There are two major accomplishment this year. First, we developed a semiparametric regression approach for bivariate failure time outcomes. This is motivated by the fact that many biomedical studies follow participants for multiple correlated health outcomes. Modeling these outcomes simultaneously can be more efficient than individual models, and allows us to characterize the risk of developing multiple diseases to facilitate risk prediction given individuals history of other diseases. We proposed a set of Cox-type semiparametric models for marginal single failure hazards and the double failure hazard. This approach is proved to provide unbiased and consistent estimates of the regression parameters, and the corresponding survivor function estimates are useful in practice. Second, we proposed a series of tools for characterizing the spatial and temporal distribution of breast cancer risk, motivated by the Sister Study. We first develop an accelerated failure time model with a spatial random effect, to handle individual-level failure time outcomes with spatial variation. Based on results from such models, a disease map can be produced. We further proposed a secondary model assessment tool to connect the observed pattern with spatial-area-level risk factors. We further proposed an accelerated failure time model that allows both time and space effect. This model allows us to identify effects due to influential events, such as natural disasters and policy changes. These methods are applied to the Sister Study.
