This project contains three topics: (1) survival analysis with multiple event-time data, (2) growth curve analysis and, (3) computerized adaptive testing. Topic (1) develops new parametric families for multiple event times that satisfy marginal proportional hazards requirement and proposes semiparametrically efficient estimator for regression parameter in the marginal Cox model. It establishes nonparametric estimation and testing procedures and their large sample properties for gap-time data, which cannot be handled directly by existing methods due to (informative) right censorship. It also introduces a class of semiparametric transformation models for recurrent event times and develops inference procedures that are easy to implement and valid under general assumptions. Topic (2) deals with random growth curves and develops nonparametric testing and semiparametric estimation procedures. A crucial issue being handled there is how to correct bias cause by incompleteness of the growth curves. Topic (3) develops statistical methods in design and analysis of computerized adaptive tests. It proposes novel approaches to item selection through suitable stratification to improve efficiency, item exposure rate distribution and test security.
The three topics are motivated directly from scientific and educational applications. The first two topics are applicable to many biomedical studies including modeling of disease development, testing superiority of a new treatment and estimation of treatment efficacy. The third topic originates from the recent emergence of computerizing standardized tests, which include such widely available tests as GRE and GMAT. The new statistical methods provide more accurate and efficient tools for measuring educational achievements.
