To address the problem of uneven sample sizes in heterogeneous multi-institution chest X-ray classification, the researchers proposed the FedDRAW federated learning aggregation method. This method combines data size priors with the cosine similarity between clients and global parameters, using two coupled annealing scheduling mechanisms for weighting: the inner scheduling shifts client reputation from size priors to similarity, while the outer delayed annealing scheduling maintains weight selectivity in the early and middle stages of training and becomes more uniform as convergence progresses. The research team conducted comparative tests with seven federal baseline methods under 12 simulated client partitioning scenarios on the CheXpert and ChestMNIST datasets. The results showed that FedDRAW achieved the highest average ranking in both AUC and geometric mean values of sensitivity and specificity. The Friedman test, combined with Nemenyi post-hoc analysis, confirmed that this method differed statistically significantly from other methods.