校正弱工具变量偏倚的孟德尔随机化方法比较及其应用

杨博然; 彭刘庆; 高雪; 王菊平; 王彤

doi:10.16462/j.cnki.zhjbkz.2024.04.019

校正弱工具变量偏倚的孟德尔随机化方法比较及其应用

doi: 10.16462/j.cnki.zhjbkz.2024.04.019

山西医科大学公共卫生学院卫生统计学教研室，太原 030001；煤炭环境致病与防治教育部重点实验室，太原 030001

基金项目:

国家自然科学基金 81872715

国家自然科学基金 82103949

山西省基础研究计划资助项目 20210302124186

山西省基础研究计划资助项目 202103021223234

详细信息

通讯作者:
王彤，E-mail：tongwang@sxmu.edu.cn

中图分类号: R195.1
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出版历程
- 收稿日期: 2023-08-23
- 修回日期: 2024-01-06
- 网络出版日期: 2024-05-17
- 刊出日期: 2024-04-10

Comparison and application of Mendelian randomization methods for correcting weak instrumental variable bias

Department of Health Statistics, School of Public Health, Shanxi Medical University, Taiyuan 030001, China, Key Laboratory of Coal Environmental Pathogenicity and Prevention (Shanxi Medical University) Ministry of Education, Taiyuan 030001, China

Funds:

National Natural Science Foundation of China 81872715

National Natural Science Foundation of China 82103949

Basic Research Project of Shanxi Province, China 20210302124186

Basic Research Project of Shanxi Province, China 202103021223234

More Information

Corresponding author: WANG Tong, E-mail: tongwang@sxmu.edu.cn

摘要

摘要: 目的探究无工具变量可用或需评估弱工具变量偏倚对结果的影响时，为选择合适的两样本孟德尔随机化(two-sample Mendelian randomization, TwoSampleMR)方法提供建议。方法分别在无多效性、均衡多效性、正向多效性模拟情形下，变换工具变量强度考察弱工具变量对修正权重的逆方差加权模型(inverse variance weighting with modified weights, MW-IVW)、稳健校正轮廓评分(robust adjusted profile score, RAPS)孟德尔随机化方法和基于混合正态分布的孟德尔随机化模型(MR mixture model, MR-Mix)3种方法的影响。正向多效性和弱工具变量同时存在时，模拟不同个数工具变量对MR-Mix的影响。MR-Mix为主分析方法，其余2方法作为敏感性分析，探究BMI、高密度脂蛋白(high-density lipoprotein, HDL)、低密度脂蛋白(low-density lipoprotein, LDL)、三酰甘油(triglyceride，TG)以及总胆固醇(total cholesterol, TC)与血清尿酸之间的因果关联。结果无多效性和均衡多效性情形下，MW-IVW表现最佳，MR-Mix表现最差。正向多效性情况下，MR-Mix表现最好，MW-IVW表现最差。BMI(β=0.280, P=0.003)和TG(β=0.370, P < 0.001)是血清尿酸升高的危险因素，HDL(β=-0.250, P=0.002)是血清尿酸的保护因素。结论在无多效性和均衡多效性情形下，MW-IVW有更好的统计学性能；但当正向多效性存在时，MR-Mix有更好的稳健性。BMI和TG为血清尿酸升高的危险因素。
- 孟德尔随机化 /
- 多效性 /
- 弱工具变量 /
- 体质指数 /
- 脂质 /
- 血清尿酸
Abstract: Objective To provide suggestions to choose the appropriate two-sample Mendelian randomization methods when no instrumental variables are available or weak instrumental variable bias exist. Methods In the case of no pleiotropy, balanced pleiotropy, and directional pleiotropy, respectively, the impact of weak instrumental variables on each method was investigated by changing the intensity of instrumental variables. The study simulated different number of instrumental variables to access the impact on MR-Mix under the condition that both directional pleiotropic effects and weak instrumental variables existed. MR-Mix served as the primary analytical method, while the other two methods were employed as sensitivity analyses to explore the causal associations between BMI, HDL, LDL, TG, TC, and serum uric acid. Results Under scenarios of no pleiotropy and balanced pleiotropy, MW-IVW performed the best, while MR-Mix performed the worst. In the case of directional pleiotropic, MR-Mix exhibited the best performed, whereas MW-IVW performed the worst. BMI(β=0.280, P=0.003) and TG(β=0.370, P < 0.001) were identified as risk factors for elevated serum uric acid. HDL(β=-0.250, P=0.002) was identified as a protective factor. Conclusions Under scenarios of no pleiotropy and balanced pleiotropy, MW-IVW demonstrates better statistical performance. However, in the presence of directional pleiotropy, MR-Mix exhibits superior robustness. BMI and TG are identified as risk factors for elevated serum uric acid.
- Mendelian randomizaiton /
- Pleiotropy /
- Weak instruments /
- Body mass index /
- Lipid traits /
- Serum urate

