A likelihood approach to analyzing clinical trial data when treatments favor different outcomes

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 it was anticipated by the investigators that each treatment may favor a different outcome. Few statistical methods exist to address the specific challenges encountered by this design. We designed a method to address the specific analytic issues raised in the planning of the CARE study. We developed a likelihood ratio approach to test whether or not a treatment difference exists at the end of the study by considering both the absolute treatment differences and the direction of the differences with respect to the treatments. This method involves simultaneously testing each component of a composite null hypothesis, while maintaining an overall type I error rate. A simulation study is performed to evaluate the operating characteristics of this test, in which we find that our joint likelihood-ratio test has a power as high as, or higher than, other commonly used methods for multiple outcomes, while maintaining a nominal type I error rate.