Generalized inferential models for censored data

TL;DR

This paper introduces a generalized inferential model approach for censored data that uses a plausibility function driven by an association with an unobserved auxiliary variable, leveraging the Kaplan--Meier estimator for improved inference.

Contribution

It proposes a novel generalized inferential model for censored data that improves inference accuracy by integrating the Kaplan--Meier estimator into the plausibility function construction.

Findings

Provides valid approximate inference for censored data

Demonstrates superior performance over existing methods

Uses a novel calibration of the plausibility function

Abstract

Inferential challenges that arise when data are censored have been extensively studied under the classical frameworks. In this paper, we provide an alternative generalized inferential model approach whose output is a data-dependent plausibility function. This construction is driven by an association between the distribution of the relative likelihood function at the interest parameter and an unobserved auxiliary variable. The plausibility function emerges from the distribution of a suitably calibrated random set designed to predict that unobserved auxiliary variable. The evaluation of this plausibility function requires a novel use of the classical Kaplan--Meier estimator to estimate the censoring rather than the event distribution. We prove that the proposed method provides valid inference, at least approximately, and our real- and simulated-data examples demonstrate its superior performance compared to existing methods.