American Journal of Epidemiology Practice of Epidemiology Instrumental Variable Estimation of Causal Risk Ratios and Causal Odds Ratios in Mendelian Randomization Analyses

In this paper, the authors describe different instrumental variable (IV) estimators of causal risk ratios and odds ratios with particular attention to methods that can handle continuously measured exposures. The authors present this discussion in the context of a Mendelian randomization analysis of the effect of body mass index (BMI; weight (kg)/height (m)(2)) on the risk of asthma at age 7 years (Avon Longitudinal Study of Parents and Children, 1991-1992). The authors show that the multiplicative structural mean model (MSMM) and the multiplicative generalized method of moments (MGMM) estimator produce identical estimates of the causal risk ratio. In the example, MSMM and MGMM estimates suggested an inverse relation between BMI and asthma but other IV estimates suggested a positive relation, although all estimates had wide confidence intervals. An interaction between the associations of BMI and fat mass and obesity-associated (FTO) genotype with asthma explained the different directions of the different estimates, and a simulation study supported the observation that MSMM/MGMM estimators are negatively correlated with the other estimators when such an interaction is present. The authors conclude that point estimates from various IV methods can differ in practical applications. Based on the theoretical properties of the estimators, structural mean models make weaker assumptions than other IV estimators and can therefore be expected to be consistent in a wider range of situations.

[1]  Jonathan H. Wright,et al.  A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments , 2002 .

[2]  J. Robins,et al.  Instruments for Causal Inference: An Epidemiologist's Dream? , 2006, Epidemiology.

[3]  James M. Robins,et al.  Causal Inference from Complex Longitudinal Data , 1997 .

[4]  Vanessa Didelez,et al.  Assumptions of IV methods for observational epidemiology , 2010, 1011.0595.

[5]  J. Angrist,et al.  Digitized by the Internet Archive in 2011 with Funding from Estimation of Limited-dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice , 2011 .

[6]  M. Tobin,et al.  Adjusting for bias and unmeasured confounding in Mendelian randomization studies with binary responses. , 2008, International journal of epidemiology.

[7]  M Alan Brookhart,et al.  American Journal of Epidemiology Practice of Epidemiology Instrumental Variable Analysis for Estimation of Treatment Effects with Dichotomous Outcomes , 2022 .

[8]  N. Sheehan,et al.  Mendelian randomization as an instrumental variable approach to causal inference , 2007, Statistical methods in medical research.

[9]  J. S. Silva,et al.  Endogeneity in Count Data Models: An Application to Demand for Health Care , 1997 .

[10]  Richard Blundell,et al.  Estimation in a class of simultaneous equation limited dependent variable models , 1989 .

[11]  J. Robins.  Correcting for non-compliance in randomized trials using structural nested mean models , 1994 .

[12]  A. Wald.  The Fitting of Straight Lines if Both Variables are Subject to Error , 1940 .

[13]  Richard Blundell,et al.  An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply , 1986 .

[14]  P Gustafson,et al.  Use of instrumental variables in the analysis of generalized linear models in the presence of unmeasured confounding with applications to epidemiological research , 2008, Statistics in medicine.

[15]  E Goetghebeur,et al.  Practical properties of some structural mean analyses of the effect of compliance in randomized trials. , 1997, Controlled clinical trials.

[16]  M. Pembrey,et al.  ALSPAC--the Avon Longitudinal Study of Parents and Children. I. Study methodology. , 2001, Paediatric and perinatal epidemiology.

[17]  F. Windmeijer.  GMM for Panel Count Data Models , 2006 .

[18]  Frank Windmeijer,et al.  Instrumental Variable Estimators for Binary Outcomes , 2009 .

[19]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[20]  Jeffrey M. Wooldridge,et al.  Quasi‐Likelihood Methods for Count Data , 2008 .

[21]  Richard Blundell,et al.  Endogeneity in Nonparametric and Semiparametric Regression Models , 2022 .

[22]  F. Windmeijer.  Expend, a Gauss Programme for Non-Linear GMM Estimation of Exponential Models with Endogenous Regressors for Cross Section and Panel Data , 2002 .

[23]  David M. Kreps,et al.  Advances In Economics and Econometrics: Theory And Applications: Seventh World Congress , 1997 .

[24]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[25]  Qiang Wang,et al.  Crystal structure of the FTO protein reveals basis for its substrate specificity , 2010, Nature.

[26]  A. Nichols.  IVPOIS: Stata module to estimate an instrumental variables Poisson regression via GMM , 2008 .

