Mendelian Randomization Report [T2D and Graves’ disease (GD)]

[Graves’ disease (GD) on T2D]

Introduction

Data Preparation

1- Number of total SNPs in exposure: 18,904,735 SNPs

2- Number of SNPs exposure with p-value < \(5\times 10^-5\): 11,794 SNPs

3- Number of SNPs exposure after clumping : 31 SNPs

4- Number of total SNPs in outcome: 10,454,875 SNPs

5- Number of common variants between exposure and outcome: 25 SNPs (“rs531136107” “rs11933469” “rs146114215” “rs1055821” “rs9274257” “rs1087056” have been eliminated)

6- Number of SNPs after replacing proxies: 3 SNPs from NIH LDproxy database according to EUR ancestry have been selected: 7 SNPs remained (We replace rs1087056&rs9274257&rs11933469 by rs793102&rs1049053&rs144334834 with R2 0.99&0.91&0.94, respectively).So, 28 SNPs remained.

7- Number of SNPs after harmonization (action=2) = 27 SNPs (Removing the following SNPs for incompatible alleles:rs11933469)

8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 27 SNP

9- Number of SNPs after removing those that have MAF < 0.01 = 27 SNPs

10- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 25 SNPs (rs2476601,rs9275576 were removed)

Checking weakness of the instruments

data <- fread("dataAftScan_GD_T2D.txt")
data$F<-(data$beta.exposure/data$se.exposure)^2
summary(data$F)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   19.62   20.00   21.08   29.13   25.89  109.46

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

RUN an initial MR:

res<-mr(data)
res
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      m3uO9x     DQN8hD outcome exposure                  MR Egger   25
## 2      m3uO9x     DQN8hD outcome exposure           Weighted median   25
## 3      m3uO9x     DQN8hD outcome exposure Inverse variance weighted   25
## 4      m3uO9x     DQN8hD outcome exposure               Simple mode   25
## 5      m3uO9x     DQN8hD outcome exposure             Weighted mode   25
##             b         se       pval
## 1 0.065288410 0.02871384 0.03263161
## 2 0.009136803 0.01052227 0.38521385
## 3 0.018997587 0.01113032 0.08785329
## 4 0.002902478 0.01399873 0.83749458
## 5 0.005399537 0.01199450 0.65662955
plot(data$beta.exposure,data$beta.outcome)
text(data$beta.exposure,                                
     data$beta.outcome,
     labels = data$SNP,
     pos = 4)

#scatter plot
p1 <- mr_scatter_plot(res, data)    
p1[[1]]

#Heterogeneity testing
mr_heterogeneity<- mr_heterogeneity(data); mr_heterogeneity
##   id.exposure id.outcome outcome exposure                    method        Q
## 1      m3uO9x     DQN8hD outcome exposure                  MR Egger 62.24479
## 2      m3uO9x     DQN8hD outcome exposure Inverse variance weighted 70.41025
##   Q_df       Q_pval
## 1   23 1.798162e-05
## 2   24 1.894690e-06
#pleiotropy testing
mr_pleiotropy_test<- mr_pleiotropy_test(data); mr_pleiotropy_test
##   id.exposure id.outcome outcome exposure egger_intercept          se
## 1      m3uO9x     DQN8hD outcome exposure     -0.01312795 0.007557778
##         pval
## 1 0.09576112
#plot of single SNP MR:
res_single <- mr_singlesnp(data); p2 <- mr_forest_plot(res_single); p2[[1]]

#plot of LOO:
res_loo <- mr_leaveoneout(data); p3 <- mr_leaveoneout_plot(res_loo); p3[[1]]

#Funnel plot
p4 <- mr_funnel_plot(res_single); p4[[1]]

