Positive-Unlabelled Survival Data Analysis

TL;DR

This paper introduces a new framework for analyzing positive-unlabeled survival data, addressing challenges in bias and estimation accuracy with novel models and strategies.

Contribution

It develops parametric, nonparametric, and machine learning models for positive-unlabeled survival data, including estimation methods for cases with and without observed censoring times.

Findings

Traditional survival analysis can be biased under this data setup.

Proposed methods yield valid survival estimates in simulations.

Models outperform existing approaches in handling positive-unlabeled data.

Abstract

In this paper, we consider a novel framework of positive-unlabeled data in which as positive data survival times are observed for subjects who have events during the observation time as positive data and as unlabeled data censoring times are observed but whether the event occurs or not are unknown for some subjects. We consider two cases: (1) when censoring time is observed in positive data, and (2) when it is not observed. For both cases, we developed parametric models, nonparametric models, and machine learning models and the estimation strategies for these models. Simulation studies show that under this data setup, traditional survival analysis may yield severely biased results, while the proposed estimation method can provide valid results.