Final answer:
Anticoagulant therapy contraindicates the use of epidural analgesia in this patient.
Step-by-step explanation:
The factor that contraindicates the use of epidural analgesia in this patient is Anticoagulant therapy. Anticoagulant therapy is a medical treatment used to prevent the formation of blood clots. In this patient's case, the history of mitral valve replacement and the presence of an embolus in her right leg indicate a high risk of blood clot formation. The use of epidural analgesia in this situation can further increase the risk of bleeding due to the anticoagulant therapy, potentially leading to complications. Therefore, it is contraindicated in this patient.