Competing risks occur frequently in survival analysis, and in some cases, the competingrisks are not discrete. In this dissertation, we develop some statistical inferences to analyzecontinuous competing risks.In Chapter 2, inspired by the HIV vaccine trials, we extend the modeling of markspecifichazards function to multivariate marks to better fit the HIV data. We develop thepartial likelihood based parametric procedure to estimate the coefficents. The asymptoticproperties of the proposed estimators are derived. We propose some tests to examine avariety of null hypotheses to understand how relevant the two distances are for protection.Finite sample performances of the proposed methods, are examined through extensivesimulations and are shown satisfying. The methods are applied to STEP data to evaluatethe vaccine efficacy and its dependence on the multivariate marks. A goodness of fitprocedure is also developed. The test statistics are constructed based on the score functionand the generalized weighted martingale residuals. The performance of tests are alsoexamined through simulations. And the tests are used to check adequacy of the multivariatemark-specific proportional hazard model for STEP data. In Chapter 3, we develop a goodness of fit procedure for the stratified mark-specificproportional hazard model with continuous marks. Coefficents are estimated through partiallikelihood based kernel smoothing method. The asymptotic properties of the proposedestimators are derived. We also construct confidence bands for vaccine efficacy. We focuson the goodness of fit test of the model. The test statistics are constructed based on thegeneralized weighted martingale residuals. The finite sample properties of proposed testsare examined through simulations.