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd   T-stat
## 1 beta.exposure               Raw     0.018997587 0.011130321 1.706832
## 2 beta.exposure Outlier-corrected     0.007311073 0.006674337 1.095401
##     P-value
## 1 0.1007613
## 2 0.2857456
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 79.2061
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  5.431799e-05      1
## 2  1.603200e-05      1
## 3  7.444958e-04      1
## 4  4.339455e-04      1
## 5  1.810411e-04      1
## 6  1.135760e-04      1
## 7  2.368345e-04      1
## 8  1.949326e-05      1
## 9  1.279222e-04      1
## 10 8.665048e-04 <0.025
## 11 3.082925e-07      1
## 12 2.914853e-06      1
## 13 2.146959e-05      1
## 14 3.443934e-05      1
## 15 5.828032e-06      1
## 16 8.740802e-04  0.025
## 17 3.557999e-05      1
## 18 4.886994e-05      1
## 19 4.081558e-06      1
## 20 4.547381e-04    0.2
## 21 7.469633e-04      1
## 22 1.849826e-05      1
## 23 4.333935e-05      1
## 24 1.728062e-03 <0.025
## 25 1.157323e-04      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 10 16 24
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##      159.8468 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] "<0.001"
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      m3uO9x     DQN8hD outcome exposure                  MR Egger   25
## 2      m3uO9x     DQN8hD outcome exposure           Weighted median   25
## 3      m3uO9x     DQN8hD outcome exposure Inverse variance weighted   25
## 4      m3uO9x     DQN8hD outcome exposure               Simple mode   25
## 5      m3uO9x     DQN8hD outcome exposure             Weighted mode   25
##             b         se       pval
## 1 0.065288410 0.02871384 0.03263161
## 2 0.009136803 0.01027267 0.37377284
## 3 0.018997587 0.01113032 0.08785329
## 4 0.002902478 0.01542967 0.85237175
## 5 0.005399537 0.01200487 0.65690612

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      m3uO9x     DQN8hD outcome exposure                  MR Egger 62.24479
## 2      m3uO9x     DQN8hD outcome exposure Inverse variance weighted 70.41025
##   Q_df       Q_pval
## 1   23 1.798162e-05
## 2   24 1.894690e-06
##   id.exposure id.outcome outcome exposure egger_intercept          se
## 1      m3uO9x     DQN8hD outcome exposure     -0.01312795 0.007557778
##         pval
## 1 0.09576112

Studentized residuals:

reg_1<-lm(data$beta.outcome~data$beta.exposure-1)
data$st_1<-rstandard(reg_1)

#Histogram plot
hist(data$st_1)

Radial test

## 
## Radial IVW
## 
##                    Estimate  Std.Error  t value    Pr(>|t|)
## Effect (Mod.2nd) 0.01901729 0.01114274 1.706698 0.087878249
## Iterative        0.01901729 0.01114274 1.706698 0.087878249
## Exact (FE)       0.02097768 0.00655203 3.201707 0.001366159
## Exact (RE)       0.01962752 0.01286620 1.525510 0.140203136
## 
## 
## Residual standard error: 1.703 on 24 degrees of freedom
## 
## F-statistic: 2.91 on 1 and 24 DF, p-value: 0.101
## Q-Statistic for heterogeneity: 69.61735 on 24 DF , p-value: 2.498265e-06
## 
##  Outliers detected 
## Number of iterations = 2
##          SNP Q_statistic      p.value
## 1 rs17651741    12.11457 5.002940e-04
## 2  rs4338740    15.86951 6.786339e-05
## 3  rs9274257    20.72924 5.290192e-06

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

par(mfrow = c(2, 2))
model <- lm(data$beta.outcome~data$beta.exposure-1)
plot(model)

par(mfrow = c(1, 1))

cooksD <- cooks.distance(model)
influential <- cooksD[(cooksD > (3 * mean(cooksD, na.rm = TRUE)))]
influential
##         3        24 
## 0.5869178 0.2487492

Run After deleting new outlier: Final Results:

data <- data[(data$SNP!="rs17651741" & data$SNP!="rs4338740" &  data$SNP!="rs9274257" 
              & data$SNP!="rs79636620" &data$SNP!="rs73409559" 
              & data$SNP!="rs12371558" & data$SNP!="rs114824864" 
              & data$SNP!="rs12294180" & data$SNP!="rs10732976"),]

res<-mr(data)

res
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      m3uO9x     DQN8hD outcome exposure                  MR Egger   16
## 2      m3uO9x     DQN8hD outcome exposure           Weighted median   16
## 3      m3uO9x     DQN8hD outcome exposure Inverse variance weighted   16
## 4      m3uO9x     DQN8hD outcome exposure               Simple mode   16
## 5      m3uO9x     DQN8hD outcome exposure             Weighted mode   16
##             b          se       pval
## 1 0.021353684 0.020203463 0.30844033
## 2 0.009198712 0.010697285 0.38983813
## 3 0.017017499 0.007860121 0.03038439
## 4 0.004328740 0.015344174 0.78171456
## 5 0.006117096 0.012059544 0.61936129
plot(data$beta.exposure,data$beta.outcome)
text(data$beta.exposure,                                
     data$beta.outcome,
     labels = data$SNP,
     pos = 4)

