  In prediction settings where data are collected over time, 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. These
measures can be estimated and the same approaches for inference can be applied
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, and we illustrate their use by investigating the longitudinal
importance of risk factors for suicide attempt.
