Penalized spline estimation in varying coefficient models with censored data

Abstract

We consider P-spline smoothing in a varying coefficient regression model when the response is subject to random right censoring.We introduce two data transformation approaches to construct a synthetic response vector that is used in a penalized least squares optimization problem. We prove the consistency and asymptotic normality of the P-spline estimators for a diverging number of knots and show by simulation studies and real data examples that the combination of a data transformation for censored observations with P-spline smoothing leads to good estimators of the varying coefficient functions.