[27]  D. Lawlor,et al.  Re: Estimation of bias in nongenetic observational studies using "Mendelian triangulation" by Bautista et al. , 2007, Annals of epidemiology.

[28]  M. Jarvelin,et al.  A Common Variant in the FTO Gene Is Associated with Body Mass Index and Predisposes to Childhood and Adult Obesity , 2007, Science.

[29]  George Davey Smith,et al.  Mendelian randomization: Using genes as instruments for making causal inferences in epidemiology , 2008, Statistics in medicine.

[30]  S. Vansteelandt,et al.  Mendelian randomization analysis of case‐control data using structural mean models , 2011, Statistics in medicine.

[31]  R. L. Basmann.  A GENERALIZED CLASSICAL METHOD OF LINEAR ESTIMATION OF COEFFICIENTS IN A STRUCTURAL EQUATION , 1957 .

[32]  M. Tobin,et al.  Mendelian Randomisation and Causal Inference in Observational Epidemiology , 2008, PLoS medicine.

[33]  J. Pearl.  Causal diagrams for empirical research , 1995 .

[34]  J. Robins,et al.  Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models , 2000 .

[35]  E. C. Fieller.  SOME PROBLEMS IN INTERVAL ESTIMATION , 1954 .

[36]  J. Angrist,et al.  Estimation of Limited Dependent Variable Models With Dummy Endogenous Regressors , 2001 .

[37]  Maia Berkane.  Latent Variable Modeling and Applications to Causality , 1997 .

[38]  David V Conti,et al.  Commentary: the concept of 'Mendelian Randomization'. , 2004, International journal of epidemiology.

[39]  Jeffrey M. Woodbridge.  Econometric Analysis of Cross Section and Panel Data , 2002 .

[40]  E. Michael Foster,et al.  Instrumental Variables for Logistic Regression: An Illustration ☆ ☆☆ ★ , 1997 .

[41]  J. Robins,et al.  Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models , 2004 .

[42]  Alberto Abadie.  Semiparametric instrumental variable estimation of treatment response models , 2003 .

[43]  P. Dhrymes.  Econometrics : statistical foundations and applications , 1971 .

[44]  George Davey Smith,et al.  Mendelian Randomization for Strengthening Causal Inference in Observational Studies , 2010, Perspectives on psychological science : a journal of the Association for Psychological Science.

[45]  John E. Garen,et al.  The Returns to Schooling: A Selectivity Bias Approach with a Continuous Choice Variable , 1984 .

[46]  David J. Spiegelhalter,et al.  Probabilistic Networks and Expert Systems , 1999, Information Science and Statistics.

[47]  N. Nagelkerke,et al.  Estimating treatment effects in randomized clinical trials in the presence of non-compliance. , 2000, Statistics in medicine.

[48]  Michael Wooldridge,et al.  Econometric Analysis of Cross Section and Panel Data, 2nd Edition , 2001 .

[49]  W. Greene,et al.  计量经济分析 = Econometric analysis , 2009 .

[50]  Paul J Rathouz,et al.  Two-stage residual inclusion estimation: addressing endogeneity in health econometric modeling. , 2008, Journal of health economics.

[51]  A. Nichols.  Weak Instruments: An Overview and New Techniques , 2006 .

[52]  J. Mullahy.  Instrumental-Variable Estimation of Count Data Models: Applications to Models of Cigarette Smoking Behavior , 1997, Review of Economics and Statistics.

[53]  D. Rivers,et al.  Limited Information Estimators and Exogeneity Tests for Simultaneous Probit Models , 1988 .

[54]  S. Ebrahim,et al.  'Mendelian randomization': can genetic epidemiology contribute to understanding environmental determinants of disease? , 2003, International journal of epidemiology.

[55]  D. Berry,et al.  Statistical models in epidemiology, the environment, and clinical trials , 2000 .

[56]  D. Lawlor,et al.  Clustered Environments and Randomized Genes: A Fundamental Distinction between Conventional and Genetic Epidemiology , 2007, PLoS medicine.

[57]  A. Cameron,et al.  Microeconometrics: Methods and Applications , 2005 .

[58]  Frank Windmeijer,et al.  Identification of causal effects on binary outcomes using structural mean models , 2010, Biostatistics.

[59]  J. Wooldridge.  On two stage least squares estimation of the average treatment effect in a random coefficient model , 1997 .

[60]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[61]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[62]  Stijn Vansteelandt,et al.  Causal inference with generalized structural mean models , 2003 .