Statistical methodologies for survival data with possible correlated survival times or a possible surviving fraction

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The objective of this research program is to investigate some important statistical issues related to survival data and to propose innovative statistical models and methods to analyze the data. Some of the issues relate to properly handling survival data with a possible surviving or cure fraction. We will propose new test procedures to detect the presence of the surviving fraction, new models to deal with possible correlation among survival times in clustered data, and new models and methods to deal with possible missing covariates. We will investigate the model identifiability and asymptotic properties of some recently proposed semiparametric cure models. We will also investigate new statistical approaches that improve the robustness or the efficiency of existing models and methods. We will consider similar issues for discrete data based on zero-inflated Poisson model. Other issues relate to measuring diagnostic and predictive power of time-dependent covariates/markers for survival data. We will propose new methods to evaluate diagnostic and predictive accuracy of time-dependent covariates/markers for survival data. We will consider new evaluation methods for survival data with a surviving fraction. We will also investigate new methods to locate markers/covariates that provide better guidelines in treatment selection in clinical trails with multiple treatments available. When finished, this program will contribute to survival analysis by providing novel statistical models and methods for analyzing survival data with possible correlated survival times or a possible surviving fraction. It will greatly expand the applicability of the survival models in health related studies, engineering, econometrics, and biology, where the types of the data investigated in this program are commonly found. It will also contribute to graduate students training, both Master's level and PhD level, and research fellows by providing various levels of research projects suitable for the training. High quality publications in the first rate biostatistical journals can be expected from this research program.