Statistical Methods for Analyzing Incomplete Lifetime Data

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The proposed research program aims to develop advanced statistical methods to model event history data involving latent processes that can arise in medical research, social sciences and system reliability. The topics build on my past research experience and recent developments in the literature. ******Research in the first theme will consider issues in data analysis with incomplete covariates in length-biased samples. Truncated data naturally arise in studies of progressive multi-state Markov processes due to the delayed entry to a given state. Large cohort studies can result in truncated and clustered failure time data. Competing risk models for multiple causes of death and semi-competing risk models involving multiple processes in which one process may censor the others may both result in truncated data. I plan to develop methods to address the challenges in parameter estimation where the sample covariate distribution involves parameters of the survival distribution when event times are truncated. ******Research in the second theme is on the analysis of recurrent event processes subject to resolution. I plan to use random effects to account for other heterogeneities in a mover-stayer model and build enriched mixture models to jointly analyze the recurrent events, resolution processes and mortality when event times are either observed or interval-censored. Competing risk models with a mover-stayer structure will be developed to ensure that the hazard functions and the covariate effects are correctly estimated. I also plan to construct flexible models to handle the temporary resolution, allowing transitions between different states before entering the terminating state under intermittent observations. ******Research in the third theme will look into causal inference in observational studies where treatment allocations are unbalanced by potential confounders affecting the treatment selection and prediction of the response. I plan to address the challenge of missing covariate data in methods for dealing with confounding. The methods will be developed in the framework of semiparametric accelerated failure time models and additive hazards models, as Cox proportional hazards assumptions may not hold. ******The proposed research focuses on developing innovative statistical methods to handle certain incomplete data problems by using likelihood-based techniques and inferences. It will shed light on point and variance estimation via computational effective methods and verify the theoretical properties of the estimators. It will provide new understandings and valuable results that will benefit both statistical methodology development and applications in multiple areas. It is also anticipated to stimulate interests of both graduate students and senior undergraduate students and provide abundant opportunities for them to get involved, trained and inspired for new research ideas.**