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图 1 弱工具变量个数对MR-Mix效能的影响

图A: 无多效性情形弱工具变量个数对MR-Mix效能的影响; 图B: 均衡多效性情形弱工具变量个数对MR-Mix效能的影响; 图C: 正向多效性情形弱工具变量个数对MR-Mix效能的影响。

Figure 1. Effect of the number of weak tool variables on the performance of MR-Mix

Figure A: illustrates the effect of the number of weak instrumental variables on the efficiency of MR-Mix under the scenario of no pleiotropy; Figure B: illustrates the effect of the number of weak instrumental variables on the efficiency of MR-Mix under the scenario of balanced pleiotropy; Figure C: illustrates the effect of the number of weak instrumental variables on the efficiency of MR-Mix under the scenario of directional pleiotropy.

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表 1 不同强度工具变量下各方法表现

Table 1. The performance of methods under different intensity tool variables

Mean F	MW-IVW			RAPS			MR-Mix
Mean F	$\widehat{\beta}$(s_x)	TIE/P	CF	$\widehat{\beta}$(s_x)	TIE/P	CF	$\widehat{\beta}$(s_x)	TIE/P	CF
无多效性方案No pleiotropy
β=0
100	0.000(0.008)	0.055	0.948	0.000(0.008)	0.052	0.949	0.000(1.942)	0.003	0.998
50	0.000(0.008)	0.057	0.950	0.000(0.008)	0.053	0.948	0.000(1.308)	0.005	0.995
25	0.000(0.007)	0.051	0.955	0.000(0.008)	0.045	0.955	0.000(0.840)	0.005	0.995
10	0.000(0.006)	0.035	0.970	0.000(0.015)	0.050	0.951	0.000(0.897)	0.006	0.994
β=0.05
100	0.050(0.008)	1.000	0.950	0.051(0.008)	1.000	0.951	0.050(0.872)	0.458	0.995
50	0.050(0.008)	0.999	0.952	0.051(0.008)	0.999	0.956	0.051(0.513)	0.451	0.997
25	0.050(0.008)	1.000	0.965	0.054(0.009)	1.000	0.963	0.055(0.371)	0.420	0.999
10	0.050(0.007)	1.000	0.962	0.061(0.012)	1.000	0.958	0.060(0.251)	0.431	0.978
β=0.1
100	0.100(0.008)	1.000	0.952	0.101(0.008)	1.000	0.957	0.101(2.821)	0.683	0.997
50	0.100(0.008)	1.000	0.954	0.102(0.009)	1.000	0.961	0.102(0.439)	0.673	0.996
25	0.100(0.008)	1.000	0.962	0.105(0.010)	1.000	0.962	0.106(0.386)	0.702	0.998
10	0.100(0.008)	1.000	0.958	0.111(0.014)	1.000	0.977	0.100(0.117)	0.752	0.952
均衡多效性方案Balanced pleiotropy
β=0
100	0.000(0.027)	0.058	0.949	0.000(0.036)	0.070	0.930	0.000(0.723)	0.007	0.993
50	0.000(0.010)	0.056	0.947	0.000(0.010)	0.075	0.925	0.000(0.753)	0.021	0.976
