| A number of statistical tools have been developed under the scope of survival analysis, where time to event is the response, to reveal the regression relationship between potential factors (covariates) and some event of interest. The Cox proportional hazard model and accelerated failure time (AFT) are commonly-made assumptions. In this dissertation, two issues in which traditional approaches are not directly applicable are discussed: (1) The situation in which two serial events are of interest, while only current-status information at two pre-scheduled visits are available; (2) The situation in which some covariates are observed only for a subset of the data.;In the first chapter, a fully parametric model is developed, based on the AFT assumption, in analysis of multivariate two-stage current-status survival data from the 1996 breeding success study of common ravens. Association between farmland use and two breeding stages---hatching and fledgling---is of main interest. Correlation among eggs within the same nest is explained by a shared random-effect term while correlated terms account for the dependency between the timing of two breeding events for the same egg. In regression parameter estimation, the EM algorithm and a Monte Carlo version of the Newton-Raphson maximizer are adapted. Food abundance in farmland mainly contributes to the hatching stage, while nest security seems more important for the fledgling stage.;Missing-covariate problems are common in medical studies with survival outcomes, and naively deleting the incomplete cases may not only lead to loss of efficiency but also biased estimation. The second chapter is motivated by the CHARGE study of autistic children where PBDE exposure, a potential environmental factor of language development, is only observed for a small subset of cases. Two approaches to estimation when covariates are missing at random (MAR) are compared under the Cox proportional hazard setting: fully augmented weighted estimators (FAWE) and multiple imputation. In addition, we also consider a way to accommodate the right-censoring structure of survival outcomes in multiple imputation. A marginally significant PBDE effect is demonstrated by FAWE, which is confirmed through simulations to be an advantageous approach in many scenarios. |
