Authors list

Mahdi Akbarzadeh
Sahand Tehrani Fateh
Aysan Moeinafshar
Danial Habibi;
Amir Hossein Ghanooni
Hesam Saeidian
Parisa Riahi
Maryam Zarkesh
Hossein Lanjanian
Mina Jahangiri
Maryam Moazzam-Jazi
Farshad Teymoori
Fereidoun Azizi
Mehdi Hedayati
Maryam Sadat Daneshpour

Abbreviations: (Follow tabs by these terms)
- VitD : 25-Hydroxyvitamin D level
- Hypo : Hypothyroidism
- HT : Hashimoto’s thyroiditis
- fT4 : Free T4 level
- TSH : TSH level

[VitD and Hypo]

Introduction

Title: Investigating the causality between 25-Hydroxyvitamin D level on Hypothyroidism
- Exposure: 25-Hydroxyvitamin D level, Data downloaded from GWAS catalog Database | Reference paper: Joana A. Revez Paper 2020 | GWAS ID: GCST90000616
- Sample size: 417,580
- Outcome: Hypothyroidism, Data downloaded from GWAS catalog Database | Reference paper: Samuel Mathieu 2022 | GWAS ID: GCST90204167
- Sample size:494,577 , Number of cases:51,194 , Number of controls: 443,383
- Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 7,250,104 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^-8\): 16,012 SNPs

3- Number of SNPs exposure after clumping : 115 SNPs

4- Number of total SNPs in outcome: 10,836,150 SNPs

5- Number of common variants between exposure and outcome: 109 SNPs

6- Number of SNPs after harmonization (action=3) = 90 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 89 SNP (rs28407950 was removed)

8- Number of SNPs after removing those that have MAF < 0.01 = 89 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.78   36.13   42.63  117.54   70.06 2567.54

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	avirfC	outcome	exposure	MR Egger	89	-0.1464337	0.0916311	0.1136513
oUw2e5	avirfC	outcome	exposure	Weighted median	89	-0.1237461	0.0664158	0.0624335
oUw2e5	avirfC	outcome	exposure	Inverse variance weighted	89	-0.1307693	0.0577112	0.0234559
oUw2e5	avirfC	outcome	exposure	Simple mode	89	-0.1865331	0.1400346	0.1862833
oUw2e5	avirfC	outcome	exposure	Weighted mode	89	-0.1418811	0.0613496	0.0230741

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	avirfC	outcome	exposure	MR Egger	180.7067	87	0
oUw2e5	avirfC	outcome	exposure	Inverse variance weighted	180.8081	88	0

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	avirfC	outcome	exposure	0.0005249	0.0023765	0.8257019

Testing Outlier with PRESSO test

## [1] "Two SNPs (rs73413596 and rs9861009) were detected by MRPRESSO and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	avirfC	outcome	exposure	MR Egger	87	-0.1334385	0.0800126	0.0990519
oUw2e5	avirfC	outcome	exposure	Weighted median	87	-0.1247436	0.0672326	0.0635386
oUw2e5	avirfC	outcome	exposure	Inverse variance weighted	87	-0.1267930	0.0505315	0.0121008
oUw2e5	avirfC	outcome	exposure	Simple mode	87	-0.1848303	0.1496629	0.2202023
oUw2e5	avirfC	outcome	exposure	Weighted mode	87	-0.1337747	0.0657218	0.0448821

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	avirfC	outcome	exposure	MR Egger	134.4047	85	0.0005139
oUw2e5	avirfC	outcome	exposure	Inverse variance weighted	134.4230	86	0.0006569

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	avirfC	outcome	exposure	0.0002243	0.0020857	0.9146166

Studentized residuals:

