A 14-year-old boy presents with acute onset of right flank pain, which developed after he helped his father paint the ceiling of his bedroom. Physical examination demonstrates an area of ecchymosis in the right flank that is tender to palpation. The patient has a lifelong history of easy bruising. His brother shows the same tendency. The serum level of clotting factor VIII is less than 2% of normal. Which of the following is the most likely underlying mechanism for bleeding tendency in this patient?