#Heterogeneity testing
mr_heterogeneity<- mr_heterogeneity(data); mr_heterogeneity
##   id.exposure id.outcome outcome exposure                    method        Q
## 1      m3uO9x     DQN8hD outcome exposure                  MR Egger 7.746462
## 2      m3uO9x     DQN8hD outcome exposure Inverse variance weighted 7.800742
##   Q_df    Q_pval
## 1   14 0.9021120
## 2   15 0.9315224
#pleiotropy testing
mr_pleiotropy_test<- mr_pleiotropy_test(data); mr_pleiotropy_test
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      m3uO9x     DQN8hD outcome exposure    -0.001290484 0.005539017 0.8191482
#scatter plot
p1 <- mr_scatter_plot(res, data); p1[[1]]

#plot of single SNP MR:
res_single <- mr_singlesnp(data); p2 <- mr_forest_plot(res_single); p2[[1]]

#plot of LOO:
res_loo <- mr_leaveoneout(data); p3 <- mr_leaveoneout_plot(res_loo); p3[[1]]

#Funnel plot
p4 <- mr_funnel_plot(res_single); p4[[1]]

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 16 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.017     0.008 0.002, 0.032   0.030
## ------------------------------------------------------------------
## Residual standard error =  0.721 
## 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) = 7.8007 on 15 degrees of freedom, (p-value = 0.9315). I^2 = 0.0%. 
## F statistic = 30.2.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.011     0.011  -0.010 0.032   0.317
##            Weighted median    0.009     0.011  -0.012 0.030   0.390
##  Penalized weighted median    0.009     0.011  -0.012 0.030   0.390
##                                                                    
##                        IVW    0.017     0.008   0.002 0.032   0.030
##              Penalized IVW    0.017     0.008   0.002 0.032   0.030
##                 Robust IVW    0.015     0.010  -0.005 0.035   0.132
##       Penalized robust IVW    0.015     0.010  -0.005 0.035   0.132
##                                                                    
##                   MR-Egger    0.021     0.020  -0.018 0.061   0.291
##                (intercept)   -0.001     0.006  -0.012 0.010   0.816
##         Penalized MR-Egger    0.021     0.020  -0.018 0.061   0.291
##                (intercept)   -0.001     0.006  -0.012 0.010   0.816
##            Robust MR-Egger    0.023     0.031  -0.038 0.084   0.458
##                (intercept)   -0.002     0.009  -0.020 0.015   0.789
##  Penalized robust MR-Egger    0.023     0.031  -0.038 0.084   0.458
##                (intercept)   -0.002     0.009  -0.020 0.015   0.789

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
m3uO9x DQN8hD exposure outcome 0.00036 2.73e-05 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] 0.01734983
## 
## $beta.se
## [1] 0.008294435
## 
## $beta.p.value
## [1] 0.03646143
## 
## $naive.se
## [1] 0.0081497
## 
## $chi.sq.test
## [1] 7.724973
##   over.dispersion loss.function   beta.hat     beta.se
## 1           FALSE            l2 0.01734983 0.008294435
## 2           FALSE         huber 0.01730813 0.008509423
## 3           FALSE         tukey 0.01668880 0.008502398
## 4            TRUE            l2 0.01735043 0.008298819
## 5            TRUE         huber 0.01730812 0.008513589
## 6            TRUE         tukey 0.01669042 0.008506434
## 
## MR-Lasso method 
## 
## Number of variants : 16 
## Number of valid instruments : 16 
## Tuning parameter : 0.3514503 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.017     0.008 0.002, 0.032   0.030
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  16 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.017 0.008  0.031 [0.002,0.033]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 16 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.018     0.008 0.002, 0.034   0.031   116.631
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 16 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.006     0.013 -0.020, 0.032   0.646
## ------------------------------------------------------------------

[T2D on Graves’ disease (GD)]

Introduction

Data Preparation

1- Number of total SNPs in exposure: 10,454,875 SNPs

2- Number of SNPs exposure with p-value < \(5\times 10^-8\) = 17,450 SNPs

3- Number of SNPs exposure after clumping = 187 SNPs

4- Number of total SNPs in outcome: 18,904,735 SNPs

5- Number of common variants between exposure and outcome: 170 SNPs

6- Number of SNPs after harmonization (action=2) = 165 SNPs

8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 165 SNP

9- Number of SNPs after removing those that have MAF < 0.01 = 165 SNPs

Checking pleiotropy by Phenoscanner:

