Biological systems are governed by structured molecular interactions, where pathways, regulatory circuits, and functional gene relationships shape cellular behavior and disease progression. Much of this knowledge is naturally represented as graphs. However, most biomedical AI models cannot directly use graph-encoded biological knowledge and instead require compressed low-dimensional representations, which can lose important structure and reduce performance, especially in limited-sample clinical studies. Here, we introduce Graph-in-Graph (GiG), a knowledge graph-modulated deep learning framework for data-efficient clinical prediction. GiG represents each patient as a standalone modular graph, in which curated biological knowledge graphs define edges and patient-specific measurements, such as gene expression, define node features. This design allows multiple biological knowledge graphs to be integrated while preserving gene-gene interactions and pathway topology during patient-level representation learning. Across cohorts comprising nearly 9,700 patients and five clinical tasks, including liquid biopsy cancer detection, prostate cancer diagnosis, and 32-class pan-cancer classification, GiG consistently outperforms traditional and state-of-the-art methods, with the largest gains in limited-sample settings. On the challenging prostate cancer diagnosis task, GiG improves macro-F1 by up to 49 percentage points relative to competing methods. Control experiments replacing real pathway graphs with random topologies confirm that these gains arise from biologically grounded knowledge graph structure rather than graph modeling alone. These findings show that knowledge graph-modulated deep learning can improve robustness, interpretability, and sample efficiency in clinical data analysis, and provide a principled framework for integrating biological knowledge graphs into predictive modeling.