Personalized medicine involves the co-development of both the therapeutic agent (Rx) and a companion diagnostic device (CDx), which directs a group of patients to a particular treatment. There are instances, however, when there are competing, or multiple CDx products for a given Rx. Drivers for multiple CDx products can be driven by improved efficiency, cost, novel technologies, or updated techniques over time. In these instances, concordance between the old assay (e.g., the assay used in the clinical trial or comparator companion diagnostic device in this paper) and a new assay (follow-on companion diagnostic device) needs to be assessed. Discrepancies between the old and new assays, and specifically the impact of discordance on clinical efficacy, need to be evaluated. Studies that establish similarity between two or more CDx products are called bridging studies. We provide a statistical framework for method comparison studies where there is bias in measurement of one or both assessments. We then present a simulation study to evaluate the statistical impact of an imperfect CDx on the sensitivity and specificity of the follow-on companion diagnostic device. Further, we demonstrate the influence of the CDx accuracy on clinical efficacy in the context of an enrichment clinical trial.