Title: Flexible parametric generalised additive survival models with informative censoring
Authors: Robinson Dettoni - University College London (United Kingdom) [presenting]
Giampiero Marra - University College London (United Kingdom)
Rosalba Radice - Cass Business School (United Kingdom)
Abstract: Most estimation methodologies for censored time to event data assume that censoring is non-informative. In many applications, the censoring scheme may be in effect informative. The aim is to introduce a survival model with informative censoring which is flexible and easy to apply. The estimation of such models poses several challenges, and we propose a penalized maximum likelihood approach to this end. This framework allows us to incorporate the information provided by the censoring times to improve the efficiency of the proposed estimator. We also estimate the baseline functions flexibly via means of monotonic $P$-splines. Covariate effects are flexibly determined using additive predictors. Such a framework allows one to calculate easily several quantities of interest and their variances, such as time-dependent hazard or odds ratios, which would otherwise be difficult to obtain with a non-parametric approach. Confidence intervals for linear and non-linear functions of the model's coefficients, with good finite sample properties, are also provided. Information criteria and cross-validation can be employed to detect informative censoring in applications. The performance of the proposed method is investigated theoretically and via simulation studies. Both theory and simulation highlight the usefulness of the proposal. The proposed framework has been implemented in the R package GJRM, and applied to data on infants hospitalized for pneumonia.