Design and Evaluation of Robust Statistical Methods for Small-Sample Survival Data

Thesis Abstract

In biomedical research and clinical settings, accurate analysis of small-sample survival data presents significant challenges due to limited data points, censoring issues, and the sensitivity of traditional statistical methods to outliers and deviations from underlying assumptions. These challenges often lead to biased estimates, reduced statistical power, and unreliable inference, thereby impeding effective decision-making and clinical interventions. This study aims to design and evaluate robust statistical methodologies tailored for small-sample survival datasets, with a focus on enhancing the accuracy, stability, and interpretability of survival analysis results under data sparsity. The specific objectives include (1) reviewing current survival analysis techniques and their limitations in small samples, (2) developing modified estimators and modeling strategies to improve robustness against outliers and assumption violations, (3) implementing these methods on real-world small-sample datasets from oncology clinical trials, and (4) comparing their performance against existing methods through simulation studies. The research adopts a quantitative, methodological design integrating both theoretical development and empirical evaluation. The population comprises clinical trial datasets with sample sizes ranging from 15 to 50 subjects, derived from collaborative oncology research centers. Purposive sampling is employed to select datasets characterized by high censoring rates (above 30%) and heterogeneous patient profiles. Data collection involves extraction from institutional research databases, supplemented by structured data abstraction forms to ensure consistency and completeness. The instruments include standardized data extraction templates and custom-coded statistical software routines developed in R, incorporating survival analysis packages such as survival and survminer. The validity and reliability of the developed methods are assessed through multiple simulation experiments, carefully controlling for distributional assumptions, censoring mechanisms, and the presence of outliers. Data analysis entails applying the proposed robust survival models—such as weighted Kaplan-Meier estimators, Cox proportional hazards models with robust variance adjustments, and Bayesian survival models using prior distributions tolerant to small samples—and comparing their performance with classical approaches. Performance metrics include bias, mean squared error, coverage probability of confidence intervals, and robustness against outliers, evaluated through extensive simulation. The analytical framework also incorporates sensitivity analyses to determine the stability of estimates under varying degrees of data contamination and censoring. Ethical considerations focus on anonymizing patient data and obtaining necessary institutional approvals for data use. Expected findings anticipate that the newly designed robust methods will outperform conventional techniques in accuracy and stability within small-sample contexts, demonstrating reduced bias and improved confidence interval coverage even in the presence of heavy censoring and outliers. It is also projected that these methods will provide more reliable hazard ratio estimates, thereby offering clearer insights into treatment effects with limited data. This research contributes to the advancement of survival analysis by providing pragmatic, statistically sound methods specifically tailored for small-sample scenarios prevalent in early-phase clinical trials and rare disease studies, filling a notable gap in existing methodological literature. The main conclusion underscores the necessity for adopting robust statistical techniques in small-sample survival analysis to improve the validity of clinical research outcomes. Based on the empirical evidence, the study recommends best-practice protocols for applied statisticians and clinicians handling small datasets, emphasizing the importance of robustness features in model selection. Future research directions include extending the developed methods to multi-center studies, integrating machine-learning-based survival models, and exploring their applications in other domains such as environmental risk assessment and engineering reliability analysis. Overall, this study enhances both methodological rigor and practical utility in small-sample survival studies, fostering more reliable and actionable clinical insights.