Statistical Analysis of Incomplete lifetime Data: Theory, Stochastic Models and Empirical Likelihood

University Of Maryland, College Park, College Park MD

Investigators

Abstract

The investigator plans to further the development of the theory and statistical methods for the analysis of incomplete lifetime data with special focus on censored data in survival analysis. The proposed research consists of two interrelated research thrusts: (A) The development of the empirical likelihood (EL)-based inference procedures. Motivated by the proven advantages of the EL method, a novel approach is proposed. The PI and her collaborator plan to develop asymptotically optimal statistical procedures that are computationally feasible and efficient, and (B) Extension of the Fix-Neyman competing risks model which focuses on a feature of recurrent events of recovery and relapse of a disease in the model. For many diseases, such as breast cancer and aplastic anemia (AA), recovery and relapse are important events affecting a patient's survival probability. Most of the currently employed competing risks models lack this feature. The research team plans to develop statistical inference procedures under the new model for censored data. The extended model can be applied to other types of recurrent events such as in epidemiology surveys (current status data) and engineering reliability. Lifetime or "time-to-event" data, commonly collected in science and engineering, could be time to loss of immunity, survival time of a cancer patient after a treatment, time to failure of a bridge and others. Due to sampling methods, sampling subjects, experimental protocols and limitations of recording instruments and possibly other reasons, data sets often contain a significant number of incompletely observed lifetimes. Incomplete data may include right or left censored, interval censored and truncation data. Without proper corrections for incompleteness, data analysis and uncertainty measures would produce biased and unreliable scientific findings. It is therefore of paramount importance to develop sound statistical methods and theory for the analyses of incomplete data. Despite significant advances in theory and applications, burgeoning applications in diverse science fields continues to present new challenging mathematical problems and computational issues. For example, the proposed extension would extend the popular Kaplan-Meier estimator by including recovery and relapse data in the prediction of a patient's survival probability. It is hoped that better utilization of available data would yield more accurate prediction of survival probability for some diseases and help to identify important factors affecting a patient's survival. Developing numerical solutions will be an integral part of the project. Algorithms will be developed for data analysis. The success of the project will advance the statistical theory of incomplete lifetime data and its applications. Novel use of the empirical likelihood method will result in computationally efficient algorithms for applications. Research and education for this project are inseparable. Training of graduate students and recruiting students from under represented group are planned.