We introduce a new end-to-end computer aided detection and diagnosis system for lung cancer screening using low-dose CT scans. Our system is based on 3D convolutional neural networks and achieves state-of-the-art performance for both lung nodule detection and malignancy classification tasks on the publicly available LUNA16 and Kaggle Data Science Bowl challenges. Furthermore, we characterize model uncertainty in our system and show that we can use this to provide well-calibrated classification probabilities for nodule detection and patient malignancy diagnosis. To the best of our knowledge, model uncertainty has not been considered in the context of lung CT analysis before. These calibrated probabilities informed by model uncertainty can be used for subsequent risk-based decision making towards diagnostic interventions or disease treatments, as we demonstrate using a probability-based patient referral strategy to further improve our results.