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Theory and Methods

Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization

Pages 132-144 | Received 01 Nov 2013, Published online: 05 May 2016

REFERENCES

  • Andrews, W. K.D. (1999), “Consistent Moment Selection Procedures for Generalized Method of Moments Estimation,” Econometrica, 67, 543–563.
  • Angrist, J.D., and Imbens, G.W. (1995), “Two-Stage Least Squares Estimation of Average Causal Effects in Models With Variable Treatment Intensity,” Journal of the American Statistical Association, 90, 431–442.
  • Angrist, J.D., Imbens, G.W., and Rubin, D.B. (1996), “Identification of Causal Effects Using Instrumental Variables,” Journal of the American Statistical Association, 91, 444–455.
  • Beckers, S., Peeters, A.V., de Freitas, F., Mertens, I.L., Verhulst, S.L., Haentjens, D., Desager, K.N., Van Gaal, L.F., and Van Hul, W. (2009), “Association Study and Mutation Analysis of Adiponectin Shows Association of Variants in APM1 With Complex Obesity in Women,” Annals of Human Genetic, 73, 492–501.
  • Belloni, A., Chen, D., Chernozhukov, V., and Hansen, C. (2012), “Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain,” Econometrica, 80, 2369–2429.
  • Björklund, A., and Moffitt, R. (1987), “The Estimation of Wage Gains and Welfare Gains in Self-Selection Models,” The Review of Economics and Statistics, 69, 42–49.
  • Bouatia-Naji, N., Meyre, D., Lobbens, S., Séron, K., Fumeron, F., Balkau, B., Heude, B., Jouret, B., Scherer, P.E., Dina, C., Weill, J., and Froquel, P. (2006), “ACDC/Adiponectin Polymorphisms are Associated with Severe Childhood and Adult Obesity,” Diabetes, 55, 545–550.
  • Brennan, P. (2004), “Commentary: Mendelian Randomization and Gene–Environment Interaction,” International Journal of Epidemiology, 33, 17–21.
  • Cai, T.T., and Zhang, A. (2013), “Compressed Sensing and Affine Rank Minimization Under Restricted Isometry,” IEEE Transactions on Signal Processing, 61, 3279–3290.
  • Candes, E.J., and Tao, T. (2005), “Decoding by Linear Programming,” IEEE Transactions on Information Theory, 51, 4203–4215.
  • Cawley, J., and Meyerhoefer, C. (2012), “The Medical Care Costs of Obesity: An Instrumental Variables Approach,” Journal of Health Economics, 31, 219–230.
  • Davey Smith, G., and Ebrahim, S. (2003), “Mendelian Randomization: Can Genetic Epidemiology Contribute to Understanding Environmental Determinants of Disease? International Journal of Epidemiology, 32, 1–22.
  • ——— (2004), “Mendelian Randomization: Prospects, Potentials, and Limitations,” International Journal of Epidemiology, 33, 30–42.
  • Dina, C., Meyre, D., Gallina, S., Durand, E., Kórner, A., Jacobson, P., Carlsson, L. M.S., Kiess, W., Vatin, V., Lecoeur, C., Delplanque, J., Vaillant, E., Pattou, F., Ruiz, J., Weill, J., Levy-Marchal, C., Horber, F., Potoczna, N., Hercberg, S., Le Stunff, C., Bougneres, P., Kovacs, P., Marre, M., Balkau, B., Cauchi, S., Chevre, J.C., and Froguel, P. (2007), “Variation in FTO Contributes to Childhood Obesity and Severe Adult Obesity,” Nature Genetics, 39, 724–726.
  • Didelez, V., and Sheehan, N. (2007), “Mendelian Randomization as an Instrumental Variable Approach to Causal Inference,” Statistical Methods in Medical Research, 16, 309–330.
  • Donoho, D.L. (2006), “For Most Large Underdetermined Systems of Linear Equations the Minimal L1-norm Solution is Also the Sparsest Solution,” Communications on Pure and Applied Mathematics, 59, 797–829.
  • Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression,” The Annals of Statistics, 32, 407–499.
  • Gautier, E., and Tsybakov, A.B. (2011), “High-Dimensional Instrumental Variables Regression and Confidence Sets,” arXiv:1105.2454 [math.ST].
  • Glymour, M.M., Tchetgen, E.T., and Robins, J.M. (2012), “Credible Mendelian Randomization Studies: Approaches for Evaluating the Instrumental Variable Assumptions,” American Journal of Epidemiology, 175, 332–339.
  • Hansen, L.P. (1982), “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, 1029–1054.
  • Hastie, T., Tibshirani, R., and Friedman, H. (2009), The Elements of Statistical Learning (2nd ed.), New York: Springer.
