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Title: Estimation and testing of survival functions via generalized fiducial inference with censored data Authors:  Yifan Cui - University of North Carolina at Chapel Hill (United States)
Jan Hannig - University of North Carolina at Chapel Hill (United States) [presenting]
Abstract: Fiducial Inference has a long history, which at times aroused passionate disagreements. However, its application has been largely confined to relatively simple parametric problems. 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. 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.