A-Spline Regression for Fitting a Nonparametric Regression Function with Censored Data

Dursun Aydın,Ersin Yılmaz,Syed Ejaz Ahmed

doi:10.3390/stats3020011

Abstract

This paper aims to solve the problem of fitting a nonparametric regression function with right-censored data. In general, issues of censorship in the response variable are solved by synthetic data transformation based on the Kaplan–Meier estimator in the literature. In the context of synthetic data, there have been different studies on the estimation of right-censored nonparametric regression models based on smoothing splines, regression splines, kernel smoothing, local polynomials, and so on. It should be emphasized that synthetic data transformation manipulates the observations because it assigns zero values to censored data points and increases the size of the observations. Thus, an irregularly distributed dataset is obtained. We claim that adaptive spline (A-spline) regression has the potential to deal with this irregular dataset more easily than the smoothing techniques mentioned here, due to the freedom to determine the degree of the spline, as well as the number and location of the knots. The theoretical properties of A-splines with synthetic data are detailed in this paper. Additionally, we support our claim with numerical studies, including a simulation study and a real-world data example.

Highlights

This paper demonstrates that a modified A-spline estimator can be used to estimate the rightcensored nonparametric regression model successfully
This paper demonstrates that a modified A-spline estimator can be used to estimate the right-censored nonparametric regression model successfully
This is because it uses an adaptive procedure for determining the penalty term and works with only optimum knot points

Summary

Introduction

Let (xi , yi ), 1 ≤ i ≤ n be a sample of observations where xi ’s are values of a one-dimensional covariate x and yi ’s denote the values of the completely observed response (lifetime) variable y In medical studies such as clinical trials, y is often subject to random right-censoring and censored by a random variable c with ci values representing the censorship times, i.e., patient withdrawal time. In this case, the observed response values at designed points x1 , x2 , . The relationship between the distribution of t and (y, c) can be written as follows, in terms of corresponding survival functions:

Objectives

Methods

Conclusion