An empirical saddlepoint approximation method for producing smooth survival and hazard functions under interval‐censoring

We devise a new method to produce smooth estimates of baseline survival and hazard functions for incomplete data observed subject to interval‐censoring, that can in principle be viewed as being nonparametric. The key idea is to start from the nonparametric maximum likelihood estimate, and to then construct an empirical moment generating function for the underlying data generating mechanism, which is subsequently inverted via a saddlepoint approximation in order to obtain smooth distributional estimates. Unlike the typical spline‐based and other semiparametric methods that have thus far been devised for the same purpose, the proposed approach is unencumbered by the choice of tuning parameters. Simulation studies show that in terms of integrated squared error, the method is very close in performance to the parametric gold standard, and should generally be preferred over the well‐established spline‐based approach implemented in R package logspline . The methodology is illustrated on some publicly available real datasets, and its implications and limitations are discussed.