Confirmatory Biomarker Identification with k-FWER Control Using Derandomized Knockoffs with Cox Regression

Selecting important features in high-dimensional survival analysis is critical for identifying confirmatory biomarkers while maintaining rigorous error control. In this paper, we propose a derandomized knockoffs procedure for Cox regression that enhances stability in feature selection while maintaining rigorous control over the k-familywise error rate (k-FWER). By aggregating across multiple randomized knockoff realizations, our approach mitigates the instability commonly observed with conventional knockoffs. Through extensive simulations, we demonstrate that our method consistently outperforms standard knockoffs in both selection power and error control. Moreover, we apply our procedure to a clinical dataset on primary biliary cirrhosis (PBC) to identify key prognostic biomarkers associated with patient survival. The results confirm the superior stability of the derandomized knockoffs method, allowing for a more reliable identification of important clinical variables. Additionally, our approach is applicable to datasets containing both continuous and categorical covariates, broadening its utility in real-world biomedical studies. This framework provides a robust and interpretable solution for high-dimensional survival analysis, making it particularly suitable for applications requiring precise and stable variable selection.

💡 Research Summary

This paper addresses the critical challenge of variable selection in high-dimensional survival analysis, with a focus on confirmatory biomarker discovery. The authors propose a novel methodological framework that integrates derandomized knockoffs with Cox proportional hazards regression to achieve both enhanced selection stability and rigorous control over the k-familywise error rate (k-FWER).

The research is motivated by the limitations of existing methods. While the knockoff filter provides flexible false discovery rate (FDR) control, its inherent randomness leads to instability in selected variables across different runs. Furthermore, for confirmatory studies like clinical biomarker validation, a more stringent error metric than FDR is often required. The k-FWER, which controls the probability of making at least k false discoveries, offers a stricter guarantee suitable for such settings.

The proposed method consists of two key innovations. First, it adapts the derandomized knockoffs procedure to the Cox model. Instead of relying on a single, potentially volatile run of the knockoff algorithm, the method aggregates results over M independent runs. For each run, knockoff copies of the original covariates are generated, and a Cox LASSO model is fitted. Importance statistics (W_j) are derived based on the maximum regularization parameter (λ) at which each variable’s coefficient becomes non-zero. A k-FWER-controlling threshold is then applied to select variables in each run. Finally, the selection frequency (π_j) for each variable across all M runs is computed. Variables with a selection frequency exceeding a pre-defined threshold (η) constitute the final, stable selection set. This aggregation step effectively averages out the randomness inherent in individual knockoff constructions.

Second, the method employs a sequential testing procedure to control the k-FWER at a desired level α, providing a stronger error guarantee than FDR for confirmatory analysis. The procedure is designed to handle datasets containing both continuous and categorical covariates without the need for problematic rescaling, broadening its applicability to real-world biomedical studies.

The authors validate their method through extensive simulations under various correlation structures, signal strengths, and dimensionality. The results consistently demonstrate that the derandomized approach (DeRand-k-FWER) achieves higher power (true positive rate) for identifying important variables while maintaining the target k-FWER level, outperforming the standard knockoff procedure (Standard-k-FWER). The superior stability of the derandomized method is a key highlight.

The practical utility of the framework is illustrated through an application to a real-world clinical dataset on Primary Biliary Cirrhosis (PBC). The method identifies a stable set of prognostic biomarkers, such as serum bilirubin and age, associated with patient survival time, confirming its effectiveness in deriving reliable insights from complex survival data.

In conclusion, this paper presents a robust and interpretable solution for high-dimensional survival analysis. By combining the stability of derandomized aggregation with the rigorous error control of k-FWER within the Cox model framework, it provides a powerful tool for precise and reliable variable selection, particularly valuable in confirmatory biomedical research contexts like clinical trial analysis and precision medicine.