A 28-year-old woman with newly diagnosed type 1 diabetes mellitus presents with severe hyperglycemia (450 mg/dL), metabolic acidosis (pH 7.15, HCO₃⁻ 12 mEq/L), and ketonemia. Her serum insulin level is < 2 mIU/mL. To assess the degree of pancreatic beta-cell dysfunction and predict long-term insulin requirement, which investigation is most appropriate?