How many SNPs have been eliminated with checking the phenoscanner website: 165 SNPs (rs3094682,rs601945)

Checking weakness of the instruments

data <- fread("dataAftScan_T2D_GD.txt")
data$F<-(data$beta.exposure/data$se.exposure)^2
summary(data$F)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   29.75   35.12   47.69   75.24   68.49 1415.77

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

RUN an initial MR:

res<-mr(data)
res
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      nMQuaa     WAeJus outcome exposure                  MR Egger  163
## 2      nMQuaa     WAeJus outcome exposure           Weighted median  163
## 3      nMQuaa     WAeJus outcome exposure Inverse variance weighted  163
## 4      nMQuaa     WAeJus outcome exposure               Simple mode  163
## 5      nMQuaa     WAeJus outcome exposure             Weighted mode  163
##             b         se       pval
## 1  0.12276715 0.13784561 0.37446555
## 2 -0.01189484 0.08627093 0.89033706
## 3  0.12682621 0.05867995 0.03067055
## 4  0.12024736 0.21696751 0.58019373
## 5 -0.05824805 0.12422362 0.63977382
plot(data$beta.exposure,data$beta.outcome)
text(data$beta.exposure,                                
     data$beta.outcome,
     labels = data$SNP,
     pos = 4)

#scatter plot
p1 <- mr_scatter_plot(res, data)    
p1[[1]]

#Heterogeneity testing
mr_heterogeneity<- mr_heterogeneity(data); mr_heterogeneity
##   id.exposure id.outcome outcome exposure                    method        Q
## 1      nMQuaa     WAeJus outcome exposure                  MR Egger 221.0518
## 2      nMQuaa     WAeJus outcome exposure Inverse variance weighted 221.0533
##   Q_df      Q_pval
## 1  161 0.001187660
## 2  162 0.001413119
#pleiotropy testing
mr_pleiotropy_test<- mr_pleiotropy_test(data); mr_pleiotropy_test
##   id.exposure id.outcome outcome exposure egger_intercept          se      pval
## 1      nMQuaa     WAeJus outcome exposure    0.0002939165 0.009025637 0.9740621
#plot of single SNP MR:
res_single <- mr_singlesnp(data); p2 <- mr_forest_plot(res_single); p2[[1]]

#plot of LOO:
res_loo <- mr_leaveoneout(data); p3 <- mr_leaveoneout_plot(res_loo); p3[[1]]

#Funnel plot
p4 <- mr_funnel_plot(res_single); p4[[1]]

