# How to interpret Mendelian randomization results?

I did Mendelian randomization using this software: https://cran.r-project.org/web/packages/MendelianRandomization/vignettes/Vignette_MR.pdf

library(MendelianRandomization)
rs exposure.beta exposure.se outcome.beta outcome.se
1  rs1029830      0.723525  0.03026430  0.066715400  0.0359278
2  rs1029832      0.723785  0.03029603  0.064105600  0.0359021
3 rs11078374     -0.411789  0.04189295 -0.000376929  0.0406439
4 rs11078382      0.882549  0.14275799 -0.197074000  0.1247720
5  rs1124961     -0.333763  0.05589377 -0.075468600  0.0576012
6  rs1135237     -0.316831  0.05552530 -0.074086200  0.0573111

MRInputObject <- mr_input(bx = f$exposure.beta,bxse = f$exposure.se,by = f$outcome.beta,byse = f$outcome.se)
EggerObject <- mr_egger(MRInputObject,robust = FALSE,penalized = FALSE,correl = FALSE,distribution = "normal",alpha = 0.05)

MR-Egger method
(variants uncorrelated, random-effect model)

Number of Variants =  246

------------------------------------------------------------------
Method     Estimate Std Error  95% CI       p-value
MR-Egger    0.115     0.016  0.084, 0.146   3.28e-13
(intercept) -0.010     0.008 -0.025, 0.006   0.226
------------------------------------------------------------------
Residual Standard Error :  1.106
Heterogeneity test statistic = 298.4508 on 244 degrees of freedom,     (p-value = 0.0099)
I^2_GX statistic: 97.2%


Let's say that my exposure is called Retina and my outcome is called Biobank. Can someone please help me interpret these results in terms of 'horizontal pleiotropy' as mentioned here: https://www.ncbi.nlm.nih.gov/pubmed/29771313

It looks like you have linkage as opposed to linkage disequilibrium, therefore horizontal pleiotropy is an explanation of the calculation.

The calculation appears to be a GLMM around the beta distribution, the residual looks low (which is good). The heterogeneity statistic is significant, you would need to assess whether this is an index of heterozygosity, but it will relate to expectation of Mendellian inhertiance based around the Hardy Weinberg equilibrium.