Multi-omics data present significant challenges for statistical inference due to the complex interdependencies among biological layers. In this paper, we introduce a novel Multi-Omics Factor-Adjusted Cox (MOFA-Cox) model for analyzing multi-omics survival data, effectively addressing the intricate correlations across various omics layers. We provide a factor-adjusted decorrelated score test for the MOFA-Cox model in high-dimensional survival analysis. Our method accommodates situations where the dimension of the parameters being tested exceeds the sample size, while not imposing a sparsity assumption on them. We establish the limiting null distribution of the proposed test and analyze its power under local alternatives. Numerical studies and an application to the TCGA breast cancer dataset demonstrate the effectiveness of our method.

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