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate         Sd   T-stat
## 1 beta.exposure               Raw      0.12682621 0.05867995 2.161321
## 2 beta.exposure Outlier-corrected      0.06955232 0.05694722 1.221347
##      P-value
## 1 0.03213897
## 2 0.22375128
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 224.9441
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##           RSSobs Pvalue
## 1   8.931449e-05      1
## 2   2.045406e-02      1
## 3   2.552503e-03      1
## 4   7.157608e-06      1
## 5   5.324489e-04      1
## 6   9.672164e-04      1
## 7   8.200812e-07      1
## 8   1.343561e-03      1
## 9   1.192281e-03      1
## 10  3.590095e-04      1
## 11  7.467802e-03      1
## 12  6.272117e-04      1
## 13  2.107816e-03      1
## 14  3.167176e-04      1
## 15  7.246978e-04      1
## 16  6.458283e-06      1
## 17  3.184424e-03      1
## 18  2.738495e-04      1
## 19  7.866133e-04      1
## 20  3.355180e-03      1
## 21  8.152612e-03      1
## 22  1.900234e-03      1
## 23  1.136469e-04      1
## 24  5.418553e-03      1
## 25  8.853825e-04      1
## 26  8.287586e-04      1
## 27  3.457091e-03      1
## 28  1.642272e-03      1
## 29  6.525446e-04      1
## 30  4.337706e-03      1
## 31  1.372984e-03      1
## 32  1.258235e-03      1
## 33  5.966107e-09      1
## 34  2.311342e-05      1
## 35  2.349859e-04      1
## 36  6.139497e-04      1
## 37  1.704599e-04      1
## 38  7.806715e-04      1
## 39  5.021536e-03      1
## 40  3.696132e-05      1
## 41  1.761044e-05      1
## 42  1.245397e-02      1
## 43  5.170332e-05      1
## 44  5.899961e-05      1
## 45  4.191981e-02      1
## 46  3.844198e-03      1
## 47  9.414305e-05      1
## 48  6.961186e-03      1
## 49  5.799711e-03      1
## 50  3.757669e-03      1
## 51  4.042328e-03      1
## 52  1.487592e-03      1
## 53  2.389210e-02      1
## 54  9.949793e-05      1
## 55  1.643959e-02 <0.163
## 56  1.604371e-03      1
## 57  1.290824e-02      1
## 58  3.631837e-03      1
## 59  1.390080e-02      1
## 60  2.139883e-05      1
## 61  6.620741e-04      1
## 62  1.271068e-04      1
## 63  1.520316e-03      1
## 64  1.519768e-07      1
## 65  5.070099e-06      1
## 66  8.569165e-04      1
## 67  3.417571e-04      1
## 68  1.967738e-04      1
## 69  2.380750e-03      1
## 70  6.909608e-03      1
## 71  9.477248e-04      1
## 72  8.643898e-04      1
## 73  1.747497e-04      1
## 74  5.146514e-03      1
## 75  1.246314e-03      1
## 76  1.298788e-04      1
## 77  8.148527e-03      1
## 78  2.555592e-05      1
## 79  7.288184e-04      1
## 80  2.052938e-03      1
## 81  1.267888e-04      1
## 82  3.317556e-03      1
## 83  9.001229e-03      1
## 84  4.615560e-04      1
## 85  9.446499e-03      1
## 86  9.057162e-04      1
## 87  6.138851e-03      1
## 88  8.559997e-06      1
## 89  3.304342e-04      1
## 90  4.595027e-04      1
## 91  4.399532e-03      1
## 92  4.384239e-03      1
## 93  2.764905e-03      1
## 94  1.119184e-03      1
## 95  1.763158e-03      1
## 96  6.225070e-03      1
## 97  9.897842e-04      1
## 98  4.170352e-03      1
## 99  6.484876e-05      1
## 100 3.076314e-03      1
## 101 8.781083e-04      1
## 102 1.590347e-04      1
## 103 1.029789e-04      1
## 104 8.753353e-05      1
## 105 2.049889e-04      1
## 106 6.736777e-03      1
## 107 3.944904e-05      1
## 108 2.742712e-04      1
## 109 4.486879e-05      1
## 110 2.015661e-03      1
## 111 3.196914e-04      1
## 112 1.282041e-03      1
## 113 4.495824e-04      1
## 114 5.513560e-03      1
## 115 8.152684e-03      1
## 116 9.668876e-04      1
## 117 1.176904e-04      1
## 118 1.313846e-03      1
## 119 2.634257e-04      1
## 120 1.491155e-03      1
## 121 1.085390e-03      1
## 122 1.178167e-04      1
## 123 9.045227e-04      1
## 124 2.267315e-02      1
## 125 6.074106e-03      1
## 126 4.521957e-04      1
## 127 3.784220e-04      1
## 128 4.666339e-03      1
## 129 1.750470e-04      1
## 130 2.342458e-04      1
## 131 7.883763e-04      1
## 132 1.973288e-04      1
## 133 1.730379e-03      1
## 134 8.326136e-04      1
## 135 8.851355e-03      1
## 136 5.857528e-03      1
## 137 7.044322e-04      1
## 138 3.020335e-03      1
## 139 5.881334e-03      1
## 140 7.985017e-04      1
## 141 1.218269e-02      1
## 142 5.404117e-02      1
## 143 9.140577e-05      1
## 144 1.572592e-03      1
## 145 1.006281e-03      1
## 146 7.478748e-04      1
## 147 5.232402e-03      1
## 148 1.424428e-04      1
## 149 1.503360e-03      1
## 150 5.263970e-05      1
## 151 2.663449e-03      1
## 152 1.078993e-04      1
## 153 8.511318e-04      1
## 154 6.170011e-04      1
## 155 1.328027e-03      1
## 156 1.677076e-03      1
## 157 1.236513e-04      1
## 158 8.626046e-05      1
## 159 2.573809e-04      1
## 160 1.813394e-02 <0.163
## 161 8.085405e-03      1
## 162 1.099037e-03      1
## 163 6.690311e-04      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1]  55 160
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##       82.3465 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.138
##   id.exposure id.outcome outcome exposure                    method nsnp
## 1      nMQuaa     WAeJus outcome exposure                  MR Egger  143
## 2      nMQuaa     WAeJus outcome exposure           Weighted median  143
## 3      nMQuaa     WAeJus outcome exposure Inverse variance weighted  143
## 4      nMQuaa     WAeJus outcome exposure               Simple mode  143
## 5      nMQuaa     WAeJus outcome exposure             Weighted mode  143
##           b         se       pval
## 1 0.1909742 0.23806056 0.42378242
## 2 0.1619115 0.09742277 0.09652330
## 3 0.1119229 0.06505319 0.08534469
## 4 0.2864514 0.24572685 0.24567747
## 5 0.3222973 0.22603017 0.15609072

