Biased Sampling In Survival Analysis And Causal Inference In Observational Studies

This dissertation addresses three issues:statistical inference for the ad-ditive hazards model under outcome-dependent sampling scheme, statistical inference with an outcome-dependent sampling scheme under the Cox pro-portional hazards model, and adjusting complex heterogeneity in treatment assignment in observational studies.Outcome-dependent sampling designs have been widely used as a cost-effectiveness design in medical studies and other research fields. We propose an outcome-dependent sampling scheme for survival data with right censoring under the additive hazards model and the Cox proportional hazards model, respectively. We develop a weighted estimating equation for the regression parameters for the proposed design and derive the asymptotic properties of the proposed estimator. We also evaluate the relative efficiency of the proposed method against simple random sampling design and derive the optimal allocation of the subsamples for the proposed design. A data set from the cancer incidence and mortality of uranium miners study is analyzed to illustrate the proposed method.There exists complex heterogeneity in treatment assignment in obser-vational studies. If not properly adjust them, the estimator of treatment effect will be seriously biased. Through a series of models that mimic vari-ous level of heterogeneity in treatment assignment in observational studies, we evaluate, through simulation study, the performance of several method-s. These methods include propensity score stratification, propensity score inverse probability weighting, propensity score regression, classification and regression tree and the partial least squares. Our results suggest that the par-tial least squares method is most robust and efficient. We illustrate the pro-posed method with real data from the German Breast Cancer Study Group study.