Advanced statistical methods for failure time data : variable selection, subgroup analysis, and conformal inference
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[EMBARGOED UNTIL 05/01/2026] Failure time data, often subject to censoring, arise frequently in biomedical and clinical research. This dissertation develops advanced statistical methodologies to address key challenges in analyzing such data, particularly in the presence of interval censoring, high-dimensional covariates, and heterogeneity across subjects. The work is organized around three main contributions. First, we propose a group variable selection procedure for the Cox model with interval-censored data, using a penalized sieve maximum likelihood approach and establishing its oracle properties. Second, to account for heterogeneity in treatment effects and patient characteristics, we develop a method for simultaneous subgroup identification and variable selection in high-dimensional survival settings via penalized fusion and model averaging. Third, we introduce a novel nonparametric conformal inference framework for comparing two conditional survival distributions, accommodating both regular and high-dimensional covariates under right censoring. Each method is supported by theoretical justification, extensive simulation studies, and real data applications, including analyses of Alzheimer's disease and cancer genomics datasets. The proposed techniques advance the toolkit for survival analysis, with significant implications for precision medicine and high-dimensional data modeling.
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Ph. D.