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Multi-omics profiling characterizes cancer biology and supports biomarker discovery for prognosis and therapy selection. Although numerous computational multi-omics biomarker identification methods have been proposed, their ability to identify clinically relevant biomarkers has not been systematically evaluated, leaving it unclear whether the resulting biomarker nominations are reliable for downstream validation. Here, we systematically benchmark 20 representative statistical, machine learning and deep learning methods using curated gold-standard prognostic and therapeutic biomarkers across five real-world datasets. We evaluate performance in terms of both biomarker identification accuracy and stability. Overall, DeePathNet and DeepKEGG achieve the best performance. Across methods, effective biomarker recovery is associated with the integration of biological knowledge, global feature interactions, multivariate feature attribution, and effective regularization. Analysis of omics type contributions reveals method- and modality-specific biases, highlighting the importance of broader omics integration. We further evaluate methods on simulated datasets to probe sensitivity with controlled signal and noise. By aggregating results from top-performing methods, we construct consensus biomarker panels that nominate candidates for potential investigations. Finally, we provide user-friendly interfaces to allow researchers to benchmark new methods against the 20 baselines or apply selected methods for biomarker identification on custom multi-omics datasets. Our benchmark is publicly available at https://github.com/athanzli/CancerMOBI-Bench.