Selection instability and coefficient uncertainty in Cox modelling after Lasso selection
Abstract
After variable selection, uncertainty quantification often treats the selected model as fixed, although it may change under repeated sampling. We investigate whether this variability can be incorporated by repeating Cox-Lasso selection within a model-based bootstrap after unpenalised Cox refitting. We compare conventional post-selection Cox Wald intervals and a model-based bootstrap without re-selection, both of which keep the selected predictor set fixed, with two re-selection procedures: one retains the observed tuning-parameter value, whereas the other reapplies the cross-validation minimum (CV-min) tuning rule within each bootstrap sample. Against the data-generating coefficients, procedures holding the selected predictor set fixed frequently showed substantial undercoverage. Re-selection generally moved coverage closer to the nominal level, although performance varied across simulation regimes and coefficients. Sensitivity analyses evaluating coverage against the population Cox coefficients corresponding to each originally selected predictor set gave similar aggregate coverage for the primary interval comparison. In the NKI70 breast-cancer data, the four selected genes appeared together in only 0.6% of bootstrap samples under re-selection at the observed tuning-parameter value. These results suggest that selection instability can be an important component of post-selection coefficient uncertainty and that bootstrap re-selection can help incorporate this variability.
Related
- Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty
- Numerical Realization of an Entropy-Based Selection Principle in the Example of Kelvin-Helmholtz Instability
- Model selection for imperfect computer codes under discrepancy-aware calibration: application to IATE closure modelling
- MCMC-Free Uncertainty Quantification for Deep Generative Inference for Spatially Varying Coefficient Models at Scale
- Empowering Bayes with sources of uncertainty: from confidence modelling to sparse estimation
BibTeX
@misc{schemet2026selection,
title = {{Selection instability and coefficient uncertainty in Cox modelling after Lasso selection}},
author = {Lena Schemet and Andreas Groll and Sarah Friedrich-Welz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04765},
eprint = {2611.04765},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04765},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Selection instability and coefficient uncertainty in Cox modelling after Lasso selection
AU - Lena Schemet
AU - Andreas Groll
AU - Sarah Friedrich-Welz
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04765
UR - https://arxiv.org/abs/2611.04765
AB - After variable selection, uncertainty quantification often treats the selected model as fixed, although it may change under repeated sampling. We investigate whether this variability can be incorporated by repeating Cox-Lasso selection within a model-based bootstrap after unpenalised Cox refitting. We compare conventional post-selection Cox Wald intervals and a model-based bootstrap without re-selection, both of which keep the selected predictor set fixed, with two re-selection procedures: one retains the observed tuning-parameter value, whereas the other reapplies the cross-validation minimum (CV-min) tuning rule within each bootstrap sample. Against the data-generating coefficients, procedures holding the selected predictor set fixed frequently showed substantial undercoverage. Re-selection generally moved coverage closer to the nominal level, although performance varied across simulation regimes and coefficients. Sensitivity analyses evaluating coverage against the population Cox coefficients corresponding to each originally selected predictor set gave similar aggregate coverage for the primary interval comparison. In the NKI70 breast-cancer data, the four selected genes appeared together in only 0.6% of bootstrap samples under re-selection at the observed tuning-parameter value. These results suggest that selection instability can be an important component of post-selection coefficient uncertainty and that bootstrap re-selection can help incorporate this variability.
ER -