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Chronic obstructive pulmonary disease (COPD) is one of the most common chronic illnesses in the world and the third leading cause of mortality worldwide. It is often underdiagnosed or not diagnosed until later in the disease course. Spirometry tests are the gold standard for diagnosing COPD but can be difficult to obtain, especially in resource-poor countries. Chest X-rays (CXRs), however, are readily available and may serve as a screening tool to identify patients with COPD who should undergo further testing. Currently, no research applies deep learning (DL) algorithms that use large multi-site and multi-modal data to detect COPD patients and evaluate fairness across demographic groups. We use three CXR datasets in our study, CheXpert to pre-train models, MIMIC-CXR to develop, and Emory-CXR to validate our models. The CXRs from patients in the early stage of COPD and not on mechanical ventilation are selected for model training and validation. We visualize the Grad-CAM heatmaps of the true positive cases on the base model for both MIMIC-CXR and Emory-CXR test datasets. We further propose two fusion schemes, (1) model-level fusion, including bagging and stacking methods using MIMIC-CXR, and (2) data-level fusion, including multi-site data using MIMIC-CXR and Emory-CXR, and multi-modal using MIMIC-CXRs and MIMIC-IV EHR, to improve the overall model performance. Fairness analysis is performed to evaluate if the fusion schemes have a discrepancy in the performance among different demographic groups. The results demonstrate that DL models can detect COPD using CXRs, which can facilitate early screening, especially in low-resource regions where CXRs are more accessible than spirometry. The multi-site data fusion scheme could improve the model generalizability on the Emory-CXR test data. Further studies on using CXR or other modalities to predict COPD ought to be in future work.