25	0.000(0.009)	0.057	0.946	0.000(0.011)	0.068	0.932	0.000(0.641)	0.019	0.981
10	0.000(0.008)	0.047	0.958	0.000(0.015)	0.061	0.939	0.000(0.493)	0.034	0.966
β=0.05
100	0.050(0.010)	0.996	0.951	0.051(0.010)	0.994	0.929	0.044(1.250)	0.503	0.981
50	0.050(0.009)	0.995	0.950	0.052(0.010)	0.993	0.930	0.048(0.652)	0.496	0.986
25	0.050(0.010)	0.998	0.959	0.055(0.011)	0.994	0.922	0.053(3.862)	0.443	0.988
10	0.050(0.009)	1.000	0.972	0.057(0.015)	0.999	0.938	0.060(2.129)	0.330	0.989
β=0.1
100	0.100(0.009)	1.000	0.954	0.101(0.010)	1.000	0.931	0.094(0.650)	0.699	0.987
50	0.100(0.010)	1.000	0.960	0.103(0.011)	1.000	0.934	0.097(0.844)	0.645	0.986
25	0.100(0.011)	1.000	0.969	0.108(0.012)	1.000	0.915	0.105(1.611)	0.528	0.996
10	0.100(0.010)	1.000	0.964	0.100(0.017)	1.000	0.947	0.100(0.338)	0.611	0.964
正向多效性方案Directional pleiotropy
β=0
100	0.063(0.029)	0.477	0.544	0.000(0.007)	0.128	0.872	0.006(0.025)	0.055	0.945
50	0.060(0.030)	0.465	0.567	0.000(0.006)	0.193	0.807	0.002(0.041)	0.091	0.909
25	0.055(0.029)	0.379	0.642	0.001(0.005)	0.307	0.693	0.000(0.063)	0.044	0.956
10	0.021(0.026)	0.373	0.670	0.000(0.004)	0.571	0.429	0.001(0.034)	0.094	0.906
β=0.05
100	0.112(0.030)	1.000	0.548	0.051(0.007)	1.000	0.866	0.050(0.025)	0.909	0.943
50	0.110(0.029)	0.998	0.570	0.052(0.007)	1.000	0.824	0.045(0.031)	0.893	0.915
25	0.105(0.030)	0.985	0.665	0.055(0.006)	1.000	0.710	0.048(0.030)	0.886	0.960
10	0.107(0.030)	0.973	0.699	0.064(0.006)	1.000	0.398	0.058(0.054)	0.888	0.784
β=0.1
100	0.162(0.030)	1.000	0.550	0.101(0.007)	1.000	0.885	0.098(0.021)	0.955	0.953
50	0.160(0.030)	1.000	0.579	0.103(0.007)	1.000	0.833	0.085(0.161)	0.943	0.921
25	0.156(0.031)	1.000	0.673	0.107(0.007)	1.000	0.765	0.094(0.029)	0.934	0.942
10	0.160(0.031)	1.000	0.660	0.117(0.009)	1.000	0.566	0.098(0.139)	0.901	0.659
注：Mean F, 平均因果效应估计值; MW-IVW, 修正权重的逆方差加权方法; RAPS, 稳健校正的轮廓评分模型; MR-Mix, 效应大小混合正态分布的孟德尔随机化方法; s_x, 标准误；TIE, 一型错误率; CF, 95% CI覆盖率。 Note: Mean F, average causal effect estimates; MW-IVW, inverse variance weighting with modified weights; RAPS, robust adjusting profile score; MR-Mix, Mendelian Randomization mixture model; s_x, standard error; TIE, type I error; CF, 95% CI coverage frequency.

