Smoothing survival densities in practice

Abstract

Many nonparametric smoothing procedures consider independent identically distributed stochastic variables. There are also many important nonparametric smoothing applications where the data is more complicated. Survival data or filtered data, defined as following Aalen’s multiplicative hazard model and aggregated versions of this model, are considered. Aalen’s model based on counting process theory allows multiple left truncations and multiple right censoring to be present in the data. This type of filtering is omnipresent in biostatistical and demographical applications, where people can join a study, leave the study and perhaps join the study again. The estimation methodology is based on a recent class of local linear density estimators. A new stable bandwidth-selector is developed for these estimators. A data application to aggregated national mortality data is provided, where immigrations to and from the country correspond to respectively left truncation and right censoring. The aggregated mortality data study illustrates that the new practical density estimators provide an important extra element in the visual toolbox for understanding survival data.