ABSTRACT
The conditional distribution functions and their functionals discussed in Chapter 12 are only limited to the situations with time-invariant and categorical covariates. For this reason, nonparametric estimators of the conditional distribution functions can be constructed using the kernel smoothing methods without imposing any modeling structures between the response variable and the covariates. This unstructured estimation approach may not work well when there are time-varying and continuous covariates, because unstructured estimation in such situations requires high-dimensional multivariate kernel smoothing that may only work when the sample size is unusually large. In this chapter, we introduce a class of structured nonparametric models, namely the time-varying transformation models, for the conditional distribution functions, which can incorporate the time-varying and continuous covariates. This class of models, which was first suggested by Wu, Tian and Yu (2010), provides a simple and flexible framework for connecting the well-known regression models in survival analysis with the time-varying random variables.