Radial test

## 
## Radial IVW
## 
##                    Estimate  Std.Error   t value    Pr(>|t|)
## Effect (Mod.2nd) -0.1267937 0.05053137 -2.509208 0.012100225
## Iterative        -0.1267937 0.05053137 -2.509208 0.012100225
## Exact (FE)       -0.1284882 0.04043783 -3.177427 0.001485882
## Exact (RE)       -0.1278726 0.05773297 -2.214896 0.029410571
## 
## 
## Residual standard error: 1.25 on 86 degrees of freedom
## 
## F-statistic: 6.3 on 1 and 86 DF, p-value: 0.014
## Q-Statistic for heterogeneity: 134.2939 on 86 DF , p-value: 0.0006739595
## 
##  No significant outliers 
## Number of iterations = 2

## [1] "No significant outliers"

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

##        23        82 
## 7.9211985 0.3927332

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	avirfC	outcome	exposure	MR Egger	77	-0.3186386	0.1133876	0.0063124
oUw2e5	avirfC	outcome	exposure	Weighted median	77	-0.2144203	0.0786440	0.0064016
oUw2e5	avirfC	outcome	exposure	Inverse variance weighted	77	-0.1973681	0.0535110	0.0002257
oUw2e5	avirfC	outcome	exposure	Simple mode	77	-0.2324364	0.1715690	0.1795047
oUw2e5	avirfC	outcome	exposure	Weighted mode	77	-0.2661283	0.1027979	0.0115342

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	avirfC	outcome	exposure	MR Egger	73.88599	75	0.5147087
oUw2e5	avirfC	outcome	exposure	Inverse variance weighted	75.35763	76	0.4992441

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	avirfC	outcome	exposure	0.002823	0.0023271	0.2288948

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 77 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI        p-value
##     IVW   -0.197     0.054 -0.302, -0.092   0.000
## ------------------------------------------------------------------
## Residual standard error =  0.996 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 75.3576 on 76 degrees of freedom, (p-value = 0.4992). I^2 = 0.0%.

##                     Method Estimate Std Error 95% CI         P-value
##              Simple median   -0.202     0.084  -0.367 -0.036   0.017
##            Weighted median   -0.215     0.082  -0.375 -0.054   0.009
##  Penalized weighted median   -0.215     0.082  -0.375 -0.054   0.009
##                                                                     
##                        IVW   -0.197     0.054  -0.302 -0.092   0.000
##              Penalized IVW   -0.197     0.054  -0.302 -0.092   0.000
##                 Robust IVW   -0.202     0.052  -0.304 -0.099   0.000
##       Penalized robust IVW   -0.202     0.052  -0.304 -0.099   0.000
##                                                                     
##                   MR-Egger   -0.319     0.113  -0.541 -0.096   0.005
##                (intercept)    0.003     0.002  -0.002  0.007   0.225
##         Penalized MR-Egger   -0.319     0.113  -0.541 -0.096   0.005
##                (intercept)    0.003     0.002  -0.002  0.007   0.225
##            Robust MR-Egger   -0.317     0.094  -0.502 -0.133   0.001
##                (intercept)    0.003     0.002  -0.002  0.007   0.230
##  Penalized robust MR-Egger   -0.317     0.094  -0.502 -0.133   0.001
##                (intercept)    0.003     0.002  -0.002  0.007   0.230

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
oUw2e5	avirfC	exposure	outcome	0.0138834	0.0001799	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] -0.1999762
## 
## $beta.se
## [1] 0.05431763
## 
## $beta.p.value
## [1] 0.0002317672
## 
## $naive.se
## [1] 0.05395171
## 
## $chi.sq.test
## [1] 75.17799

##   over.dispersion loss.function   beta.hat    beta.se
## 1           FALSE            l2 -0.1999762 0.05431763
## 2           FALSE         huber -0.2055908 0.05573633
## 3           FALSE         tukey -0.2049427 0.05573554
## 4            TRUE            l2 -0.1999772 0.05432156
## 5            TRUE         huber -0.2056785 0.05588018
## 6            TRUE         tukey -0.2050190 0.05627405

