The patient presented with hematuria, normotension, and pedal edema, but crucial details include a high creatinine value of 9 mg% and no glucosuria, which indicates renal impairment without diabetic involvement. Based on the provided renal biopsy image and clinical presentation, the suspicion leans towards a condition affecting the glomerular basement membrane.
The appropriate investigation to confirm this would be Anti-GBM antibodies testing, which is typically indicated in cases where conditions such as Goodpasture syndrome are suspected. This condition involves antibodies attacking the glomerular and alveolar basement membranes, leading to renal manifestations such as hematuria and elevated creatinine.
Other options like ANA are generally associated with autoimmune conditions like lupus, HIV RNA is specific to HIV-associated nephropathy, and urine immunoelectrophoresis is for conditions like multiple myeloma affecting kidneys, none of which align with the given clinical presentation.
Thus, the most appropriate investigation to identify the etiology of the disease in this scenario is the ANTI GBM antibodies test.