Integrative multi-omics studies consider the molecular events at different levels, and a major focus has been on leveraging information of different platforms to identify regulatory modules/gene-sets associated with clinical outcomes. A common strategy for such gene-set integrative analysis is to regress the clinical outcomes on all genomic variables in a gene set. However, the joint modeling methods encounter the challenges of high dimensional genomic variables, especially the sample size is usually moderate either due to research resources or missing data. In this work, we propose a tensor-based framework to enhance model efficiency while retaining the variable-wise resolution. We explore the variable-specific test procedure under tensor regression framework, and derive an alternative variance formula of the coefficient estimator that does not depend on the permutation matrix as required in previous work, which permits a systematic expression of the variance formula in computational coding. Finally, we demonstrate the utility of the tensor-based test using simulations and real data application on the TCGA dataset.