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In healthcare applications, temporal variables that encode movement, health status, and longitudinal patient evolution are often accompanied by rich structured information such as demographics, diagnostics and medical exam data. However, current methods do not jointly optimize over structured covariates and time series in the feature extraction process. We present ShortFuse, a method that boosts the accuracy of deep learning models for time series by explicitly modeling temporal interactions and dependencies with structured covariates. ShortFuse introduces hybrid convolutional and LSTM cells that incorporate the covariates via weights that are shared across the temporal domain. ShortFuse outperforms competing models by 3% on two biomedical applications, forecasting osteoarthritis-related cartilage degeneration and predicting surgical outcomes for cerebral palsy patients.