## 
## MR-Lasso method 
## 
## Number of variants : 77 
## Number of valid instruments : 77 
## Tuning parameter : 0.2793058 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI        p-value
##  exposure   -0.197     0.054 -0.302, -0.092   0.000
## ------------------------------------------------------------------

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  77 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue          95% CI
##  cML-MA-BIC   -0.200 0.054  0.000 [-0.306,-0.095]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 77 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI        p-value Condition
##    dIVW   -0.200     0.054 -0.307, -0.094   0.000   652.186
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 77 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI        p-value
##     MBE   -0.266     0.112 -0.486, -0.046   0.018
## ------------------------------------------------------------------

[VitD and HT]

Introduction

Title: Investigating the causality between 25-Hydroxyvitamin D level on Hashimoto’s Disease
- Exposure: 25-Hydroxyvitamin D level, Data downloaded from GWAS catalog Database | Reference paper: Joana A. Revez Paper 2020 | GWAS ID: GCST90000616
- Sample size: 417,580
- Outcome: Hashimoto’s Disease, Data downloaded from GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of cases:15,654 , Number of controls: 379,986
- Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 7,250,104 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^-8\): 16,012 SNPs

3- Number of SNPs exposure after clumping : 115 SNPs

4- Number of total SNPs in outcome: 25,797,652 SNPs

5- Number of common variants between exposure and outcome: 106 SNPs

6- Number of SNPs after harmonization (action=3) = 88 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 87 SNP (rs28407950 was removed)

8- Number of SNPs after removing those that have MAF < 0.01 = 87 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.78   35.78   43.13  118.55   67.82 2567.54

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	jVh3lS	outcome	exposure	MR Egger	87	-0.1767241	0.1667552	0.2922463
oUw2e5	jVh3lS	outcome	exposure	Weighted median	87	-0.0450173	0.1511758	0.7658700
oUw2e5	jVh3lS	outcome	exposure	Inverse variance weighted	87	-0.0469765	0.1008700	0.6414211
oUw2e5	jVh3lS	outcome	exposure	Simple mode	87	0.1921724	0.2781094	0.4914291
oUw2e5	jVh3lS	outcome	exposure	Weighted mode	87	-0.0462505	0.1263834	0.7152983

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	jVh3lS	outcome	exposure	MR Egger	112.7475	85	0.0237107
oUw2e5	jVh3lS	outcome	exposure	Inverse variance weighted	114.0142	86	0.0233072

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	jVh3lS	outcome	exposure	0.004073	0.0041678	0.3312166

Testing Outlier with PRESSO test

## [1] "Two SNPs (rs73413596 and rs9861009) were detected by MRPRESSO and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	jVh3lS	outcome	exposure	MR Egger	87	-0.1767241	0.1667552	0.2922463
oUw2e5	jVh3lS	outcome	exposure	Weighted median	87	-0.0450173	0.1584242	0.7762901
oUw2e5	jVh3lS	outcome	exposure	Inverse variance weighted	87	-0.0469765	0.1008700	0.6414211
oUw2e5	jVh3lS	outcome	exposure	Simple mode	87	0.1921724	0.2743620	0.4855471
oUw2e5	jVh3lS	outcome	exposure	Weighted mode	87	-0.0462505	0.1295946	0.7220515

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	jVh3lS	outcome	exposure	MR Egger	112.7475	85	0.0237107
oUw2e5	jVh3lS	outcome	exposure	Inverse variance weighted	114.0142	86	0.0233072

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	jVh3lS	outcome	exposure	0.004073	0.0041678	0.3312166

Studentized residuals:

Radial test

## 
## Radial IVW
## 
##                     Estimate  Std.Error    t value  Pr(>|t|)
## Effect (Mod.2nd) -0.04697674 0.10087009 -0.4657153 0.6414193
## Iterative        -0.04697674 0.10087009 -0.4657153 0.6414193
## Exact (FE)       -0.04752580 0.08760697 -0.5424887 0.5874819
## Exact (RE)       -0.04738330 0.08539171 -0.5548935 0.5804079
## 
## 
## Residual standard error: 1.151 on 86 degrees of freedom
## 
## F-statistic: 0.22 on 1 and 86 DF, p-value: 0.643
## Q-Statistic for heterogeneity: 114.0109 on 86 DF , p-value: 0.02331904
## 
##  No significant outliers 
## Number of iterations = 2

