Model-based bootstrap inference for Cox models after Lasso selection

2026-08-19

AI Summary

该研究针对Cox回归变量选择后的推断问题，提出了一种基于模型的bootstrap方法，通过固定选择变量集并重拟合非惩罚Cox模型来改善有限样本条件下的覆盖率。

Abstract

Inference after variable selection in Cox regression is difficult because simple Wald-type intervals after selection can have poor finite-sample conditional coverage. We study a model-based bootstrap for inference after Cox-Lasso variable selection. The Cox-Lasso is fitted once to the original data to select a set of variables, after which an unpenalized Cox model is fitted using only those variables. Bootstrap samples are generated from a semiparametric plug-in Cox model specified by the coefficient estimate from this unpenalized Cox refit, the Breslow baseline cumulative hazard estimator, and a plug-in censoring distribution. In every bootstrap sample, the selected variable set is kept fixed and only the unpenalized Cox model is refitted. Under oracle-type sparse-model assumptions and standard Cox model regularity conditions, we prove first-order bootstrap validity for this procedure. In the simulation scenarios considered, percentile and studentized bootstrap intervals showed improved conditional coverage relative to the bootstrap-Wald interval in several small- and moderate-sample settings. Their performance was broadly competitive with debiased intervals, although the comparison depended on signal strength, tuning, and selection stability. A SEER breast cancer example illustrates that the procedure can be implemented in a realistic survival analysis and provides interpretable uncertainty quantification for effects reported after variable selection.

Problem

• Cox regression
• variable selection
• inference
• Wald-type intervals
• finite-sample conditional coverage

Innovation

• model-based bootstrap
• Cox-Lasso
• variable selection
• unpenalized Cox model
• conditional coverage