Gout: This condition is characterized by high uric acid levels, which can cause kidney disease (nephropathy) and joint pain, including hip pain. The presence of sciatica could be related to the inflammation and pain associated with gout.

Pseudogout (Calcium Pyrophosphate Deposition Disease, CPPD): Similar to gout, pseudogout can cause joint pain and is associated with kidney disease. It might also lead to secondary hyperuricemia.
Osteoarthritis: While primarily a degenerative joint disease, osteoarthritis can cause hip pain and sciatica. High uric acid levels might be coincidental or related to decreased kidney function, which can occur with aging.
Kidney Stones: High uric acid levels can increase the risk of developing kidney stones, which can cause severe pain (renal colic) and potentially lead to kidney disease. The pain can sometimes radiate to the hip area.

Spinal Stenosis: A condition that can cause sciatica and hip pain due to the narrowing of the spinal canal. It's crucial not to miss this diagnosis as it can lead to significant disability if not properly managed.
Infection (Septic Arthritis or Osteomyelitis): Infections in the hip or spine can cause severe pain and are medical emergencies, especially in patients with compromised kidney function who might be more susceptible to infections.
Tumor (Bone or Spinal): Although less common, tumors can cause hip pain, sciatica, and elevated uric acid levels if they lead to kidney dysfunction or are associated with a paraneoplastic syndrome.

Amyloidosis: A condition where abnormal proteins (amyloid) accumulate in various organs, including the kidneys, leading to kidney disease. It can also cause joint pain and might be associated with high uric acid levels.
Sarcoidosis: A multisystem inflammatory disease that can affect the kidneys, joints, and potentially cause elevated uric acid levels. It's a rare cause of the combination of symptoms presented.