Hypergraph neural networks can model multi-way connections among nodes of the graphs, which are common in real-world applications such as genetic medicine. In particular, genetic pathways or gene sets encode molecular functions driven by multiple genes, naturally represented as hyperedges. Thus, hypergraph-guided embedding can capture functional relations in learned representations. Existing hypergraph neural network models often focus on node-level or graph-level inference. There is an unmet need in learning powerful representations of subgraphs of hypergraphs in real-world applications. For example, a cancer patient can be viewed as a subgraph of genes harboring mutations in the patient, while all the genes are connected by hyperedges that correspond to pathways representing specific molecular functions. For accurate inductive subgraph prediction, we propose SubHypergraph Inductive Neural nEtwork (SHINE). SHINE uses informative genetic pathways that encode molecular functions as hyperedges to connect genes as nodes. SHINE jointly optimizes the objectives of end-to-end subgraph classification and hypergraph nodes' similarity regularization. SHINE simultaneously learns representations for both genes and pathways using strongly dual attention message passing. The learned representations are aggregated via a subgraph attention layer and used to train a multilayer perceptron for subgraph inferencing. We evaluated SHINE against a wide array of state-of-the-art (hyper)graph neural networks, XGBoost, NMF and polygenic risk score models, using large scale NGS and curated datasets. SHINE outperformed all comparison models significantly, and yielded interpretable disease models with functional insights.