  • Hauser, R.M. (2005), “Survey Response in the Long Run: The Wisconsin Longitudinal Study,” Field Methods, 17, 3–29.
  • Hernán, M.A., and Robins, J.M. (2006), “Instruments for Causal Inference: An Epidemiologist’s Dream,” Epidemiology, 17, 360–372.
  • Heckman, J.J., and Robb, R. (1985), “Alternative Methods for Evaluating the Impact of Interventions: An Overview,” Journal of Econometrics, 30, 239–267.
  • Holland, P.W. (1988), “Causal Inference, Path Analysis, and Recursive Structural Equations Models,” Sociological Methodology, 18, 449–484.
  • Hwang, J.-P., Tsai, S.-J., Hong, C.-J., Yang, C.-H., Lirng, J.-F., and Yang, Y.-M. (2006), “The Val66Met Polymorphism of the Brain-Derived Neurotrophic-factor Gene is Associated With Geriatric Depression,” Neurobiology of Aging, 27, 1834–1837.
  • Katan, M.B. (1986), “Apolipoprotein E Isoforms, Serum Cholesterol, and Cancer,” Lancet, 327, 507–508.
  • Kolesár, M., Chetty, R., Friedman, J.N., Glaeser, E.L., and Imbens, G.W. (2011), “Identification and Inference With Many Invalid Instruments,” NBER Working Paper No. 17519, National Bureau of Economic Research.
  • Koopmans, T.C., Rubin, H., and Leipnik, R.B. (1950), “Measuring the Equation Systems of Dynamic Economics,” in Statistical Inference in Dynamic Economic Models, New York: Wiley, pp. 54–237.
  • Lawlor, D.A., Harbord, R.M., Sterne, J. A.C., Timpson, N., and Smith, G.D. (2008), “Mendelian Randomization: Using Genes as Instruments for Making Causal Inferences in Epidemiology,” Statistics in Medicine, 27, 1133–1163.
  • Little, J., and Khoury, M.J. (2003), “Mendelian Randomisation: A New Spin or Real Progress? The Lancet, 362, 930–931.
  • Martínez-Calleja, A., Quiróz-Vargas, I., Parra-Rojas, I., Muñoz-Valle, J.F., Leyva-Vázquez, M.A., Fernández-Tilapa, G., Vences-Velázquez, A., Cruz, M., Salazar-Martínez, E., and Flores-Alfaro, E. (2012), “Haplotypes in the CRP Gene Associated With Increased BMI and Levels of CRP in Subjects With Type 2 Diabetes or Obesity From Southwestern Mexico,” Experimental Diabetes Research, 2012, 1–7, Article ID 982683.
  • Mealli, F., and Pacini, B. (2013), “Using Secondary Outcomes to Sharpen Inference in Randomized Experiments With Noncompliance,” The Journal of the American Statistical Association, 108, 1120–1131.
  • Murray, M.P. (2006), “Avoiding Invalid Instruments and Coping with Weak Instruments,” The Journal of Economic Perspectives, 20, 111–132.
  • Natarajan, B.K. (1995), “Sparse Approximate Solutions to Linear Systems,” SIAM Journal on Computing, 24, 227–234.
  • National Institutes of Health (1998), “Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults: The Evidence Report,” Obesity Research, 2, 51S–209S.
  • Neyman, J. (1923), “On the Application of Probability Theory to Agricultural Experiments,” Statistical Science, 5, 463–480.
  • Price, R.A., Li, W.-D., and Zhao, H. (2008), “FTO Gene SNPs Associated With Extreme Obesity in Cases, Controls and Extremely Discordant Sister Pairs,” BMC Medical Genetics, 9, 1–5.
  • Richardson, D.H., and Wu, D. (1971), “A Note on the Comparison of Ordinary and Two-Stage Least Squares Estimators,” Econometrica, 39, 973–981.
  • Roetker, N.S., Yonker, J.A., Lee, C., Chang, V., Basson, J.J., Roan, C.L., Hauser, T.S., Hauser, R.M., and Atwood, C.S. (2012), “Multigene Interactions and Prediction of Depression in the Wisconsin Longitudinal Study,” British Medical Journal Open, 2, e000944, 1–7.
  • Rubin, D.B. (1974), “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,” Journal of Educational Psychology, 66, 688–701.
  • Rybakowski, J.K., Borkowska, A., Skibinska, M., Szczepankiewicz, A., Kapelski, P., Leszczynska-rodziewicz, A., Czerski, P.M., and Hauser, J. (2006), “Prefrontal Cognition in Schizophrenia and Bipolar Illness in Relation to Val66Met Polymorphism of the Brain-Derived Neurotrophic Factor Gene,” Psychiatry and Clinical Neurosciences, 60, 70–76.
  • Sach, T.H., Barton, G.R., Doherty, M., Muir, K.R., Jenkinson, C., and Avery, A.J. (2007), “The Relationship Between Body Mass Index and Health-Related Quality of Life: Comparing the EQ-5D, EuroQol VAS and SF-6D,” International Journal of Obesity, 31, 189–196.
