Inference on summaries of a model-agnostic longitudinal variable importance trajectory with application to suicide prevention

Risk of suicide attempt varies over time. Understanding the importance of risk factors measured at a mental health visit can help clinicians evaluate future risk and provide appropriate care during the visit. In prediction settings where data are collected over time, such as in mental health care, it is often of interest to understand both the importance of variables for predicting the response at each time point and the importance summarized over the time series. Building on recent advances in estimation and inference for variable importance measures, we define summaries of variable importance trajectories and corresponding estimators. The same approaches for inference can be applied to these measures regardless of the choice of the algorithm(s) used to estimate the prediction function. We propose a nonparametric efficient estimation and inference procedure as well as a null hypothesis testing procedure that are valid even when complex machine learning tools are used for prediction. Through simulations, we demonstrate that our proposed procedures have good operating characteristics. We use these approaches to analyze electronic health records data from two large health systems to investigate the longitudinal importance of risk factors for suicide attempt to inform future suicide prevention research and clinical workflow.