## [1] "No significant outliers"

Cook’s distance

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

##        22        26        28        81 
## 2.2775207 0.1161799 0.3026865 0.3128092

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	jVh3lS	outcome	exposure	MR Egger	81	-0.1444301	0.1675495	0.3912886
oUw2e5	jVh3lS	outcome	exposure	Weighted median	81	-0.0405204	0.1530674	0.7912231
oUw2e5	jVh3lS	outcome	exposure	Inverse variance weighted	81	-0.0213403	0.0985213	0.8285153
oUw2e5	jVh3lS	outcome	exposure	Simple mode	81	0.2127241	0.3004208	0.4809492
oUw2e5	jVh3lS	outcome	exposure	Weighted mode	81	-0.0244143	0.1329955	0.8548133

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	jVh3lS	outcome	exposure	MR Egger	95.32294	79	0.1019003
oUw2e5	jVh3lS	outcome	exposure	Inverse variance weighted	96.31948	80	0.1032066

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	jVh3lS	outcome	exposure	0.0037247	0.0040985	0.3662284

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 81 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW   -0.021     0.099 -0.214, 0.172   0.829
## ------------------------------------------------------------------
## Residual standard error =  1.097 
## Heterogeneity test statistic (Cochran's Q) = 96.3195 on 80 degrees of freedom, (p-value = 0.1032). I^2 = 16.9%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.081     0.155  -0.223 0.386   0.600
##            Weighted median   -0.040     0.150  -0.335 0.254   0.788
##  Penalized weighted median   -0.042     0.150  -0.336 0.253   0.782
##                                                                    
##                        IVW   -0.021     0.099  -0.214 0.172   0.829
##              Penalized IVW   -0.036     0.095  -0.221 0.150   0.706
##                 Robust IVW   -0.032     0.069  -0.167 0.104   0.648
##       Penalized robust IVW   -0.036     0.069  -0.171 0.099   0.599
##                                                                    
##                   MR-Egger   -0.144     0.168  -0.473 0.184   0.389
##                (intercept)    0.004     0.004  -0.004 0.012   0.363
##         Penalized MR-Egger   -0.121     0.163  -0.441 0.198   0.457
##                (intercept)    0.003     0.004  -0.005 0.011   0.499
##            Robust MR-Egger   -0.113     0.095  -0.298 0.073   0.234
##                (intercept)    0.003     0.004  -0.005 0.010   0.485
##  Penalized robust MR-Egger   -0.105     0.091  -0.283 0.073   0.249
##                (intercept)    0.002     0.004  -0.005 0.010   0.533

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
oUw2e5	jVh3lS	exposure	outcome	0.0171032	0.0002433	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] -0.02158423
## 
## $beta.se
## [1] 0.09058503
## 
## $beta.p.value
## [1] 0.8116671
## 
## $naive.se
## [1] 0.0901482
## 
## $chi.sq.test
## [1] 96.31883

##   over.dispersion loss.function    beta.hat    beta.se
## 1           FALSE            l2 -0.02158423 0.09058503
## 2           FALSE         huber -0.03384769 0.09293915
## 3           FALSE         tukey -0.03399085 0.09293933
## 4            TRUE            l2 -0.02255761 0.09770638
## 5            TRUE         huber -0.03664930 0.10136241
## 6            TRUE         tukey -0.03232759 0.10111534

## 
## MR-Lasso method 
## 
## Number of variants : 81 
## Number of valid instruments : 78 
## Tuning parameter : 0.2830687 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure   -0.070     0.090 -0.247, 0.107   0.436
## ------------------------------------------------------------------

