Although the terms direct and indirect bilirubin are used equivalently with conjugated and unconjugated bilirubin, this is not quantitatively correct, because the direct fraction includes both conjugated bilirubin and δ bilirubin.
Delta bilirubin is albumin-bound conjugated bilirubin. In the other words, delta bilirubin is the kind of bilirubin covalently bound to albumin, which appears in the serum when hepatic excretion of conjugated bilirubin is impaired in patients with hepatobiliary disease. Furthermore, direct bilirubin tends to overestimate conjugated bilirubin levels due to unconjugated bilirubin that has reacted with diazosulfanilic acid, leading to increased azobilirubin levels (and increased direct bilirubin).
δ bilirubin = total bilirubin – (unconjugated bilirubin + conjugated bilirubin)