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Deep neural network models, especially Long Short Term Memory (LSTM), have shown great success in analyzing Electronic Health Records (EHRs) due to their ability to capture temporal dependencies in time series data. When applying the deep learning models to EHRs, we are generally confronted with two major challenges: high rate of missingness and time irregularity. Motivated by the original PACIFIER framework which utilized matrix decomposition for data imputation, we applied and further extended it by including three components: forecasting future events, a time-aware mechanism, and a subgroup basis approach. We evaluated the proposed framework with real-world EHRs which consists of 52,919 visits and 4,224,567 events on a task of early prediction of septic shock. We compared our work against multiple baselines including the original PACIFIER using both LSTM and Time-aware LSTM (T-LSTM). Experimental results showed that our proposed framework significantly outperformed all competitive baseline approaches. More importantly, the extracted interpretative latent patterns from subgroups could shed some lights for clinicians to discover the progression of septic shock patients.