Generalized Link-Based Additive Survival Models with Informative Censoring

Time to event data differ from other types of data because they are censored. Most of the related estimation techniques assume that the censoring mechanism is non-informative while in many applications it can actually be informative. The aim of this work is to introduce a class of flexible survival models which account for the information provided by the censoring times. The baseline functions are estimated non-parametrically by monotonic Psplines, whereas covariate effects are flexibly determined using additive predictors. Parameter estimation is reliably carried out within a penalised maximum likelihood framework with integrated automatic multiple smoothing parameter selection. We derive the √n-consistency and asymptotic normality of the non-informative and informative estimators, and shed light on the efficiency gains produced by the newly introduced informative estimator when compared to its non-informative counterpart. The finite sample properties of the estimators are investigated via a Monte Carlo simulation study which highlights the good empirical performance of the proposal. The modelling framework is illustrated on data about infants hospitalised for pneumonia. The models and methods discussed in the paper have been implemented in the R package GJRM to allow for transparent and reproducible researc