A unified nonparametric fiducial approach to interval-censored data

TL;DR

This paper introduces a versatile nonparametric fiducial method for interval-censored data that automatically adapts to various censoring types, providing more accurate confidence intervals and estimators than existing methods.

Contribution

A novel nonparametric fiducial approach that universally handles different non-informative censoring mechanisms with improved accuracy and automatic adaptation.

Findings

Fiducial confidence intervals outperform existing methods in coverage and length.

Fiducial point estimator has smaller errors than nonparametric MLE.

Method successfully applied to real-world medical data.

Abstract

Censored data, where the event time is partially observed, are challenging for survival probability estimation. In this paper, we introduce a novel nonparametric fiducial approach to interval-censored data, including right-censored, current status, case II censored, and mixed case censored data. The proposed approach leveraging a simple Gibbs sampler has a useful property of being "one size fits all", i.e., the proposed approach automatically adapts to all types of non-informative censoring mechanisms. As shown in the extensive simulations, the proposed fiducial confidence intervals significantly outperform existing methods in terms of both coverage and length. In addition, the proposed fiducial point estimator has much smaller estimation errors than the nonparametric maximum likelihood estimator. Furthermore, we apply the proposed method to Austrian rubella data and a study of hemophiliacs infected with the human immunodeficiency virus. The strength of the proposed fiducial approach is not only estimation and uncertainty quantification but also its automatic adaptation to a variety of censoring mechanisms.