Title
mregger -- Mendelian randomization Egger regression
Syntax
mregger varname_gd varname_gp [aweight] [if] [in] [, options]
options Description ---------------------------------------------------------------------------------------------- fe Fixed effect standard errors (default is multiplicative) gxse(varname) variable of genotype-phenotype (SNP-exposure) SEs heterogi Display heterogeneity/pleiotropy statistics ivw Inverse-variance weighted estimator (default is MR-Egger) level(#) set confidence level; default is level(95) norescale Do not rescale residual variance to be 1 (if less than 1) oldnames Revert to using longer outcome name in b and V ereturned matrices penweighted Use penalized weights radial Use radial formulations of the models tdist Use t-distribution for Wald test and CI limits unwi2gx Additionally report unweighted Q_GX and I^2_GX statistics
Description
mregger performs inverse-variance weighted (IVW; Burgess et al., 2013) and Mendelian randomization Egger (MR-Egger) regression (Bowden et al., 2015) using summary level data (i.e. using genotype-disease [SNP-outcome] and genotype-phenotype [SNP-exposure] association estimates and their standard errors).
varname_gd variable containing the genotype-disease (SNP-outcome) association estimates.
varname_gp variable containing the genotype-phenotype (SNP-exposure) association estimates.
For the analytic weights you need to specify the inverse of the genotype-disease (SNP-outcome) standard errors squared, i.e. aw=1/(gdse^2).
Options
fe specifies fixed effect standard errors (i.e. variance of residuals constrained to 1 as in fixed effect meta-analysis models). The default is to use multiplicative standard errors (i.e. variance of residuals unconstrained as in standard linear regression), see Thompson and Sharp (1999) for further details. We recommend specifying this option when using an allelic score as the instrumental variable.
gxse(varname) specifies the variable containing the genotype-phenotype (SNP-exposure) association standard errors. These are required for calculating the I^2_GX statistic (Bowden et al., 2016). An I^2_GX statistic of 90% means that the likely bias due measurement error in the MR-Egger slope estimate is around 10%. If I^2_GX values are less than 90% estimates should be treated with caution.
heterogi displays heterogeneity/pleiotropy statistics. In the heterogeneity output the model based Q-statistic is reported by multiplying the variance of the residuals by the degrees of freedom (Del Greco et al., 2015). For the IVW model this is the Cochran Q-statistic, and for the MR-Egger model this is the Ruecker's Q-statistic. The corresponding I-squared statistic and its 95% CI is also reported.
ivw specifies inverse-variance weighted (IVW) model (Burgess et al., 2013), the default is MR-Egger.
level(#); see [R] estimation options.
norescale specifies that the residual variance is not set to 1 (if it is found to be less than 1). Bowden et al. (2016) rescale the residual variance to be 1 if it is found to be less than 1.
oldnames revert to using the longer outcome variable name in the b and V ereturned matrices.
penweighted specifies using penalized weights as described in Burgess et al. (2016).
radial specifies the radial formulation of the IVW and MR-Egger models (Bowden et al., 2017). Note there is only a difference for the MR-Egger model.
tdist specifies using the t-distribution, instead of the normal distribution, for calculating the Wald test and the confidence interval limits.
unwi2gx specifies the unweighted Q_GX and I^2_GX statistics to be additionally displayed in the output and in the ereturn scalars.
Examples
Using the data provided by Do et al. (2013) recreate Bowden et al. (2016), Table 4, LDL-c "All genetic variants" estimates.
Setup . use https://raw.github.com/remlapmot/mrrobust/master/dodata, clear
Select observations (p-value with exposure < 10^-8) . gen byte sel1 = (ldlcp2 < 1e-8)
IVW (with fixed effect standard errors) . mregger chdbeta ldlcbeta [aw=1/(chdse^2)] if sel1==1, ivw fe
MR-Egger (with SEs using an unconstrained residual variance) . mregger chdbeta ldlcbeta [aw=1/(chdse^2)] if sel1==1
MR-Egger reporting I^2_GX statistic and heterogeneity Q-test . mregger chdbeta ldlcbeta [aw=1/(chdse^2)] if sel1==1, gxse(ldlcse) heterogi
MR-Egger using a t-distribution for inference & CI limits . mregger chdbeta ldlcbeta [aw=1/(chdse^2)] if sel1==1, tdist
MR-Egger using the radial formulation . mregger chdbeta ldlcbeta [aw=1/(chdse^2)] if sel1==1, radial
MR-Egger using the radial formulation and reporting heterogeneity Q-test . mregger chdbeta ldlcbeta [aw=1/(chdse^2)] if sel1==1, radial heterogi
Stored results
mregger stores the following in e():
Scalars e(df_r) residual degrees of freedom (with tdist option) e(k) number of instruments e(I2GX) I^2_GX (with gxse() option) e(QGX) Q_GX (with gxse() option) e(phi) Scale parameter (root mean squared error)
Macros e(cmd) mregger e(cmdline) command as typed
Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimates
If heterogi is specified mregger additionally returns the r-class results of heterogi in the e-class results.
If unwi2gx is specified mregger additionally returns e(I2GXunw) Unweighted I^2_GX statistic e(QGXunw) Unweighted Q_GX statistic
mregger stores the following in r():
Matrices r(table) Coefficient table with rownames: b, se, z, pvalue, ll, ul, df, crit, eform
References
Bowden J, Davey Smith G, Burgess S. Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression. International Journal of Epidemiology, 2015, 44, 2, 512-525. DOI
Bowden J, Davey Smith G, Haycock PC, Burgess S. Consistent estimation in Mendelian randomization with some invalid instruments using a weighted median estimator. Genetic Epidemiology, 2016, 40, 4, 304-314. DOI
Bowden J, Del Greco F, Minelli C, Davey Smith G, Sheehan NA, Thompson JR. Assessing the suitability of summary data for two-sample Mendelian randomization analyses using MR-Egger regression: the role of the I-squared statistic. International Journal of Epidemiology, 2016, 45, 6, 1961-1974. DOI
Bowden J, Spiller W, Del-Greco F, Sheehan NA, Thompson JR, Minelli C, Davey Smith G. Improving the visualisation, interpretation and analysis of two-sample summary data Mendelian randomization via the radial plot and radial regression. International Journal of Epidemiology, 2018, 47, 4, 1264-1278. DOI
Burgess S, Bowden J, Dudbridge F, Thompson SG. Robust instrumental variable methods using candidate instruments with application to Mendelian randomization. arXiv:1606.03729v1, 2016. Link
Burgess S, Butterworth A, Thompson S. Mendelian randomization analysis with multiple genetic variants using summarized data. Genetic Epidemiology, 2013, 37, 7, 658-665. DOI
Del Greco F M, Minelli C, Sheehan NA, Thompson JR. Detecting pleiotropy in Mendelian randomization studies with summary data and a continuous outcome. Statistics in Medicine, 2015, 34, 21, 2926-2940. DOI
Do R et al. Common variants associated with plasma triglycerides and risk for coronary artery disease. Nature Genetics, 2013, 45, 1345-1352. DOI: DOI
Thompson SG, Sharp SJ. Explaining heterogeneity in meta-analysis: a comparison of methods. Statistics in Medicine, 1999, 18, 20, 2693-2708. DOI
Author
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