Although there is a rich literature on methods for assessing the impact of functional predictors, the focus has been on approaches for dimension reduction that do not suit certain applications. Examples of standard approaches include functional linear models, functional principal components regression and cluster-based approaches, such as latent trajectory analysis. This article is motivated by applications in which the dynamics in a predictor, across times when the value is relatively extreme, are particularly informative about the response. For example, physicians are interested in relating the dynamics of blood pressure changes during surgery to post-surgery adverse outcomes, and it is thought that the dynamics are more important when blood pressure is significantly elevated or lowered.