连续贝叶斯网络在尿酸与慢性代谢性疾病相关性中的应用

崔宇; 宋伟梅; 赵瑞青; 任浩; 王旭春; 乔宇超; 赵执扬; 任家辉; 刘静; 李一汀; 仇丽霞

doi:10.16462/j.cnki.zhjbkz.2023.09.016

连续贝叶斯网络在尿酸与慢性代谢性疾病相关性中的应用

doi: 10.16462/j.cnki.zhjbkz.2023.09.016

山西医科大学公共卫生学院卫生统计学教研室, 太原 030001

基金项目:

国家自然科学基金 81973155

详细信息

通讯作者:
仇丽霞，E-mail: qlx_1126@163.com

中图分类号: R195.1
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- 被引次数: 0
出版历程
- 收稿日期: 2022-09-16
- 修回日期: 2022-12-05
- 网络出版日期: 2023-10-12
- 刊出日期: 2023-09-10

Application of continuous Bayesian networks in the association study between uric acid and chronic metabolic diseases

Department of Health Statistics, School of Public Health, Shanxi Medical University, Taiyuan 030001, China

Funds:

National Natural Science Foundation of China 81973155

More Information

Corresponding author: QIU Lixia, E-mail: qlx_1126@163.com

摘要

摘要: 目的基于改进的偏相关(improved partial-correlation-based, IPCB)算法建立连续贝叶斯网络模型，探寻尿酸(uric acid, UA)的代谢性影响因素，并通过与传统的多重线性回归模型分析比较，分析连续贝叶斯网络模型对疾病影响因素的效果和优势。方法以2015年山西省慢性病监测的4 846例监测人群数据为研究对象，分别用多重线性回归模型和连续贝叶斯网络模型分析UA与其余9个代谢性疾病的特征指标的相关性，比较两种方法结果的优劣。结果经多重线性回归模型逐步分析，三酰甘油(triglyceride, TG)、SBP、DBP、低密度脂蛋白(low density lipoprotein, LDL)、高密度脂蛋白(high density lipoprotein, HDL)共5个变量与UA水平直接相关，解释了UA 9.5%的变异。连续贝叶斯网络模型共包含24条有向边，年龄、TG、LDL、HDL、SBP、DBP与UA水平直接相关，随着年龄、TG、LDL的增加和HDL的降低均会导致UA水平升高，而UA水平升高又导致SBP、DBP升高；总胆固醇(total cholesterol, TC)与UA间接相关。结论连续贝叶斯网络模型能发现更多UA的直接影响因素，还可以找到UA的间接影响因素，整体解释度更好。
- 连续贝叶斯网络 /
- 改进的偏相关算法 /
- 多重线性回归 /
- 尿酸
Abstract: Objective The study aimed to construct a continuous Bayesian networks using improved partial-correlation-based (IPCB) algorithm, investigate the metabolic influencing factors of blood uric acid (UA). Meanwhile, traditional multiple linear regression model was compared to discuss the effect and advantages of Bayesian network in disease risk factor detection. Methods Chronic disease surveillance data involving 4 846 cases in Shanxi Province in 2015 was taken for study. Both continuous Bayesian networks and multiple linear regression models were utilized for correlation analysis between UA and the indexes of nine metabolic diseases. Afterwards, the advantages and disadvantages of the two models were compared. Results Multiple linear regression stepwise analysis showed that triglyceride (TG), systolic blood pressure (SBP), diastolic blood pressure (DBP), low density lipoprotein (LDL) and high density lipoprotein (HDL) were directly correlated with UA, explaining 9.5% of the variation. The continuous Bayesian networks comprised 24 directed edges, and age, TG, LDL, HDL, SBP, and DBP were directly related to UA. As age, TG, LDL increase and HDL decreases, UA levels rise, which in turn leads to an increase in SBP and DBP. Besides, total cholesterol (TC) was indirectly related to UA. Conclusions Continuous Bayesian networks allows for more direct and indirect influencing factors for UA, which features a better overall explanation.
- Continuous bayesian network /
- Improved partial-correlation-based algorithm /
- Multiple linear regression /
- Uric acid

