Matching in observational studies: Time dependency and balance

In observational studies, matching can be used to remove bias between treated and control subjects. Novel matching schemes and tools for analyzing matched data are developed in this thesis. Modified sign and signed rank tests statistics are created to allow for the possibility that the effect of a treatment is not seen until some time has passed, a late effect. These statistics are invertible and can be used to construct confidence intervals for censored, matched pairs. In simulation studies, these modified tests are shown to have very high power to detect a late effect in contrast to conventional techniques. These modified tests are used to ascertain whether the administering of chemotherapy by gynecological or medical oncologists creates the apparent late effect in their survival curves. While the incidence rate of endometrial cancer is lower for black than for white women, black women have much higher mortality rates. In order to distinguish whether biological factors or quality of care is responsible for this discrepancy in survival, a tapered matched comparison is developed. In this procedure, a group of individuals is compared to two or more nonoverlapping group of controls created through the optimal assignment algorithm. In the endometrial data the black women are matched to whites at diagnosis and then each black is rematched to different whites based on both diagnosis and treatment characteristics. While the tapered matching scheme implemented on the endometrial cancer data proved effective, it was not able to match well on all comorbidities of interest. Thus, a balance match algorithm is developed. This technique exchanges a member of the pool of controls that is unassigned with one that is assigned in order to maintain homogenous strata and provide better overall balance of covariates of interest. A simulation study shows that for a small penalty in the quality of the matches, balance across pairs is greatly enhanced. This flexible algorithm when implemented on endometrial data put in balance four key comorbidity covariates that were previously unbalanced for a minimal sacrifice in the quality of the matches