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Modeling patient disease progression using Electronic Health Records (EHRs) is critical to assist clinical decision making. While most of prior work has mainly focused on developing effective disease progression models using EHRs collected from an individual medical system, relatively little work has investigated building robust yet generalizable diagnosis models across different systems. In this work, we propose a general domain adaptation (DA) framework that tackles two categories of discrepancies in EHRs collected from different medical systems: one is caused by heterogeneous patient populations (covariate shift) and the other is caused by variations in data collection procedures (systematic bias). Prior research in DA has mainly focused on addressing covariate shift but not systematic bias. In this work, we propose an adversarial domain separation framework that addresses both categories of discrepancies by maintaining one globally-shared invariant latent representation across all systems} through an adversarial learning process, while also allocating a domain-specific model for each system to extract local latent representations that cannot and should not be unified across systems. Moreover, our proposed framework is based on variational recurrent neural network (VRNN) because of its ability to capture complex temporal dependencies and handling missing values in time-series data. We evaluate our framework for early diagnosis of an extremely challenging condition, septic shock, using two real-world EHRs from distinct medical systems in the U.S. The results show that by separating globally-shared from domain-specific representations, our framework significantly improves septic shock early prediction performance in both EHRs and outperforms the current state-of-the-art DA models.