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  81 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC   -0.024 0.091  0.788 [-0.202,0.153]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 81 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW   -0.022     0.100 -0.217, 0.174   0.829   968.842
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 81 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE   -0.024     0.146 -0.310, 0.261   0.867
## ------------------------------------------------------------------

[VitD and fT4]

Introduction

Title: Investigating the causality between 25-Hydroxyvitamin D level on fT4
- Exposure: 25-Hydroxyvitamin D level, Data downloaded from GWAS catalog Database | Reference paper: Joana A. Revez Paper 2020 | GWAS ID: GCST90000616
- Sample size: 417,580
- Outcome: fT4, Data downloaded from Thyroid Omics Consortium | Reference paper: Alexander Teumer 2018 | GWAS ID: phs000930
- Sample size:49,269
- Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 7,250,104 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^-8\): 16,012 SNPs

3- Number of SNPs exposure after clumping : 115 SNPs

4- Number of total SNPs in outcome: 7,745,739 SNPs

5- Number of common variants between exposure and outcome: 101 SNPs

6- Number of SNPs after harmonization (action=3) = 84 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 84 SNP (rs28407950 was removed)

8- Number of SNPs after removing those that have MAF < 0.01 = 84 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.78   36.14   43.18  121.47   70.46 2567.54

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	daasDf	outcome	exposure	MR Egger	84	-0.0418438	0.0854867	0.6258107
oUw2e5	daasDf	outcome	exposure	Weighted median	84	0.0722727	0.0617734	0.2420150
oUw2e5	daasDf	outcome	exposure	Inverse variance weighted	84	0.0122784	0.0543298	0.8212032
oUw2e5	daasDf	outcome	exposure	Simple mode	84	0.0189745	0.1576589	0.9044954
oUw2e5	daasDf	outcome	exposure	Weighted mode	84	0.0498572	0.0567387	0.3820925

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	daasDf	outcome	exposure	MR Egger	198.4561	82	0
oUw2e5	daasDf	outcome	exposure	Inverse variance weighted	200.0878	83	0

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	daasDf	outcome	exposure	0.0018081	0.0022021	0.413966

Testing Outlier with PRESSO test

## [1] "Two SNPs (rs12317268 and rs7439366) were detected by MRPRESSO and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	daasDf	outcome	exposure	MR Egger	82	-0.0185637	0.0754185	0.8062026
oUw2e5	daasDf	outcome	exposure	Weighted median	82	0.0730557	0.0619674	0.2384231
oUw2e5	daasDf	outcome	exposure	Inverse variance weighted	82	0.0507501	0.0486693	0.2970623
oUw2e5	daasDf	outcome	exposure	Simple mode	82	0.0252830	0.1530636	0.8692142
oUw2e5	daasDf	outcome	exposure	Weighted mode	82	0.0432513	0.0609228	0.4797819

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	daasDf	outcome	exposure	MR Egger	149.4853	80	4.1e-06
oUw2e5	daasDf	outcome	exposure	Inverse variance weighted	152.1795	81	2.9e-06

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	daasDf	outcome	exposure	0.0023277	0.0019385	0.2333822

Studentized residuals:

Radial test

## 
## Radial IVW
## 
##                    Estimate  Std.Error   t value  Pr(>|t|)
## Effect (Mod.2nd) 0.05074888 0.04866908 1.0427335 0.2970718
## Iterative        0.05074888 0.04866908 1.0427335 0.2970718
## Exact (FE)       0.05160059 0.03551133 1.4530740 0.1462032
## Exact (RE)       0.05120977 0.05328849 0.9609911 0.3394166
## 
## 
## Residual standard error: 1.371 on 81 degrees of freedom
## 
## F-statistic: 1.09 on 1 and 81 DF, p-value: 0.3
## Q-Statistic for heterogeneity: 152.146 on 81 DF , p-value: 2.936746e-06
## 
##  No significant outliers 
## Number of iterations = 2

