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. 2024 Feb 14:15:1291895.
doi: 10.3389/fendo.2024.1291895. eCollection 2024.

Correlation analysis of diabetes based on Copula

Chang Liu  1 , Hu Yang  1 , Junjie Yang  2 , Hongqing Wang  1
Affiliations

Correlation analysis of diabetes based on Copula

Chang Liu et al. Front Endocrinol (Lausanne). .

Abstract

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

Methods: 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).

Results: 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.

Discussion: 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.

Keywords: fasting blood glucose; glycosylated hemoglobin; high-density lipoprotein cholesterol; nonlinear correlation; triglyceride.

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Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Figures

Figure 1
Figure 1
Heat map of correlation between Glu, HbA1C and TG/HDL-C. Glu, fasting blood glucose; HbA1C, glycosylated hemoglobin; TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C).
Figure 2
Figure 2
Scatter plots and histograms of density distributions of Glu (A), HbA1C (B), and TG/HDL-C (C). Glu, fasting blood glucose; HbA1C, glycosylated hemoglobin; TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C). When the curves are approximately normally distributed, the data can be considered to be approximately fitted with a normal distribution.
Figure 3
Figure 3
Q-Q plot test for Glu (A), HbA1C (B), and TG/HDL-C (C). Glu, fasting blood glucose; HbA1C, glycosylated hemoglobin; TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C). Data are considered to pass the Q-Q plot normality test when the data points fall approximately on a straight line.
Figure 4
Figure 4
Joint distribution function images of six copulas fitting for TG/HDL-C and Glu. (A) Clayton Copula, (B) Gumbel Copula, (C) Frank Copula, (D) Ali–Mikhail–Haq Copula, (E) Gauss Copula, (F) student Copula. TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C); Glu, fasting blood glucose.
Figure 5
Figure 5
Probability distribution function images of six copulas fitting for TG/HDL-C and Glu. (A) Clayton Copula, (B) Gumbel Copula, (C) Frank Copula, (D) Ali–Mikhail–Haq Copula, (E) Gauss Copula, (F) student Copula. TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C); Glu, fasting blood glucose.
Figure 6
Figure 6
Joint distribution function images of six copulas fitting for TG/HDL-C and HbA1C. (A) Clayton Copula, (B) Gumbel Copula, (C) Frank Copula, (D) Ali–Mikhail–Haq Copula, (E) Gauss Copula, (F) student Copula. TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C); HbA1C, glycosylated hemoglobin.
Figure 7
Figure 7
Probability distribution function images of six copulas fitting for TG/HDL-C and HbA1C. (A) Clayton Copula, (B) Gumbel Copula, (C) Frank Copula, (D) Ali–Mikhail–Haq Copula, (E) Gauss Copula, (F) student Copula. TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C); HbA1C, glycosylated hemoglobin.
Figure 8
Figure 8
Plot of the effect of fitting the Vine Copula function for TG/HDL-C, Glu and HbA1C. Glu, fasting blood glucose; HbA1C, glycosylated hemoglobin; TG/HDL-C, the ratio of Triglyceride(TG) to high-density lipoprotein cholesterol(HDL-C). (A) is the scatter plot of the real dataset in this paper; (B) is the scatter plot of the randomized data generated after fitting by the Vine Copula function.
See this image and copyright information in PMC

References

    1. Moin ASM, Butler AE. Alterations in beta cell identity in type 1 and type 2 diabetes. Curr Diabetes Rep (2019) 19:1–12. doi: 10.1007/s11892-019-1194-6 - DOI - PMC - PubMed
    1. Chen Z, Hu H, Chen M, Luo X, Yao W, Liang Q, et al. . Association of triglyceride to high-density lipoprotein cholesterol ratio and incident of diabetes mellitus: a secondary retrospective analysis based on a chinese cohort study. Lipids Health Dis (2020) 19:1–11. doi: 10.1186/s12944-020-01213-x - DOI - PMC - PubMed
    1. Zheng D, Li H, Ai F, Sun F, Singh M, Cao X, et al. . Association between the triglyceride to high-density lipoprotein cholesterol ratio and the risk of type 2 diabetes mellitus among chinese elderly: the beijing longitudinal study of aging. BMJ Open Diabetes Res Care (2020) 8:e000811. doi: 10.1136/bmjdrc-2019-000811 - DOI - PMC - PubMed
    1. Lee M-Y, Hsu W-H, Lai C-W, Chen S-C, Liang C-C. The association between glycated albumin, glycohemoglobin, and glycated albumin to glycohemoglobin ratio in diabetic retinopathy of prediabetes. Kaohsiung J Med Sci (2019) 35:695–701. doi: 10.1002/kjm2.12125 - DOI - PMC - PubMed
    1. He S, Wang S, Chen X, Jiang L, Peng Y, Li L, et al. . Higher ratio of triglyceride to high-density lipoprotein cholesterol may predispose to diabetes mellitus: 15-year prospective study in a general population. Metabolism (2012) 61:30–6. doi: 10.1016/j.metabol.2011.05.007 - DOI - PubMed

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