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It is increasingly common in clinical trials to design studies for which more than one primary outcome exists. Methods that exist for more than one outcome are generally concerned with identifying one of two situations: (1) improvement in all outcomes from one treatment, as compared to the other treatment(s); or (2) improvement in a single efficacy endpoint, without an excess of toxicity. In contrast, the Colpopexy And Urinary Reduction Effort (CARE) Study is a randomized clinical trial comparing two treatments that presents a slightly different scenario. In this study, there are two outcomes, and each treatment may favor a different outcome. Few statistical methods exist to address the specific challenges encountered by this design. In the first part of this dissertation, a likelihood ratio approach is developed to test whether or not a treatment difference exists at the end of the study. This method involves simultaneously testing each component of the null hypothesis, while maintaining an overall type I error rate. A Bayesian approach is also explored for testing whether or not a treatment difference exists at the end of the study. A simulation study is performed to evaluate the operating characteristics of both the likelihood and Bayesian methods. The second part of this dissertation addresses interim analyses of studies with hypotheses similar to the CARE study. Methodology inspired by Spiegelhalter et al.'s (1986) predictive probability approach is developed which involves determining the probability of rejecting the null hypothesis at the end of the trial, given the data collected up to the interim time point. Using the predictive probability of rejecting the null hypothesis at the end of the study, together with other factors inherent to the study, it may be possible to determine whether or not to stop the trial at an interim time point for either efficacy of treatment or due to an ineffective treatment. Limited simulations are performed to evaluate the interim methodology, using the joint likelihood ratio approach as the test for treatment difference.