We propose a novel approach to address the issue of college student attrition by developing a hybrid model that combines a structural neural network with a piecewise exponential model. This hybrid model not only shows the potential to robustly identify students who are at high risk of dropout, but also provides insights into which factors are most influential in dropout prediction. To evaluate its effectiveness, we compared the predictive performance of our hybrid model with two other survival analysis models: the piecewise exponential model and a hybrid model combining a fully-connected neural network with a piecewise exponential model. Additionally, we compared it to five other cross-sectional models: Ridge Logistic Regression, Lasso Logistic Regression, CART decision tree, Random Forest, and XGBoost decision tree. Our findings demonstrate that the hybrid model outperforms or performs comparably to the other models when predicting dropout among students at the University of Delaware in Spring 2020, Spring 2021, and Spring 2022. Moreover, by categorizing predictors into three distinct groups--academic, economic, and social-demographic--we discovered that academic predictors play a prominent role in distinguishing between dropout and retained students, while other predictors may indirectly influence predictions by impacting academic variables. Consequently, we recommend implementing an intervention program aimed at identifying at-risk students based on their academic performance and activities, with additional consideration for economic and social-demographic factors in customized intervention plans.