A transformation-based conditional IPCW kernel estimator for nonparametric regression under right censoring

Abstract

In survival analysis and reliability studies, right-censored data frequently arise, which poses significant challenges in accurately estimating regression functions. This paper proposes a transformation-based conditional inverse probability of censoring weighted kernel estimator for the regression function in the presence of right censoring. Traditional kernel-based regression techniques often fail to properly account for censoring, resulting in biased estimates. To address this issue, the proposed estimator combines a monotonic transformation of the response variable with a conditional inverse probability of censoring weighted approach. The transformation reduces variability and enhances finite-sample performance, while the conditional inverse probability of weighted censoring adjusts for the censoring mechanism through kernel smoothing in the covariate space. The asymptotic properties of the estimator, including consistency and asymptotic normality, are established. Simulation studies demonstrate improved bias reduction and competitive mean squared error performance compared to classical approaches, such as the naive, substitution, and marginal inverse probability of censoring weighted estimators, especially under moderate to heavy censoring. An application to the primary biliary cirrhosis dataset further illustrates the advantages of the proposed estimator in a real-world medical setting.

Keywords

• Asymptotic theory
• inverse probability weighting
• kernel smoothing
• nonparametric regression
• right censoring
• transformation

Supporting Institution

Ministry of Higher Education and Scientific Research (Algeria) and University of Biskra

Project Number

Not Applicable

Ethical Statement

This study does not involve any experiments on humans or animals. The data used are publicly available, and no ethical approval was required

Thanks

The author would like to express their sincere gratitude to the Ministry of Higher Education and Scientific Research (Algeria) for its financial and institutional support. The author also thank the anonymous reviewers for their valuable comments and suggestions that improved the quality of this manuscript

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