This paper presents a method for quantifying uncertainty and improving interpretability in clinical trial approval prediction. The authors propose a selective classification approach integrated with the Hierarchical Interaction Network (HINT), a state-of-the-art clinical trial prediction model. The selective classification approach enables the model to withhold decision-making when faced with ambiguous or low-confidence samples, thereby enhancing both prediction accuracy and model interpretability. Comprehensive experiments show that incorporating uncertainty significantly improves the model's performance, with the proposed method achieving 32.37%, 21.43%, and 13.27% relative improvements in area under the precision-recall curve for phase I, II, and III trial approvals, respectively. For phase III trials, the method achieves an area under the precision-recall curve of 0.9022. The authors also demonstrate a case study of interpretability that helps domain experts understand the model's outcomes. The code is publicly available at https://github.com/Vincent-1125/Uncertainty-Quantification-on-Clinical-Trial-Outcome-Prediction. The study highlights the importance of uncertainty quantification and interpretability in clinical trial approval prediction, emphasizing the need for precision and care in predictive analytics within clinical research. The findings advocate for the continued development and refinement of models like HINT, with potential impacts on patient outcomes and trial design efficiency.This paper presents a method for quantifying uncertainty and improving interpretability in clinical trial approval prediction. The authors propose a selective classification approach integrated with the Hierarchical Interaction Network (HINT), a state-of-the-art clinical trial prediction model. The selective classification approach enables the model to withhold decision-making when faced with ambiguous or low-confidence samples, thereby enhancing both prediction accuracy and model interpretability. Comprehensive experiments show that incorporating uncertainty significantly improves the model's performance, with the proposed method achieving 32.37%, 21.43%, and 13.27% relative improvements in area under the precision-recall curve for phase I, II, and III trial approvals, respectively. For phase III trials, the method achieves an area under the precision-recall curve of 0.9022. The authors also demonstrate a case study of interpretability that helps domain experts understand the model's outcomes. The code is publicly available at https://github.com/Vincent-1125/Uncertainty-Quantification-on-Clinical-Trial-Outcome-Prediction. The study highlights the importance of uncertainty quantification and interpretability in clinical trial approval prediction, emphasizing the need for precision and care in predictive analytics within clinical research. The findings advocate for the continued development and refinement of models like HINT, with potential impacts on patient outcomes and trial design efficiency.