Development of an equation to predict delta bilirubin levels using machine learning

Delta bilirubin (albumin-covalently bound bilirubin) may provide important clinical utility in identifying impaired hepatic excretion of conjugated bilirubin, but it cannot be measured in real-time for diagnostic purposes in clinical laboratories.

A total of 210 samples were collected, and their delta bilirubin levels were measured four times using high-performance liquid chromatography. Data collected included age, sex, diagnosis code, delta bilirubin, total bilirubin, direct bilirubin, total protein, albumin, globulin, aspartate aminotransferase, alanine transaminase, alkaline phosphatase, gamma-glutamyl transferase, lactate dehydrogenase, hemoglobin, serum hemolysis value, hemolysis index, icterus value (Iv), icterus index (Ii), lipemia value (Lv), and lipemia index. To conduct feature selection and identify the optimal combination of variables, linear regression machine learning was performed 1,000 times.

The selected variables were total bilirubin, direct bilirubin, total protein, albumin, hemoglobin, Iv, Ii, and Lv. The best predictive performance for high delta bilirubin concentrations was achieved with the combination of albumin-direct bilirubin-hemoglobin-Iv-Lv. The final equation composed of these variables was as follows: delta bilirubin = 0.35 × Iv + 0.05 × Lv - 0.23 × direct bilirubin - 0.05 × hemoglobin - 0.04 × albumin + 0.10.

The equation established in this study is practical and can be easily applied in real-time in clinical laboratories.