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表 2 强、弱工具变量分析结果

Table 2. Analysis results of strong and weak instrumental variables

暴露 Exposure	工具变量 Instrumental Variables	方法 Methods	SNP个数 nSNPs	β值value (95% CI)	P值 value
BMI	强工具变量Strong instrumental variables	IVW	20	-0.029(-0.064~0.006)	0.110
		WME	20	-0.025(-0.031~-0.009)	0.012
		MR-Egger	20	-0.065(-0.128~-0.002)	0.056
		Egger-intercept		0.000(-0.002~0.010)	0.191
	弱工具变量Weak instrumental variables	MW-IVW	45	-0.009(-0.056~0.038)	0.700
		RAPS	45	-0.013(-0.021~0.005)	0.024
		MR-Mix	45	-0.020(-0.042~0.002)	0.058
HDL	强工具变量Strong instrumental variables	IVW	21	-0.030(-0.085~0.025)	0.284
		WME	21	-0.005(-0.023~0.013)	0.606
		MR-Egger	21	0.052(-0.040~0.144)	0.284
		Egger-intercept		-0.008(-0.016~0.000)	0.048
	弱工具变量Weak instrumental variables	M-IVW	51	-0.039(-0.080~0.002)	0.067
		RAPS	51	-0.014(-0.024~-0.004)	0.005
		MR-Mix	51	0.000(-0.020~0.019)	1.000
LDL	强工具变量Strong instrumental variables	IVW	21	-0.003(-0.070~0.064)	0.938
		WME	21	0.003(-0.019~0.025)	0.752
		MR-Egger	21	0.074(-0.042~0.190)	0.222
		Egger-intercept		-0.008(-0.018~0.002)	0.131
	弱工具变量Weak instrumental variables	MW-IVW	51	0.006(-0.037~0.049)	0.785
		RAPS	51	0.007 (-0.003~0.017)	0.169
		MR-Mix	51	-0.010(-0.026~0.006)	0.239
TG	强工具变量Strong instrumental variables	IVW	21	0.109(-0.060~0.278)	0.203
		WME	21	0.007(-0.011~0.025)	0.400
		MR-Egger	21	-0.016(-0.316~0.284)	0.917
		Egger-intercept		0.012(-0.013~0.037)	0.339
	弱工具变量Weak instrumental variables	MW-IVW	51	0.111(0.011~0.211)	0.030
		RAPS	51	0.446(0.428~0.464)	0.000
		MR-Mix	51	0.010(-0.033~0.053)	0.651
TC	强工具变量Strong instrumental variables	IVW	25	0.049(-0.045~0.143)	0.300
		WME	25	0.034(-0.003~0.071)	0.073
		MR-Egger	25	0.143(-0.024~0.310)	0.105
		Egger-intercept		-0.009(-0.023~0.005)	0.197
	弱工具变量Weak instrumental variables	MW-IVW	53	0.047(-0.016~0.110)	0.146
		RAPS	53	0.053(0.029~0.077)	0.534
		MR-Mix	53	0.030(-0.025~0.085)	0.280
注：HDL, 高密度脂蛋白; LDL, 低密度脂蛋白; TG, 三酰甘油; TC, 总胆固醇; IVW, 逆方差加权方法; MWE, 加权中位数模型; MR-Egger, 孟德尔随机化-Egger方法; Egger-intercept, MR-Egger方法的截距项; MW-IVW, 修正权重的逆方差加权方法; RAPS, 稳健校正的轮廓评分模型; MR-Mix, 效应大小混合正态分布的孟德尔随机化方法。 Note: HDL, high-density lipoprotein; LDL, low-density lipoprotein; TG, triglyceride; TC, total cholesterol; IVW, inverse variance weighting; MWE, weighted median estimator; MW-IVW, inverse variance weighting with modified weights; RAPS, robust adjusting profile score; MR-Mix, Mendelian randomization mixture model.

