# Correlation analysis of diabetes based on Copula

## TL;DR

This study uses Copula functions to better understand the complex relationships between blood markers for diabetes, leading to more accurate diagnosis.

## Contribution

The study introduces Copula-based modeling as a novel approach to capture non-linear correlations in diabetes indicators.

## Key findings

- Clayton Copula best fits pairwise diabetes indicator relationships with minimal error.
- Vine Copula effectively models the joint relationship among Glu, HbA1C, and TG/HDL-C.
- Copula functions outperform linear methods in capturing lower tail correlations between indicators.

## Abstract

The ratio of Triglyceride (TG) to high-density lipoprotein cholesterol (HDL-C) is a crucial indicator for diabetes diagnosis.

This study utilizes the Copula function to model and fit the non-linear correlation among fasting blood glucose (Glu), glycosylated hemoglobin (HbA1C), and TG/HDL-C in patients with diabetes. The Copula function chosen for this study includes the two-dimensional Archimedes and Elliptical distribution family, as well as the multidimensional Vine Copula function, for fitting the data. The evaluation of the fitting effect is performed using the mean absolute error (MAE) and mean square error (MSE).

The results indicate that the Clayton Copula exhibits the highest effectiveness in fitting the pairwise relationship between Glu and TG/HDL-C, as well as HbA1C and TG/HDL-C, displaying the smallest fitting error. Additionally, the Vine Copula function produces a satisfactory fit for the relationship among all three indicators. Compared to linear analysis methods, the Copula function more accurately depicts the correlation among these three types of indicators.

Moreover, our findings indicate a stronger correlation in the lower tail between Glu and HbA1C, as well as TG/HDL-C, suggesting that the Copula function provides greater accuracy and applicability in depicting the relationship among these indicators. As a result, it can offer a more precise auxiliary diagnosis and serve as a valuable reference in clinical judgment.