In the HIV vaccine efficacy study, a very high percentage of marks of interest may be missing and the problem is attributed to the evolving nature of the HIV viruses. This proposal proposes some efficient statistical methods for dealing with missing marks under competing risks models. The investigator will investigate the mark-specific proportional hazards model and the mark-specific Cox model with time-varying effects. The mark-specific vaccine efficacies can be expressed in terms of one of the regression functions under the proposed models. To evaluate mark-specific vaccine effects and its dependence on the mark, the investigator studies the mark-specific proportional hazards model and the mark-specific Cox model with time-varying effects that hold at each level of the mark variable. There is a built-in structure between the mark, failure times and covariates. Arbitrary modeling of the conditional distributions of the mark variable given theauxiliary variables, as did in the existing literature, may run into conflicts with the underlying models and result in inconsistency. The investigator proposes a two-stage approach to achieve more efficient estimation procedures. The inverse probability weighted complete-case estimators are derived in the first stage. The two-stage efficient estimation procedure is obtained using the idea of the augmented inverse probability weighted complete-case method and based on the first stage estimators. The statistical procedures will be developed to more effectively evaluate HIV vaccine efficacies. The problems of missing marks in competing risks models are not unique to the HIV vaccine efficacy trials. The analysis of other statistical models using competing risks data with missing marks will also be studied. The proposed methods will be justified theoretically, evaluated in simulations and applied to analyze the HIV vaccine efficacy trials.
An objective of randomized placebo-controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain(s) represented in the vaccine construct. The investigator proposes some efficient statistical methods to evaluate the HIV vaccine efficacies when a high percentage of the genetic distances (or marks) may be missing due to the evolving nature of the HIV viruses. The missing marks can also occur in competing risks data from other medical studies. The investigator proposes to study the vaccine efficacies under the mark-specific proportional hazards model and the mark-specific Cox model with time-varying effects. These models have clear biological interpretations for studying HIV vaccine efficacies. Other statistical models using competing risks data with missing marks will also be studied. The proposed research would provide critical statistical tools needed for developing more effective vaccines and enrich a collection of statistical tools which have important impact on the risk analysis of competing risks data.
