Radiomics enables extraction of quantitative imaging biomarkers from medical images and has become an important tool for computer-aided cancer diagnosis. However, radiomics datasets are typically high-dimensional with limited samples, making feature selection a critical step for building reliable predictive models. This study proposes a Gradient-Loss Recursive Feature Elimination (GL-RFE) framework that integrates gradient sensitivity analysis from a deep neural network to identify the most influential radiomic features for lung cancer stage detection. A total of 106 radiomic features were extracted from chest Computed Tomography (CT) scans using the PyRadiomics extension of the 3D Slicer platform. The proposed method evaluates feature importance by computing gradients of the network loss with respect to input features and recursively eliminates features with minimal contribution. The resulting top-15 radiomic features are used to train a deep neural network classifier for distinguishing early-stage and advanced-stage lung cancer. The proposed framework achieves strong classification performance, with accuracy of 90.22%, precision of 90.10%, recall of 90.24%, and F1-score of 90.16% on the test dataset. Visualization analyses, including correlation heat maps and distribution plots, further confirm reduced feature redundancy and improved class separability. Compared to conventional feature selection techniques, GL-RFE effectively captures nonlinear feature interactions and enhances model generalization. The presented protocol provides a reproducible and interpretable methodology for radiomics-based cancer stage detection and is particularly suitable for high-dimensional, small-sample biomedical datasets, with potential applications in other domains such as genomics and multimodal clinical analysis.