In this project, the investigator studies an extension of the competing risks model to allow a continuum of competing risks, in which the cause of failure is replaced by a continuous mark variable only observed at the uncensored failure times, and its applications in the HIV vaccine efficacy studies. The investigator develops statistical methods for the mark-specific proportional hazards model, allowing the regression parameters to depend nonparametrically on the mark and the baseline hazard to depend nonparametrically on both time and mark. This research is motivated by the need to assess HIV vaccine efficacy, while taking into account the divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine, and adjusting for covariate effects. The vaccine efficacy is expressed in terms of one of the regression functions in a mark-specific proportional hazards model. The research can find applications in other medical researches as well. The mark-specific proportional hazards model and its applications to vaccine efficacy trials is investigated when the mark variable is dsicrete/continuous and univariate/multivariate. It is studied under the case-cohort designs where some of the covariates may only be observed for a subset of the sample. The semiparametric mark-specific proportional hazards model is also studied. The statistical procedures concerning the mark-specific hazards functions naturally extend the scope of methods that have been developed for competing risks data with discrete marks and for failure time data with single cause of failure. Since the mark-specific relative risks measure not only the relative risks of developing the end-point event given the marks, but also depend on differential exposure to the marks, one needs to be careful in their interpretations. To allow for greater flexibility, direct modeling of the conditional hazard function of failure time given the mark and covariate is considered. The new methods are justified theoretically, evaluated in simulations and applied to the HIV vaccine efficacy trials.
The investigator studies an extension and new applications of the classical competing risks model. The goal of the reseach is to develop statistically efficient and biologically interpretable methods for evaluating and achieving efficacious HIV vaccines. The theoretical justifications for the statistical methods are very challenging. By pursuing this research, significant progress could be made in the theory of competing risks models and its applications. The methods developed in this research will be used to analyze the data collected from the HIV vaccine efficacy trials and provide useful input for developing more effective vaccines. The research of the problems proposed here will also generate many research topics at different levels suitable for graduate and undergraduate studies, therefore promotes involvements of students in the research of current sciences.