## [1] "No significant outliers"

Cook’s distance

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

##         12         20         21         25         29         31         50 
## 0.03515705 0.04136593 0.25701721 0.03762193 0.08422961 0.08033235 0.03836803 
##         67 
## 0.06786057

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
oUw2e5	daasDf	outcome	exposure	MR Egger	70	0.2466067	0.1387102	0.0798986
oUw2e5	daasDf	outcome	exposure	Weighted median	70	0.2233635	0.0803358	0.0054296
oUw2e5	daasDf	outcome	exposure	Inverse variance weighted	70	0.2035989	0.0563823	0.0003050
oUw2e5	daasDf	outcome	exposure	Simple mode	70	0.0316973	0.1772358	0.8585853
oUw2e5	daasDf	outcome	exposure	Weighted mode	70	0.2194134	0.1176407	0.0664179

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
oUw2e5	daasDf	outcome	exposure	MR Egger	86.59380	68	0.0636779
oUw2e5	daasDf	outcome	exposure	Inverse variance weighted	86.74083	69	0.0731205

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
oUw2e5	daasDf	outcome	exposure	-0.0008971	0.00264	0.735061

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 70 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.204     0.056 0.093, 0.314   0.000
## ------------------------------------------------------------------
## Residual standard error =  1.121 
## Heterogeneity test statistic (Cochran's Q) = 86.7408 on 69 degrees of freedom, (p-value = 0.0731). I^2 = 20.5%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.123     0.080  -0.034 0.280   0.125
##            Weighted median    0.224     0.080   0.068 0.381   0.005
##  Penalized weighted median    0.223     0.080   0.066 0.380   0.005
##                                                                    
##                        IVW    0.204     0.056   0.093 0.314   0.000
##              Penalized IVW    0.204     0.056   0.093 0.314   0.000
##                 Robust IVW    0.193     0.060   0.075 0.310   0.001
##       Penalized robust IVW    0.193     0.060   0.075 0.310   0.001
##                                                                    
##                   MR-Egger    0.247     0.139  -0.025 0.518   0.075
##                (intercept)   -0.001     0.003  -0.006 0.004   0.734
##         Penalized MR-Egger    0.247     0.139  -0.025 0.518   0.075
##                (intercept)   -0.001     0.003  -0.006 0.004   0.734
##            Robust MR-Egger    0.276     0.117   0.046 0.507   0.018
##                (intercept)   -0.002     0.003  -0.007 0.003   0.486
##  Penalized robust MR-Egger    0.276     0.117   0.046 0.507   0.018
##                (intercept)   -0.002     0.003  -0.007 0.003   0.486

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
oUw2e5	daasDf	exposure	outcome	0.0109999	0.0020872	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.2075324
## 
## $beta.se
## [1] 0.05105289
## 
## $beta.p.value
## [1] 4.80227e-05
## 
## $naive.se
## [1] 0.05066738
## 
## $chi.sq.test
## [1] 86.42346

##   over.dispersion loss.function  beta.hat    beta.se
## 1           FALSE            l2 0.2075324 0.05105289
## 2           FALSE         huber 0.1909614 0.05234920
## 3           FALSE         tukey 0.1939161 0.05235445
## 4            TRUE            l2 0.2049852 0.05640578
## 5            TRUE         huber 0.1923723 0.05880302
## 6            TRUE         tukey 0.1963334 0.05908604

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  70 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.207 0.051  0.000 [0.107,0.307]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 70 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.207     0.057 0.095, 0.319   0.000   540.818
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 70 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.219     0.081 0.060, 0.379   0.007
## ------------------------------------------------------------------

[VitD and TSH]

Introduction

Title: Investigating the causality between 25-Hydroxyvitamin D level on TSH
- Exposure: 25-Hydroxyvitamin D level, Data downloaded from GWAS catalog Database | Reference paper: Joana A. Revez Paper 2020 | GWAS ID: GCST90000616
- Sample size: 417,580
- Outcome: TSH, Data downloaded from Thyroid Omics Consortium | Reference paper: Alexander Teumer 2018 | GWAS ID: phs000930
- Sample size:54,288
- Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 7,250,104 SNPs