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图 1 标准化残差的直方图

Figure 1. Histogram of standardized residuals

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图 2 标准化残差散点图

Figure 2. Standardized residual scatter plot

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图 3 连续贝叶斯网络结构

TC: 总胆固醇；TG: 三酰甘油；LDL: 低密度脂蛋白；HDL: 高密度脂蛋白；UA: 尿酸；FPG: 空腹血糖；HbA1c: 糖化血红蛋白。

Figure 3. The structure of continuous Bayesian networks

TC: total cholesterol; TG: triglyceride; LDL: low density lipoprotein; HDL: high density lipoprotein; UA: uric acid; FPG: fasting plasma glucose; HbA1c: glycosylated hemoglobin type A1c.

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表 1 Durbin-Watson统计量的计算结果

Table 1. Calculation results of Durbin-Watson statistics

RR	R²	调整后R² Adjusted R²	s	Durbin-Watson
0.308	0.095	0.094	73.567	2.034

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表 2 代谢指标统计描述和正态性检验

Table 2. Statistical description and normality test of metabolic indicators

变量 Variable	赋值 Assignment	x±s	M	正态性检验P值 Normality test P value
UA/(μmol·L^-1)	Y	268.29±77.28	257.35	＜0.001
年龄/岁Age/years	X₁	54.07±13.40	55.00	＜0.001
TC/(mmol·L^-1)	X₂	4.61±0.92	4.54	＜0.001
TG/(mmol·L^-1)	X₃	1.70±1.16	1.40	＜0.001
LDL/(mmol·L^-1)	X₄	2.91±0.80	2.84	＜0.001
HDL/(mmol·L^-1)	X₅	1.17±0.28	1.13	＜0.001
SBP/mmHg	X₆	138.69±21.58	135.00	＜0.001
DBP/mmHg	X₇	80.82 ±11.54	80.00	＜0.001
FPG/(mmol·L^-1)	X₈	5.64±1.52	5.31	＜0.001
HbA1c/%	X₉	5.03±0.91	4.90	＜0.001
注：UA, 尿酸; TC, 总胆固醇; TG, 三酰甘油; LDL, 低密度脂蛋白; HDL, 高密度脂蛋白; FPG, 空腹血糖; HbA1c, 糖化血红蛋白。 Note: UA, uric acid; TC, total cholesterol; TG, triglyceride; LDL, low density lipoprotein; HDL, high density lipoprotein; FPG, fasting plasma glucose; HbA1c, glycosylated hemoglobin type A1c.

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表 3 偏回归系数估计与检验

Table 3. Test of partial regression coefficient

变量 Variable	偏回归系数 Partial regression coefficient	s	标准化偏回归系数 Standardized partial regression coefficient	t值 value	P值 value
常数 Constant	221.767	9.989		22.201	＜0.001
TG/(mmol·L^-1)	7.968	1.119	0.119	7.122	＜0.001
HDL/(mmol·L^-1)	-35.051	4.318	-0.128	-8.118	＜0.001
LDL/(mmol·L^-1)	11.235	1.495	0.117	7.517	＜0.001
DBP/mmHg	1.295	0.119	0.193	10.904	＜0.001
SBP/mmHg	-0.458	0.064	-0.128	-7.192	＜0.001
注：1. TC, 三酰甘油；HDL, 高密度脂蛋白；LDL, 低密度脂蛋白。 2. “―”无数据。 Note: 1. TC, total cholesterol; HDL, high density lipoprotein; LDL, low density lipoprotein. 2. “―”No Date.