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表 3 逆向MR强、弱工具变量分析结果

Table 3. Analysis results of strong and weak instrumental variables of reverse MR

结局Outcome	工具变量 Instrumental variables	方法 Methods	SNP个数 nSNPs	β值value (95% CI)	P值 value
BMI	强工具变量Strong instrumental variables	IVW	443	0.310(0.245~0.375)	7.799×10^-21
		WME	443	0.306(0.243~0.369)	9.027×10^-22
		MR-Egger	443	0.290(0.119~0.461)	9.153×10^-4
		Egger-intercept		0.000(-0.002~0.002)	0.807
	弱工具变量Weak instrumental variables	MW-IVW	638	0.312(0.259~0.365)	7.377×10^-30
		RAPS	638	0.326(0.293~0.359)	0.000
		MR-Mix	638	0.280(0.023~0.537)	0.003
HDL	强工具变量Strong instrumental variables	IVW	109	-0.114(-0.181~-0.047)	0.0007
		WME	109	-0.007(-0.062~0.076)	0.851
		MR-Egger	109	-0.004(-0.104~0.096)	0.934
		Egger-intercept		-0.004(-0.006~-0.002)	0.005
	弱工具变量Weak instrumental variables	MW-IVW	178	-0.114(-0.169~-0.059)	4.570×10^-5
		RAPS	178	-0.098(-0.151~-0.045)	0.0003
		MR-Mix	178	-0.250(-0.64~0.140)	0.002
LDL	强工具变量Strong instrumental variables	IVW	50	0.019(-0.193~0.191)	0.826
		WME	50	-0.017(-0.123~0.098)	0.755
		MR-Egger	50	0.124(-0.195~0.443)	0.450
		Egger-intercept		-0.003(-0.013~0.007)	0.448
	弱工具变量Weak instrumental variables	MW-IVW	97	-0.069(-0.149~0.011)	0.091
		RAPS	97	-0.070(-0.123~-0.017)	0.009
		MR-Mix	97	-0.050(-0.156~0.056)	0.356
TG	强工具变量Strong instrumental variables	IVW	174	0.223(0.154~0.292)	2.279×10^-10
		WME	174	0.154(0.068~0.240)	0.0004
		MR-Egger	174	0.112(0.002~0.222)	4.661×10^-2
		Egger-intercept		0.003(0.001~0.005)	0.013
	弱工具变量Weak instrumental variables	MW-IVW	362	0.221(0.166~0.276)	2.012×10^-15
		RAPS	362	0.229(0.192~0.266)	0.000
		MR-Mix	362	0.370(0.192~0.548)	4.436×10^-5
TC	强工具变量Strong instrumental variables	IVW	77	-0.027(-0.105~0.051)	0.503
		WME	77	-0.045(-0.102~0.012)	0.121
		MR-Egger	77	0.069(-0.092~0.230)	0.405
		Egger-intercept		-0.005(-0.013~0.003)	0.185
	弱工具变量Weak instrumental variables	MW-IVW	125	-0.019(-0.082~-0.044)	0.560
		RAPS	125	-0.020(-0.049~0.009)	0.186
		MR-Mix	125	-0.040(-0.091~0.101)	0.127
注：HDL, 高密度脂蛋白; LDL, 低密度脂蛋白; TG, 三酰甘油; TC, 总胆固醇; IVW, 逆方差加权方法; MWE, 加权中位数模型; MR-Egger, 孟德尔随机化-Egger方法; Egger-intercept, MR-Egger方法的截距项; MW-IVW, 修正权重的逆方差加权方法; RAPS, 稳健校正的轮廓评分模型; MR-Mix, 效应大小混合正态分布的孟德尔随机化方法。 Note: HDL, high-density lipoprotein; LDL, low-density lipoprotein; TG, triglyceride; TC, total cholesterol; IVW, inverse variance weighting; MWE, weighted median estimator; MW-IVW, inverse variance weighting with modified weights; RAPS, robust adjusting profile score; MR-Mix, Mendelian randomization mixture model.

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