2- Number of SNPs exposure with p-value < \(5 \times 10^-8\): 16,012 SNPs

3- Number of SNPs exposure after clumping : 115 SNPs

4- Number of total SNPs in outcome: 7,742,681 SNPs

5- Number of common variants between exposure and outcome: 101 SNPs

6- Number of SNPs after harmonization (action=3) = 84 SNPs

7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 84 SNP

8- Number of SNPs after removing those that have MAF < 0.01 = 84 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 1 SNP (rs73413596)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.78   36.14   43.24  122.48   70.86 2567.54

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
qxmOS6	7CyyhT	outcome	exposure	MR Egger	83	-0.0282157	0.0675033	0.6770598
qxmOS6	7CyyhT	outcome	exposure	Weighted median	83	-0.0145698	0.0542339	0.7882004
qxmOS6	7CyyhT	outcome	exposure	Inverse variance weighted	83	-0.0469732	0.0427422	0.2717736
qxmOS6	7CyyhT	outcome	exposure	Simple mode	83	-0.0636091	0.1114217	0.5696380
qxmOS6	7CyyhT	outcome	exposure	Weighted mode	83	-0.0429973	0.0481854	0.3748270

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
qxmOS6	7CyyhT	outcome	exposure	MR Egger	138.6384	81	7.07e-05
qxmOS6	7CyyhT	outcome	exposure	Inverse variance weighted	138.8606	82	8.97e-05

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
qxmOS6	7CyyhT	outcome	exposure	-0.0006249	0.0017343	0.7195554

Testing Outlier with PRESSO test

## [1] "One SNP (rs532436) was detected by MRPRESSO and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO
id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
qxmOS6	7CyyhT	outcome	exposure	MR Egger	82	-0.0331682	0.0543454	0.5433790
qxmOS6	7CyyhT	outcome	exposure	Weighted median	82	-0.0145490	0.0546133	0.7899313
qxmOS6	7CyyhT	outcome	exposure	Inverse variance weighted	82	-0.0295222	0.0344758	0.3918233
qxmOS6	7CyyhT	outcome	exposure	Simple mode	82	-0.0579555	0.1092497	0.5972258
qxmOS6	7CyyhT	outcome	exposure	Weighted mode	82	-0.0372654	0.0476711	0.4366590

Heterogeneity testing
id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
qxmOS6	7CyyhT	outcome	exposure	MR Egger	88.73302	80	0.2360567
qxmOS6	7CyyhT	outcome	exposure	Inverse variance weighted	88.74145	81	0.2604797

pleiotropy testing
id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
qxmOS6	7CyyhT	outcome	exposure	0.0001221	0.0014005	0.9307676

Studentized residuals:

Radial test

## 
## Radial IVW
## 
##                     Estimate  Std.Error    t value  Pr(>|t|)
## Effect (Mod.2nd) -0.02952200 0.03447575 -0.8563121 0.3918252
## Iterative        -0.02952200 0.03447575 -0.8563121 0.3918252
## Exact (FE)       -0.02979675 0.03293912 -0.9046008 0.3656769
## Exact (RE)       -0.02979331 0.03355018 -0.8880223 0.3771582
## 
## 
## Residual standard error: 1.047 on 81 degrees of freedom
## 
## F-statistic: 0.73 on 1 and 81 DF, p-value: 0.394
## Q-Statistic for heterogeneity: 88.73384 on 81 DF , p-value: 0.2606622
## 
##  No significant outliers 
## Number of iterations = 2

