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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)