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Summary Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference 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 confidence intervals for 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 by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.
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This content will become publicly available on November 25, 2025
Predictive Powered Inference for Healthcare; Relating Optical Coherence Tomography Scans to Multiple Sclerosis Disease Progression
Predictive power inference (PPI and PPI++) is a recently developed statistical method for computing confidence intervals and tests. It combines observations with machine-learning predictions. We use this technique to measure the association between the thickness of retinal layers and the time from the onset of Multiple Sclerosis (MS) symptoms. Further, we correlate the former with the Expanded Disability Status Scale, a measure of the progression of MS. In both cases, the confidence intervals provided with PPI++ improve upon standard statistical methodology, showing the advantage of PPI++ for answering inference problems in healthcare.
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- Award ID(s):
- 2136228
- PAR ID:
- 10579195
- Publisher / Repository:
- Proceedings of the 9th Machine Learning for Healthcare Conference, PMLR 252, 2024.
- Date Published:
- Format(s):
- Medium: X
- Location:
- Machine Learning for Healthcare Conference 2024 Nov 25.
- Sponsoring Org:
- National Science Foundation
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