The most likely cause of this patient's gastrointestinal bleeding (GIB) is peptic ulcer disease. This patient has upper GIB, which is predicted based on four aspects of his presentation: hematemesis, melena detected on physical examination, absence of blood clots in the stool, and an elevated blood urea nitrogen to creatinine ratio (>30). The most common causes of upper GIB are peptic ulcer disease (34%), esophageal varices (33%), esophagitis (8%), and Mallory-Weiss tear (6%). Peptic ulcer disease (PUD) can cause severe upper GIB in the absence of coagulopathy. PUD is asymptomatic in 4% to 20% of patients and is commonly diagnosed because of complications such as bleeding.

Duodenal angiodysplasia is not the most likely cause of bleeding because severe GIB is rare in the absence of a bleeding diathesis or use of medications that affect hemostasis, including NSAIDs, aspirin, and anticoagulants.

Erosive gastritis is not likely in this patient because it would not cause severe GIB; the injury does not extend deeper than the mucosa, which lacks arteries and veins.

Variceal bleeding can be responsible for severe GIB that should not be overlooked because the mortality rate is high. Variceal bleeding may be the first presentation of cirrhosis, and therefore a high index of suspicion is needed. This patient has no history or biochemical evidence of cirrhosis, making variceal bleeding unlikely.

Portal gastropathy is unlikely because it is a mucosal cause of chronic, slow GIB. It can rarely cause acute but not severe GIB. In addition, this patient has no risk factors for chronic liver disease that would raise suspicion for this condition.