A three-stage approach to identify biomarker signatures for cancer genetic data with survival endpoints

The identification of prognostic and predictive biomarker signatures is crucial for drug development and providing personalized treatment to cancer patients. However, the discovery process often involves high-dimensional candidate biomarkers, leading to inflated family-wise error rates (FWERs) due to multiple hypothesis testing. This is an understudied area, particularly under the survival framework. To address this issue, we propose a novel three-stage approach for identifying significant biomarker signatures, including prognostic biomarkers (main effects) and predictive biomarkers (biomarker-by-treatment interactions), using Cox proportional hazard regression with high-dimensional covariates. To control the FWER, we adopt an adaptive group LASSO for variable screening and selection. We then derive adjusted p-values through multi-splitting and bootstrapping to overcome invalid p values caused by the penalized approach’s restrictions. Our extensive simulations provide empirical evaluation of the FWER and model selection accuracy, demonstrating that our proposed three-stage approach outperforms existing alternatives. Furthermore, we provide detailed proofs and software implementation in R to support our theoretical contributions. Finally, we apply our method to real data from cancer genetic studies.