Application of Bivariate Capula Additive Regression in Determining Factors Affecting ALT and AST Liver Enzymes

Nonparametric regression can usually be used when the distribution of the dependent variable does not follow the property of normality. In this study, due to the nature of the variables, a bivariate Capula regression model was used to identify the factors affecting the liver enzymes (ALT and AST) and the relationship between these enzymes. This type of regression is suitable when the response variables have a relatively high degree of skewness and interdependence.

In this cross-sectional study, a sample of 2000 participants in the Shahrekord cohort study were randomly selected. To achieve the Capula regression model, the inverse Gaussian margin distribution and the Gumble joint function were selected according to the Akaike criterion. Gamlss, Copula, and Ggrm statistical packages were used in the R software.
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According to the findings, some variables were identified as effective factors on the concentration of ALT and AST enzymes through marginal distribution parameters and Capula function. Blood urea, triglyceride, GGT, ALP, and BMI had a nonlinear and significant effect on the mean concentration of the ALT enzyme. The BMI, GGT, ALP, LDL, and HDL (nonlinearly), as well as blood urea (linearly), had a significant effect on the mean concentration of AST enzyme. Finally, the variables of BMI, triglycerides, GGT, and ALP affect the relationship between the concentration levels of the liver enzymes (ALT and AST).

Using this model, in addition to identifying the effective factors, it is possible to distinguish between linear and nonlinear relationships between independent and dependent variables.