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Integrating cross-department multi-modal data (e.g., radiological, pathological, genomic, and clinical data) is ubiquitous in brain cancer diagnosis and survival prediction. To date, such an integration is typically conducted by human physicians (and panels of experts), which can be subjective and semi-quantitative. Recent advances in multi-modal deep learning, however, have opened a door to leverage such a process to a more objective and quantitative manner. Unfortunately, the prior arts of using four modalities on brain cancer survival prediction are limited by a "complete modalities" setting (i.e., with all modalities available). Thus, there are still open questions on how to effectively predict brain cancer survival from the incomplete radiological, pathological, genomic, and demographic data (e.g., one or more modalities might not be collected for a patient). For instance, should we use both complete and incomplete data, and more importantly, how to use those data? To answer the preceding questions, we generalize the multi-modal learning on cross-department multi-modal data to a missing data setting. Our contribution is three-fold: 1) We introduce optimal multi-modal learning with missing data (MMD) pipeline with optimized hardware consumption and computational efficiency; 2) We extend multi-modal learning on radiological, pathological, genomic, and demographic data into missing data scenarios; 3) a large-scale public dataset (with 962 patients) is collected to systematically evaluate glioma tumor survival prediction using four modalities. The proposed method improved the C-index of survival prediction from 0.7624 to 0.8053.