219e-01 2.439e-01 3.477e-01 6.160e-01 

head(ExampleData_lowdim$test$z)
#>           Z1         Z2 Z3 Z4       Z5         Z6
#> 1 -0.4360609 -0.2970776  1  0 1.470499 -2.1341620
#> 2 -0.8269507 -0.2030743  1  0 1.144320 -0.8558692
#> 3  0.0168703 -0.7136223  0  0 2.754666 -3.2948610
#> 4  1.2085367 -1.0212701  0  0 1.634704 -2.4248350
#> 5  1.1490034  0.4739340  1  1 1.360401 -1.7800655
#> 6  0.2142821  1.1105678  1  0 2.039943 -2.4492855
table(ExampleData_lowdim$test$status)
#> 
#>    0    1 
#> 1410  590 
summary(ExampleData_lowdim$test$time)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> 3.316e-05 1.208e-01 2.265e-01 2.428e-01 3.625e-01 5.908e-01