  In survival analysis, complex machine learning algorithms have been
increasingly used for predictive modeling. Given a collection of features
available for inclusion in a predictive model, it may be of interest to
quantify the relative importance of a subset of features for the prediction
task at hand. In particular, in HIV vaccine trials, participant baseline
characteristics are used to predict the probability of infection over the
intended follow-up period, and investigators may wish to understand how much
certain types of predictors, such as behavioral factors, contribute toward
overall predictiveness. Time-to-event outcomes such as time to infection are
often subject to right censoring, and existing methods for assessing variable
importance are typically not intended to be used in this setting. We describe a
broad class of algorithm-agnostic variable importance measures for prediction
in the context of survival data. We propose a nonparametric efficient
estimation procedure that incorporates flexible learning of nuisance
parameters, yields asymptotically valid inference, and enjoys
double-robustness. We assess the performance of our proposed procedure via
numerical simulations and analyze data from the HVTN 702 study to inform
enrollment strategies for future HIV vaccine trials.
