Objectives Alkaline phosphatase is a well-known biomarker of liver disease. The article attempts to locate the determinants of alkaline phosphatase of some liver and non-liver patients. Background Many previous research reports consider alkaline phosphatase as a continuous, homogeneous and normally distributed response variable. In practice, alkaline phosphatase is positive, heterogeneous and non-Normally distributed response variable. There is a little study considering the real fact that the alkaline phosphatase as a non-Normal, heterogeneous and positive response variable. Materials and Methods The current report considers a real data set of 583 subjects with 9 continuous variables and 2 attribute characters. The patients are divided into two groups liver patients (416) and non-liver patients (167). The data set contains 441 male and 142 female patients. Source of the data set is the Machine Learning Repository's citation policy. The considered data set was obtained from the North-East of Andhra Pradesh, India. The considered response alkaline phosphatase is positive, heterogeneous and non-Normally distributed continuous variable. So, it should be analyzed using statistical joint generalized linear Gamma or Log-normal models. Results The mean alkaline phosphatase value is higher for the liver patients (P<0.001) than non-liver patients. The mean alkaline phosphatase value is high at senior ages (P=0.030) than the junior ages. The mean ALP decreases as the total bilirubin (P=0.006) increases, while it increases as the SGPT (P<0.001) increases. The mean alkaline phosphatase decreases as the albumin to globulin ratio (A/G) (P<0.001) increases. Interaction effect of age with total bilirubin (Age*TB) (P<0.001) is directly correlated with the mean alkaline phosphatase, while the joint interaction factor of age with total proteins (Age*TP) (P=0.010) is inversely correlated with the mean alkaline phosphatase. Again, the interaction effects of albumin to globulin ratio (A/G) with the total bilirubin (A/G*TB) (P<0.001), and with total proteins (A/G*TP) (P=0.003) are directly correlated with the mean alkaline phosphatase. The variance of alkaline phosphatase is higher for liver patients (P<0.001) than non-liver patients. The variance of alkaline phosphatase increases as the SGPT (P<0.001), or total bilirubin (P=0.088) increases. The variance of ALP increases as the albumin to globulin ratio (A/G) (P<0.001), or age (P=0.055) decreases. Conclusions The response alkaline phosphatase is identified as heterogeneous and Log- normally distributed. Many factors such as age, SGPT, interaction effects of albumin to globulin ratio with total bilirubin, and separately with total proteins, and also the interaction effect of age with total bilirubin are directly correlated with the mean alkaline phosphatase. The present findings, especially the interaction effects and the variance determinants of alkaline phosphatase are completely new inputs in the liver disease literature.
Rabindra Nath Das, Sabyasachi Mukherjee, Indrajit Sharma
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