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 noninformative 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 P-splines, whereas covariate effects are flexibly determined using additive predictors. Parameter estimation is reliably carried out within a penalized maximum likelihood framework with integrated automatic multiple smoothing parameter selection. We derive the n-consistency and asymptotic normality of the noninformative 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 modeling framework is illustrated on data about infants hospitalized for pneumonia. The models and methods discussed in the article have been implemented in the R package GJRM to allow for transparent and reproducible research. Supplementary materials for this article are available online.