##   id.exposure id.outcome outcome exposure                    method        Q
## 1      nMQuaa     WAeJus outcome exposure                  MR Egger 158.3569
## 2      nMQuaa     WAeJus outcome exposure Inverse variance weighted 158.4908
##   Q_df    Q_pval
## 1  141 0.1507308
## 2  142 0.1629892
##   id.exposure id.outcome outcome exposure egger_intercept         se      pval
## 1      nMQuaa     WAeJus outcome exposure    -0.004576065 0.01325284 0.7303914

Radial test

## 
## Radial IVW
## 
##                   Estimate  Std.Error  t value   Pr(>|t|)
## Effect (Mod.2nd) 0.1119262 0.06505333 1.720529 0.08533624
## Iterative        0.1119262 0.06505333 1.720529 0.08533624
## Exact (FE)       0.1141999 0.06158942 1.854212 0.06370879
## Exact (RE)       0.1139710 0.06769709 1.683544 0.09446691
## 
## 
## Residual standard error: 1.056 on 142 degrees of freedom
## 
## F-statistic: 2.96 on 1 and 142 DF, p-value: 0.0875
## Q-Statistic for heterogeneity: 158.4246 on 142 DF , p-value: 0.1638891
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"

MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 143 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW    0.112     0.065 -0.016, 0.239   0.085
## ------------------------------------------------------------------
## Residual standard error =  1.056 
## Heterogeneity test statistic (Cochran's Q) = 158.4908 on 142 degrees of freedom, (p-value = 0.1630). I^2 = 10.4%. 
## F statistic = 55.9.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.162     0.094  -0.023 0.347   0.086
##            Weighted median    0.170     0.095  -0.015 0.356   0.072
##  Penalized weighted median    0.263     0.095   0.076 0.450   0.006
##                                                                    
##                        IVW    0.112     0.065  -0.016 0.239   0.085
##              Penalized IVW    0.112     0.065  -0.015 0.240   0.084
##                 Robust IVW    0.139     0.073  -0.005 0.283   0.058
##       Penalized robust IVW    0.139     0.073  -0.004 0.283   0.057
##                                                                    
##                   MR-Egger    0.191     0.238  -0.276 0.658   0.422
##                (intercept)   -0.005     0.013  -0.031 0.021   0.730
##         Penalized MR-Egger    0.191     0.238  -0.276 0.658   0.422
##                (intercept)   -0.005     0.013  -0.031 0.021   0.730
##            Robust MR-Egger    0.239     0.259  -0.269 0.746   0.357
##                (intercept)   -0.006     0.014  -0.034 0.023   0.689
##  Penalized robust MR-Egger    0.239     0.259  -0.269 0.746   0.357
##                (intercept)   -0.006     0.014  -0.034 0.023   0.689

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
nMQuaa WAeJus exposure outcome 0.0059619 0.0003528 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] 0.1142128
## 
## $beta.se
## [1] 0.06262707
## 
## $beta.p.value
## [1] 0.0681979
## 
## $naive.se
## [1] 0.0620714
## 
## $chi.sq.test
## [1] 158.4233
##   over.dispersion loss.function  beta.hat    beta.se
## 1           FALSE            l2 0.1142128 0.06262707
## 2           FALSE         huber 0.1422205 0.06426952
## 3           FALSE         tukey 0.1427335 0.06426995
## 4            TRUE            l2 0.1161242 0.06622250
## 5            TRUE         huber 0.1401146 0.06782874
## 6            TRUE         tukey 0.1394127 0.06869771
## 
## MR-Lasso method 
## 
## Number of variants : 143 
## Number of valid instruments : 138 
## Tuning parameter : 0.1926409 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.162     0.063 0.038, 0.286   0.010
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  143 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC    0.114 0.062  0.068 [-0.008,0.236]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 143 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW    0.114     0.066 -0.016, 0.244   0.085   656.675
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 143 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.322     0.214 -0.097, 0.741   0.132
## ------------------------------------------------------------------