This study introduces FedDropoutAvg, a federated learning method that incorporates dropout into client selection and model aggregation to improve tumor detection in colon histopathology images without sharing local data. The model was trained and evaluated on 1.2 million image tiles from 21 sites and compared with other federated learning benchmarks using held-out sites for independent testing. FedDropoutAvg outperformed existing FL methods and narrowed the performance gap with centralized training to less than 3% AUC, demonstrating improved generalizability.