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In this thesis, we concern about some issues in survival data with censored covariates. In the first part, we explore the conditional modeling of the semi-competing risks data, where individuals are likely to experience two types of events: non-terminal and terminal. We propose a new semiparametric model for the terminal event time based on proportional hazards regression conditioning on the non-terminal event time. The model allows for a covariate subject to dependent and independent censoring on the hazard of the terminal event. In the second part, we propose a quantile regression model for survival data with covariates subject to limits of detection. The proposed method extends the existing work based on an AFT model to quantile regression. Thus it possesses more flexibility by relaxing stringent constraints on error distribution used in the AFT model and allowing the effects of covariates varying across different quantile levels of the survival distribution. We develop two-stage estimation procedures in both parts and establish theoretical properties of the proposed estimators. The finite sample performances are demonstrated via extensive simulation studies. Real data applications illustrate the effectiveness of the proposed methods. YU TONGHUI

Regression analysis of survival data with covariates subject to censoring