In recent years, there has been a rapid growth in the application of data science techniques that leverage aviation data collected from commercial airline operations to improve safety. This paper presents the application of machine learning to improve the understanding of risk factors during flight and their causal chains. With increasing complexity and volume of operations, rapid accumulation and analysis of this safety-related data has the potential to maintain and even lower the low global accident rates in aviation. This paper presents the development of an analytical methodology called Safety Analysis of Flight Events (SAFE) that synthesizes data cleaning, correlation analysis, classification-based supervised learning, and data visualization schema to streamline the isolation of critical parameters and the elimination of tangential factors for safety events in aviation. The SAFE methodology outlines a robust and repeatable framework that is applicable across heterogeneous data sets containing multiple aircraft, airport of operations, and phases of flight. It is demonstrated on Flight Operations Quality Assurance (FOQA) data from a commercial airline through use cases related to three safety events, namely Tire Speed Event, Roll Event, and Landing Distance Event. The application of the SAFE methodology yields a ranked list of critical parameters in line with subject-matter expert conceptions of these events for all three use cases. The work concludes by raising important issues about the compatibility levels of machine learning and human conceptualization of incidents and their precursors, and provides initial guidance for their reconciliation.