With the rapidly evolving landscape of cancer immunotherapy, traditional oncology trials that investigate one new treatment for one type of cancer within a trial face constraints due to the high cost and slow progress. New strategies have been developed over the last several years to help expedite the drug development process. One of these strategies, umbrella design, tests the effect of multiple investigational treatments in patients with the same type of cancer. When setting up an umbrella trial, a set of clinical centers will be selected for all the investigational treatments. Since trial outcomes may vary across clinical centers, clinical center variation plays a big role in the success of a trial. In this article, we evaluated the impact of clinical center variation on the efficiency of an umbrella trial where clinical centers are shared among all investigational treatments, compared to that of the traditional approach where each experimental drug is evaluated in a separate trial using different clinical centers. We demonstrate mathematically that the umbrella trial setting is more efficient than the tradition trials in terms of identifying more efficacious drugs, as sharing clinical centers among investigational treatments can reduce the impact of clinical center variation. In addition, guidance is provided on center allocation strategies, center selection, and center enrollment caps during the design stage, to further improve the efficiency of the umbrella trial. The conclusions are applicable to the clinical trials with binary endpoints and shed light on the trials with other types of endpoints.