  • Shugart, Y.Y., Chen, L., Day, I.N., Lewis, S.J., Timpson, N.J., Yuan, W., Abdollahi, M.R., Ring, S.M., Ebrahim, S., Golding, J., Lawlor, D.A., and Smith, G.D. (2009), “Two British Women Studies Replicated the Association Between the Val66Met Polymorphism in the Brain-Derived Neurotrophic Factor (BDNF) and BMI,” European Journal of Human Genetics, 17, 1050–1055.
  • Small, D.S. (2007), “Sensitivity Analysis for Instrumental Variables Regression with Overidentifying Restrictions,” Journal of the American Statistical Association, 102, 1049–1058.
  • Solovieff, N., Cotsapas, C., Lee, P.H., Purcell, S.M., and Smoller, J.W. (2013), “Pleiotropy in Complex Traits: Challenges and Strategies,” Nature Reviews Genetics, 14, 483–495.
  • Stock, J.H., Wright, J.H., and Yogo, M. (2002), “A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments,” Journal of Business and Economic Statistics, 20, 518–520.
  • Thomas, D.C., and Conti, D.V. (2004), “Commentary: The Concept of ‘Mendelian Randomization’,” International Journal of Epidemiology, 33, 21–25.
  • Thorleifsson, G., Walters, G.B., Gudbjartsson, D.F., Steinthorsdottir, V., Sulem, P., Helgadottir, A., Styrkarsdottir, U., Gretarsdottir, S., Thorlacius, S., Jonsdottir, I., Jonsdottir, T., Olafsdottir, E.J., Olafsdottir, G.H., Jonsson, T., Jonsson, F., Borch-Johnsen, K., Hansen, T., Andersen, G., Jorgensen, T., Lauritzen, T., Aben, K.K., Verbeek, A.L., Roeleveld, N., Kampman, E., Yanek, L.R., Becker, L.C., Tryggvadottir, L., Rafnar, T., Becker, D.M., Gulcher, J., Kiemeney, L.A., Pedersen, O., Kong, A., Thorsteinsdottir, U., and Stefansson, K. (2008), “Genome-Wide Association Yields New Sequence Variants at Seven Loci that Associate With Measures of Obesity,” Nature Genetics, 41, 18–24.
  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
  • ——— (2013), “The Lasso Problem and Uniqueness,” Electronic Journal of Statistics, 7, 1456–1490.
  • Timpson, N.J., Lawlor, D.A., Harbord, R.M., Gaunt, T.R., Day, I.N., Palmer, L.J., Hattersley, A.T., Ebrahim, S., Lowe, G., Rumley, A., and Smith, G.D. (2005), “C-reactive Protein and its Role in Metabolic Syndrome: Mendelian Randomisation Study,” The Lancet, 366, 1954–1959.
  • Torrance, G.W. (1987), “Utility Approach to Measuring Health-Related Quality of Life,” Journal of Chronic Disease, 40, 593–600.
  • Trakas, K., Oh, P.I., Singh, S., Risebrough, N., and Shear, N.H. (2001), “The Health Status of Obese Individuals in Canada,” International Journal of Obesity and Related Metabolic Disorders: Journal of the International Association for the Study of Obesity, 25, 662–668.
  • Tropp, J.A. (2006), “Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise,” IEEE Transactions on Information Theory, 52, 1030–1051.
  • Ukkola, O., Ravussin, E., Jacobson, P., Sjöström, L., and Bouchard, C. (2003), “Mutations in the Adiponectin Gene in Lean and Obese Subjects From the Swedish Obese Subjects Cohort,” Metabolism, 52, 881–884.
  • Wang, J., and Zivot, E. (1998), “Inference on Structural Parameters in Instrumental Variables Regression With Weak Instruments,” Econometrica, 66, 1389–1404.
  • Wehby, G.L., Ohsfeldt, R.L., and Murray, J.C. (2008), “‘Mendelian Randomization’ Equals Instrumental Variable Analysis With Genetic Instruments,” Statistics in Medicine, 27, 2745–2749.
  • Wooldridge, J.M. (2010), Econometric Analysis of Cross Section and Panel Data (2nd ed.), Cambridge, MA: MIT Press.
  • Yang, W.S., Tsou, P.L., Lee, W.J., Tseng, D.L., Chen, C.L., Peng, C.C., Lee, K.C., Chen, M.J., Huang, C.J., Tai, T.Y., and Chuang, L.M. (2003), “Allele-Specific Differential Expression of a Common Adiponectin Gene Polymorphism Related to Obesity,” Journal of Molecular Medicine, 81, 428–434.
  • Yang, W.S., Yang, Y.C., Chen, C.L., Wu, I.L., Lu, J.Y., Lu, F.H., Tai, T.Y., and Chang, C.-J. (2007), “Adiponectin SNP276 is Associated with Obesity, the Metabolic Syndrome, and Diabetes in the Elderly,” The American Journal of Clinical Nutrition, 86, 509–513.

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