In this paper, we propose a novel approach for traffic accident anticipation through (i) Adaptive Loss for Early Anticipation (AdaLEA) and (ii) a large-scale self-annotated incident database for anticipation. The proposed AdaLEA allows a model to gradually learn an earlier anticipation as training progresses. The loss function adaptively assigns penalty weights depending on how early the model can anticipate a traffic accident at each epoch. Additionally, we construct a Near-miss Incident DataBase for anticipation. This database contains an enormous number of traffic near-miss incident videos and annotations for detail evaluation of two tasks, risk anticipation and risk-factor anticipation. In our experimental results, we found our proposal achieved the highest scores for risk anticipation (+6.6% better on mean average precision (mAP) and 2.36 sec earlier than previous work on the average time-to-collision (ATTC)) and risk-factor anticipation (+4.3% better on mAP and 0.70 sec earlier than previous work on ATTC).