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This advantage increases when dimensionality increases. Our method is scalable to higher dimensional problems since the precision bound of our estimated study power is a finite number not affected by dimensionality. To design clinical trials incorporating the potential biomarkers, users can use our software "DesignCTPB". This software can be found on Github and will be available as an R package on CRAN. Although our research is motivated by the design of clinical trials, the method can be used widely to solve other optimization problems