## [1] "No significant outliers"

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 82 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW   -0.030     0.034 -0.097, 0.038   0.392
## ------------------------------------------------------------------
## Residual standard error =  1.047 
## Heterogeneity test statistic (Cochran's Q) = 88.7414 on 81 degrees of freedom, (p-value = 0.2605). I^2 = 8.7%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median   -0.031     0.059  -0.145 0.084   0.602
##            Weighted median   -0.015     0.055  -0.123 0.094   0.792
##  Penalized weighted median   -0.015     0.056  -0.123 0.094   0.794
##                                                                    
##                        IVW   -0.030     0.034  -0.097 0.038   0.392
##              Penalized IVW   -0.030     0.034  -0.097 0.038   0.392
##                 Robust IVW   -0.028     0.032  -0.090 0.034   0.383
##       Penalized robust IVW   -0.028     0.032  -0.090 0.034   0.383
##                                                                    
##                   MR-Egger   -0.033     0.054  -0.140 0.073   0.542
##                (intercept)    0.000     0.001  -0.003 0.003   0.931
##         Penalized MR-Egger   -0.033     0.054  -0.140 0.073   0.541
##                (intercept)    0.000     0.001  -0.003 0.003   0.930
##            Robust MR-Egger   -0.032     0.049  -0.128 0.063   0.507
##                (intercept)    0.000     0.001  -0.003 0.003   0.910
##  Penalized robust MR-Egger   -0.032     0.049  -0.128 0.063   0.507
##                (intercept)    0.000     0.001  -0.003 0.003   0.910

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
qxmOS6	7CyyhT	exposure	outcome	0.0192884	0.0016496	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] -0.02980411
## 
## $beta.se
## [1] 0.03321019
## 
## $beta.p.value
## [1] 0.3694849
## 
## $naive.se
## [1] 0.03306716
## 
## $chi.sq.test
## [1] 88.73377

##   over.dispersion loss.function    beta.hat    beta.se
## 1           FALSE            l2 -0.02980411 0.03321019
## 2           FALSE         huber -0.02894143 0.03407276
## 3           FALSE         tukey -0.02726968 0.03407253
## 4            TRUE            l2 -0.03147601 0.03461906
## 5            TRUE         huber -0.03107808 0.03698782
## 6            TRUE         tukey -0.03009628 0.03673932

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  82 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC   -0.030 0.033  0.371 [-0.094,0.035]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 82 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW   -0.030     0.034 -0.097, 0.038   0.388  1108.127
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 82 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE   -0.037     0.059 -0.153, 0.079   0.529
## ------------------------------------------------------------------

Supplementary Material of the paper entitled:

Genetically predicted 25-Hydroxyvitamin D levels on hypothyroidism: A two-sample Mendelian Randomization

Created by Mahdi Akbarzadeh (Email: akbarzadeh.ms@gmail.com), and Sahand Tehrani Fateh

2023-08-30

Authors list

[VitD and Hypo]

Introduction

Data Preparation

Checking weakness of the instruments

RUN an initial MR:

Testing Outlier with PRESSO test

Studentized residuals:

Radial test

Cook’s distance

Run After deleting new outlier: Final Results:

Sensitivity analyses with MendelianRandomization Package

Working with MRraps

[VitD and HT]

Introduction

Data Preparation

Checking weakness of the instruments

RUN an initial MR:

Testing Outlier with PRESSO test

Studentized residuals:

Radial test

Cook’s distance

Run After deleting new outlier: Final Results:

Sensitivity analyses with MendelianRandomization Package

Working with MRraps

[VitD and fT4]

Introduction

Data Preparation

Checking weakness of the instruments

RUN an initial MR:

Testing Outlier with PRESSO test

Studentized residuals:

Radial test

Cook’s distance

Run After deleting new outlier: Final Results:

Sensitivity analyses with MendelianRandomization Package

Working with MRraps

[VitD and TSH]

Introduction

Data Preparation

Checking weakness of the instruments

RUN an initial MR:

Testing Outlier with PRESSO test

Studentized residuals:

Radial test

Sensitivity analyses with MendelianRandomization Package

Working with MRraps