Step 1: Acute glomerulonephritis after a streptococcal sore throat or skin infection is a delayed immunological reaction, so the bug itself is usually gone when the kidney disease shows up.
Step 2: Because direct isolation fails, doctors look for the immune footprint of the infection. Antibodies against streptolysin O rise after infection, and measuring this antistreptolysin O level is the standard serological proof of preceding streptococcal disease. Values over 200 units are taken as significant.
Step 3: Throat and blood cultures are typically negative this late, and PCR is not used routinely here. Note that a raised ASO titre confirms recent streptococcal infection but does not by itself prove rheumatic fever. Hence the diagnostic test is the ASO titre.\[\boxed{\text{ASO titre}}\]