What condition is characterized by palpable purpura on lower extremities, arthralgias, abdominal pain, and renal disease?

The condition characterized by palpable purpura on the lower extremities, arthralgias, abdominal pain, and renal disease is Henoch-Schonlein purpura (HSP), also known as IgA vasculitis. This small-vessel vasculitis primarily affects children and is associated with a tetrad of symptoms: purpura, often around the buttocks and legs, joint pain (arthralgias), gastrointestinal symptoms like abdominal pain, and renal involvement, which can manifest as hematuria or proteinuria.

HSP is believed to be linked to an abnormal response to infections, particularly upper respiratory tract infections, often triggered by a preceding respiratory illness. This condition can also present with gastrointestinal bleeding due to inflammation of the blood vessels in the intestines, hence the abdominal pain. Renal involvement occurs in a significant proportion of cases, sometimes leading to conditions like IgA nephropathy, secondary to the deposition of IgA immune complexes.

The presence of palpable purpura, particularly in conjunction with the other symptoms specified, aligns closely with the diagnosis of HSP, making it the most appropriate answer for this clinical scenario.