Title



     ivtsri -- Two-stage residual inclusion estimators



Syntax



        ivtsri depvar [varlist1] (varlist2 = varlist_iv) [if] [in] [weight] [, link(string) log
              noirr gmm_options]



    varlist1 is the list of exogenous variables.



    varlist2 is the list of endogenous variables.



    varlist_iv is the list of exogenous variables used with varlist1 as instruments for varlist2.



    options               Description
    ----------------------------------------------------------------------------------------------
      noirr               Do not display exponentiated estimates
      link(string)        Link function for the second stage model (identity | logadd | logmult |
                            logit)
      log                 Show the GMM iteration log
      gmm_options         gmm##options



Description



    ivtsri implements two-stage residual inclusion (TSRI) estimators with several link functions
    for the second stage model (identity, log-additive, log-multiplicative, logit).  It is
    implemented using generalized method of moments (GMM) estimation by passing the relevant
    moment condition to the gmm command.



Options



    link(identity | logadd | logmult | logit) specifies the link function for the second stage
        model.  identity means the second stage model is a linear regression (which for a binary
        outcome estimates a causal risk difference).  logadd means the second stage model is a
        Poisson/log-binomial regression (which for a binary outcome estimates a causal risk
        ratio).  logmult means the second stage model is a gamma regression (which for a binary
        outcome estimates a causal risk ratio, Dukes and Vansteelandt, 2018).  logit means the
        second stage model is a logistic regression (which for a binary outcome estimates a causal
        odds ratio).



    Please see gmm##options



Examples



    Read in binary outcome data; y outcome, x exposure, w covariate, z* instrumental variables
    (genotypes).



        . use https://raw.github.com/remlapmot/ivonesamplemr/main/data/ivbinoutdata, clear



    Fit the model with a single instrumental variable.



        . ivtsri y (x = z1)



    Fit the model with multiple instruments.



        . ivtsri y (x = z1 z2 z3)



    Fit the model with multiple instruments, and adjusting for w.



        . ivtsri y w (x = z1 z2 z3)



    Using the log additive link function.



        . ivtsri y (x = z1 z2 z3), link(logadd)



    Using the log multiplicative link function.



        . ivtsri y (x = z1 z2 z3), link(logmult)



    Using the logit link function.



        . ivtsri y (x = z1 z2 z3), link(logit)



    Bootstrap standard errors.
        . bootstrap, reps(250): ivtsri y (x = z1 z2 z3), estonly



Stored results



    Please see gmm##results



References



    Bowden J, Vansteelandt S.  Mendelian randomization analysis of case-control data using
        structural mean models.  Statistics in Medicine, 2011, 30, 6, 678-694.  DOI



    Dukes O, Vansteelandt S.  A note on G-estimation of causal risk ratios.  American Journal of
        Epidemiology, 2018, 187, 5, 1079-1084.  DOI



    Palmer T, Thompson JR, Tobin MD, Sheehan NA, Burton PR.  Adjusting for bias and unmeasured
        confounding in Mendelian randomization studies with binary responses.  International
        Journal of Epidemiology, 2008, 37, 5, 1161-1168.  DOI



    Palmer TM, Sterne JAC, Harbord RM, Lawlor DA, Sheehan NA, Meng S, Granell R, Davey Smith G,
        Didelez V.  Instrumental variable estimation of causal risk ratios and causal odds ratios
        in Mendelian randomization analyses.  American Journal of Epidemiology, 2011, 173, 12,
        1392-1403.  DOI



    Terza JV, Basu A, Rathouz PJ.  Two-stage residual inclusion estimation:  Addressing
        endogeneity in health econometric modeling.  Journal of Health Economics. 2008, 27, 3,
        531–543.  DOI



Author



INCLUDE help ivonesamplemr-author