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表 4 UA与其直接相关变量的偏相关系数

Table 4. Partial correlation coefficient between blood uric acid and its directly related variables

变量 Variable	UA
变量 Variable	偏相关系数 Partial correlation coefficient	P值 value
年龄/岁Age/years	0.026	0.079
TG/(mmol·L^-1)	0.083	< 0.001
LDL/(mmol·L^-1)	0.028	0.057
HDL/(mmol·L^-1)	-0.048	0.001
SBP/mmHg	0.084	< 0.001
DBP/mmHg	0.147	< 0.001
注：TG, 三酰甘油; LDL, 低密度脂蛋白; HDL, 高密度脂蛋白; UA, 尿酸。 Note: TG, triglyceride; LDL, low density lipoprotein; HDL, high density lipoprotein; UA, uric acid.

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表 5 多重线性回归与连续型贝叶斯网络的比较

Table 5. Comparison between multiple linear regression and continuous Bayesian network

条目 Item	多重线性回归分析 Multiple linear regression analysis	连续贝叶斯网络 Continuous Bayesian network
建模方法 Modeling method	以逐步回归法建立多重线性回归模型 Establishing multilinear regression model by stepwise law of return	基于偏相关的结构学习算法，MDL评分确定节点之间的边及边的方向 Based on partial correlation structural learning algorithm, MDL score determines the edges and their directions between nodes
模型复杂度 Model complexity	发现了与UA水平直接相关的5个变量有统计学意义，相对简单 Five variables directly related to UA levels were found to be statistically significant and relatively simple	与UA水平相关的关系网络共24条边，相对复杂 The relationship network related to UA level has a total of 24 edges, which is relatively complex
直接相关因素 Direct related factor	TG、SBP、DBP、LDL和HDL 5个变量与UA水平直接相关，解释了UA水平变异的9.5%，决定系数较小，从专业理论的角度看，尚显不足 The five variables of TG, SBP, DBP, LDL and HDL are directly related to the level of UA, which explains 9.5% of the variation of the level of UA. The Coefficient of determination is small, which is still insufficient from the perspective of professional theory	连续型变量提供更多的信息，发现年龄、TG、LDL、HDL直接影响了UA的水平，而UA的水平直接影响了SBP和DBP的水平, 从专业理论的角度看，合理性更强 Continuous variables provide more information, and it is found that age, TG, LDL, and HDL directly affect the level of UA, while the level of UA directly affects the levels of SBP and DBP. From the perspective of professional theory, the rationality is stronger
与直接相关因素的关联强度 The correlation strength with directly related factor	自变量的偏回归系数反映对因变量的影响程度，标准化回归系数反映不同自变量在模型中的重要性 The partial regression coefficient of the independent variable reflects the degree of influence on the dependent variable, while the standardized regression coefficient reflects the importance of different independent variables in the model	子节点与父节点间的偏相关系数，描述了与UA直接相关的6个因素间相关的程度与方向，区分出4个影响因素和2个结局因素 The partial correlation coefficient between the child node and the parent node describes the degree and direction of correlation between the six factors directly related to UA, distinguishing four influencing factors and two outcome factors
间接相关因素 Indirect related factor	多重线性回归模型无法筛选与UA水平间接相关的影响因素 Multiple linear regression models cannot screen for influencing factors indirectly related to UA levels	TC与UA是间接关系，主要体现在年龄以不同的方式影响着TC、TG、LDL、HDL，血脂各指标有着复杂的关系，从而间接影响了UA的水平 TC and UA are indirectly related, mainly reflected in the fact that age affects TC, TG, LDL, HDL in different ways, and there is a complex relationship between various indicators of blood lipids, thereby indirectly affecting the level of UA
注：UA，尿酸；TG，三酰甘油；LDL，低密度脂蛋白；HDL，高密度脂蛋白；MDL，最小描述长度; TC，总胆固醇。 Note: UA, blood uric acid; TG, triglyceride; LDL, low density lipoprotein; HDL, high density lipoprotein; MDL, minimum description length; TC, total cholesterol.

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