Nonparametric generalized fiducial inference for survival functions under censoring

TL;DR

This paper introduces a novel application of generalized fiducial inference to nonparametric survival function estimation under right censoring, providing effective confidence intervals and tests with strong coverage and power.

Contribution

It systematically applies generalized fiducial inference to survival analysis, offering new methods for confidence intervals and hypothesis testing that outperform traditional approaches.

Findings

Fiducial confidence intervals maintain coverage where asymptotic methods fail.

Proposed intervals are often shorter than competing methods.

Fiducial tests show higher power than log-rank tests in some scenarios.

Abstract

Fiducial Inference, introduced by Fisher in the 1930s, has a long history, which at times aroused passionate disagreements. However, its application has been largely confined to relatively simple parametric problems. In this paper, we present what might be the first time fiducial inference, as generalized by Hannig et al. (2016), is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one sample and two sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein-von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test comparing chemotherapy against chemotherapy combined with radiotherapy using data from the treatment of locally unresectable gastric cancer.