Title



     mrmvivw/mvivw/mvmr -- Multivariable inverse variance weighted regression (MVIVW)



Syntax



        mrmvivw/mvivw/mvmr varname_gd varname_gp1 [varname_gp2 ...] [aweight] [if] [in] [,
                options]



    options               Description
    ----------------------------------------------------------------------------------------------
      fe                  fixed effect standard errors (default is multiplicative random effect)
      gxse(varlist)       varlist of genotype-phenotype (SNP-exposure) standard errors
      level(#)            set confidence level; default is level(95)
      tdist               use t-distribution for Wald test and CI limits



Description



    mrmvivw/mvivw/mvmr performs multivariable inverse-variance weighted (IVW) regression using
    summary level data.  See  Burgess et al. (2015) for more information.



    varname_gd variable containing the genotype-disease (SNP-outcome) association estimates.



    varname_gp# variable containing the #th 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 multiplicative random effect standard
        errors in which case the variance of the residuals is unconstrained and the square root of
        the estimated residual variance is displayed (Residual standard error). If the residual
        variance is found to be less than 1 an error message is shown and the model is refitted
        with it constrained to 1.



    gxse(varlist) specifies a varlist of genotype-phenotype (SNP-exposure) standard errors.  These
        should be in the same order as the genotype-phenotype (SNP-exposure) variables in the main
        varlist.  When this option is specified the Q_A statistic for instrument validity is
        calculated.  When this is specified and there are two or more phenotypes conditional F
        statistics for instrument strength are calculated.  See Sanderson et al. (2019) and
        Sanderson et al. (2021) for more information.



    level(#); see [R] estimation options.



    tdist specifies using the t-distribution, instead of the normal distribution, for calculating
        the Wald test and the confidence interval limits.



Examples



    Using the data provided by Do et al. (2013).



    Setup
        . use https://raw.github.com/remlapmot/mrrobust/master/dodata, clear



    Select observations (p-value with LDL-C < 10^-8)
        . gen byte sel1 = (ldlcp2 < 1e-8)



    Fit MVMR/MVIVW
        . mrmvivw chdbeta ldlcbeta hdlcbeta tgbeta [aw=1/(chdse^2)] if sel1==1



        . mvivw chdbeta ldlcbeta hdlcbeta tgbeta [aw=1/(chdse^2)] if sel1==1



        . mvmr chdbeta ldlcbeta hdlcbeta tgbeta [aw=1/(chdse^2)] if sel1==1



    Report Q_A statistic and conditional F-statistics
        . mrmvivw chdbeta ldlcbeta hdlcbeta tgbeta [aw=1/(chdse^2)] if sel1==1, gxse(ldlcse hdlcse
            tgse)



Stored results



    mrmvivw/mvivw/mvmr stores the following in e():



    Scalars        
      e(df_r)             residual degrees of freedom (with tdist option)
      e(N)                Number of genotypes
      e(Np)               Number of phenotypes
      e(phi)              Scale parameter (root mean squared error)
    If gxse() specified
      e(Qa)               Q_A statistic
      e(Qadf)             Degrees of freedom of Q_A statistic
      e(Qap)              P-value for Q_A chi-squared test



    Macros         
      e(cmd)              Command name
      e(cmdline)          Command issued
      e(setype)           Standard error type



    Matrices       
      e(b)                coefficient vector
      e(V)                variance-covariance matrix of the estimates
    If gxse() specified
      e(Fx)               vector of conditional F-statistics
      e(Qx)               vector of Q_x statistics



    mrmvivw/mvivw/mvmr stores the following in r():



    Matrices       
      r(table)            Coefficient table with rownames: b, se, z, pvalue, ll, ul, df, crit,
                            eform



References



    Burgess S, Dudbridge F, Thompson SG. Multivariable Mendelian randomization:  the use of
        pleiotropic genetic variants to estimate causal effects.  American Journal of
        Epidemiology, 2015, 181, 4, 251-260.  DOI



    Do et al., 2013. Common variants associated with plasma triglycerides and risk for coronary
        artery disease. Nature Genetics. 45, 1345-1352.  DOI



    Sanderson E, Davey Smith G, Windmeijer F, Bowden J. An examination of multivariable Mendelian
        randomization in the single-sample and two-sample summary data settings. International
        Journal of Epidemiology, 2019, 48, 3, 713-727.  DOI



    Sanderson E, Spiller W, Bowden J. Testing and correcting for weak and pleiotropic instruments
        in two-sample multivariable Mendelian randomization.  Statistics in Medicine, 2021, 40,
        25, 5434-5452.  DOI



Author



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