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As the problem of drug abuse intensifies in the U.S., many studies that primarily utilize social media data, such as postings on Twitter, to study drug abuse-related activities use machine learning as a powerful tool for text classification and filtering. However, given the wide range of topics of Twitter users, tweets related to drug abuse are rare in most of the datasets. This imbalanced data remains a major issue in building effective tweet classifiers, and is especially obvious for studies that include abuse-related slang terms. In this study, we approach this problem by designing an ensemble deep learning model that leverages both word-level and character-level features to classify abuse-related tweets. Experiments are reported on a Twitter dataset, where we can configure the percentages of the two classes (abuse vs. non-abuse) to simulate the data imbalance with different amplitudes. Results show that our ensemble deep learning models exhibit better performance than ensembles of traditional machine learning models, especially on heavily imbalanced datasets.