Traffic accidents are usually unique events with unpredictable geographical and temporal dimensions; thus, accident injury severity level (INJ-SL) analysis presents formidable categorization and data stability problems. Classical statistical models are limited in their ability to correctly model INJ-SL, whilst sophisticated machine learning approaches do not appear to have any equations to prioritize/analyze multiple contributing factors to forecast accidents accompanying INJ-SLs. In addition, the intercorrelations between the input variables may render the conclusions of a formal sensitivity analysis incorrectly. Rear-end collisions are the most common form of traffic accidents; consequently, their linked INJ-SL requires more research. This paper provides a complex technique based on a deep learning paradigm paired with different indicators of Global Sensitivity Analysis to address all of these concerns. Unlike existing neural network designs, this technique presents a deep residual neural network structure that employs residual shortcuts (i.e., connections). The connections enable the DRNNs to sidestep a few levels of the deep network architecture, evading the regular training with high accuracy issues. Using the trained DRNNs model, a Latin Hypercube sampling simulation was undertaken to determine each explanatory component's influence on the resulting INJ-SL. The latest available data from 2011 to 2018 is used to assess all rear-end collisions in North Carolina. A comparison was made between the performance of two different schemes of data categorization using a set of global sensitivity metrics. It was determined that the devised technique overcame the data heterogeneity problems to achieve an accuracy of 87%. In addition, the proposed sensitivity analysis identified the most relevant factors associated with INJ-SL rear-end collisions.