alpha.split             The optimal design given one set of proportion
                        for each sub-population
ctpbs                   The clinical trial design for strong biomarker
                        effect
ctpbw                   The clinical trial design for weak biomarker
                        effect
designCTPB              Optimal design for 3-dimensional with
                        visulization
phat                    Point estimator for the power value
proportion              Grid setting of proportions for each
                        sub-population
