Electronic health records (EHRs) have contributed to the computerization of patient records and can thus be used not only for efficient and systematic medical services, but also for research on biomedical data science. However, there are many missing values in EHRs when provided in matrix form, which is an important issue in many biomedical EHR applications. In this paper, we propose a two-stage framework that includes missing data imputation and disease prediction to address the missing data problem in EHRs. We compared the disease prediction performance of generative adversarial networks (GANs) and conventional learning algorithms in combination with missing data prediction methods. As a result, we obtained a level of accuracy of 0.9777, sensitivity of 0.9521, specificity of 0.9925, area under the receiver operating characteristic curve (AUC-ROC) of 0.9889, and F-score of 0.9688 with a stacked autoencoder as the missing data prediction method and an auxiliary classifier GAN (AC-GAN) as the disease prediction method. The comparison results show that a combination of a stacked autoencoder and an AC-GAN significantly outperforms other existing approaches. Our results suggest that the proposed framework is more robust for disease prediction from EHRs with missing data.