To address the privacy requirements of sensitive medical data, we present a multicenter diagnostic inference framework based on homomorphic encryption (HE). Leveraging the CKKS scheme implemented in the Lattigo library with 128-bit security, our method enables efficient and privacy-preserving inference for diseases such as bladder cancer, breast cancer, and sepsis. By exploiting the sparsity of LASSO parameters, we significantly reduce the computational overhead of encrypted inference. Notably, our LASSO-based analysis reveals a potential therapeutic target for bladder cancer. Experimental results across multiple datasets show that encrypted inference achieves performance comparable to plaintext inference, demonstrating that strong privacy can be preserved without sacrificing diagnostic performance.