Final answer:
The most likely diagnosis for the patient described is ANCA-associated vasculitis. ANCA antibodies are present in about 90% of these cases. Kidney biopsy findings usually reveal necrotizing glomerulonephritis.
Step-by-step explanation:
A 53-year-old patient presenting with cough, bloody sputum, and glomerulonephritis, alongside the findings of palpable purpura and a skin biopsy consistent with small-vessel vasculitis and without granuloma formation, is most likely diagnosed with ANCA-associated vasculitis.
2). Antibodies that are positive in 90% of patients with this disease are ANCA (antineutrophil cytoplasmic antibodies).
3). A kidney biopsy in patients with this condition would typically show necrotizing glomerulonephritis, without immune complex deposition.