ABSTRACT
This chapter introduces inferential methods for time-to-event data with functional and scalar predictors. Ideas and notation from traditional survival analysis are reviewed and then extended to account for functional predictors. The linear Functional Cox model is introduced and the connection to SoFR described in Chapter 4 is highlighted. Methods are extended to the case of survival outcomes with censoring and are applied to a study of time to death in the NHANES study where the baseline predictors include, in addition to traditional predictors, objectively measured minute-level physical activity data. Extensions of models are considered to incorporate multiple functional predictors, smooth the effects of scalar predictors, and additive functional models. Special attention is given to simulating realistic survival data sets with functional predictors using the inverse of the estimated survival distributions. Methods are implemented using both the refund::pfr function and mgcv. Just as in other chapters, an extensive discussion of correlation and multiplicity adjusted (CMA) inference (confidence intervals and p-values) is provided.
