The many weak instruments problem and mendelian randomization

Statistics in Medicine

Volumn 34, Issue 3, 2015, Pages 454-468

  Davies, Neil M ^a,b   von Hinke Kessler Scholder, Stephanie ^a   Farbmacher, Helmut ^c   Burgess, Stephen ^d   Windmeijer, Frank ^a   Smith, George Davey ^a,b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c MAX PLANCK INSTITUTE FOR SOCIAL LAW AND SOCIAL POLICY   (Germany)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Allele scores; ALSPAC; Continuously updating estimator; Height; Many weak instruments; Mendelian randomization

Indexed keywords

ADOLESCENT; ANALYTIC METHOD; ARTICLE; BIRTH WEIGHT; BODY HEIGHT; CONCEPTUAL FRAMEWORK; CONTINUOUSLY UPDATING ESTIMATOR; CONTROLLED STUDY; CORRELATION ANALYSIS; EDUCATION; FEMALE; FORCED VITAL CAPACITY; GENETIC VARIABILITY; HUMAN; LIMITED INFORMATION MAXIMUM LIKELIHOOD; LUNG FUNCTION; MAJOR CLINICAL STUDY; MALE; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MENDELIAN RANDOMIZATION ANALYSIS; METHODOLOGY; PROBABILITY; RESPIROMETRY; SIMULATION; STATISTICAL BIAS; ALLELE; COHORT ANALYSIS; COMPUTER SIMULATION; ENGLAND; EPIDEMIOLOGY; GENETIC VARIATION; GENETICS; PROCEDURES; RANDOMIZATION; REGRESSION ANALYSIS; RISK FACTOR; STATISTICAL MODEL; VITAL CAPACITY;

ADOLESCENT; ALLELES; BIAS (EPIDEMIOLOGY); BODY HEIGHT; CAUSALITY; COHORT STUDIES; COMPUTER SIMULATION; ENGLAND; FEMALE; GENETIC VARIATION; HUMANS; LEAST-SQUARES ANALYSIS; LIKELIHOOD FUNCTIONS; LINEAR MODELS; MALE; MENDELIAN RANDOMIZATION ANALYSIS; RANDOM ALLOCATION; RISK FACTORS; VITAL CAPACITY;

EID: 84920735955     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6358     Document Type: Article

References (59)

1. C Reactive Protein Coronary Heart Disease Genetics Collaboration (CCGC). Association between C reactive protein and coronary heart disease: Mendelian randomisation analysis based on individual participant data. BMJ 2011; 342:d548-d548.
2. Davey Smith G, Ebrahim S. "Mendelian randomization": can genetic epidemiology contribute to understanding environmental determinants of disease? International Journal of Epidemiology 2003; 32(1):1-22.
3. Timpson NJ, Lawlor DA, Harbord RM, Gaunt TR, Day INM, Palmer LJ, Hattersley AT, Ebrahim S, Lowe GDO, Rumley A, Davey Smith G. C-reactive protein and its role in metabolic syndrome: Mendelian randomisation study. Lancet 2005; 366(9501):1954-1959.
4. Voight BF, Peloso GM, Orho-Melander M, Frikke-Schmidt R, Barbalic M, Jensen MK, Hindy G, Hólm H, Ding EL, Johnson T, Schunkert H, Samani NJ, Clarke R, Hopewell JC, Thompson JF, Li M, Thorleifsson G, Newton-Cheh C, Musunuru K, Pirruccello JP, Saleheen D, Chen L, Stewart AFR, Schillert A, Thorsteinsdottir U, Thorgeirsson G, Anand S, Engert JC, Morgan T, Spertus J, Stoll M, Berger K, Martinelli N, Girelli D, McKeown PP, Patterson CC, Epstein SE, Devaney J, Burnett M-S, Mooser V, Ripatti S, Surakka I, Nieminen MS, Sinisalo J, Lokki M-L, Perola M, Havulinna A, de Faire U, Gigante B, Ingelsson E, Zeller T, Wild P, de Bakker PIW, Klungel OH, Maitland-van der Zee A-H, Peters BJM, de Boer A, Grobbee DE, Kamphuisen PW, Deneer VHM, Elbers CC, Onland-Moret NC, Hofker MH, Wijmenga C, Verschuren WMM, Boer JMA, van der Schouw YT, Rasheed A, Frossard P, Demissie S, Willer C, Do R, Ordovas JM, Abecasis GR, Boehnke M, Mohlke KL, Daly MJ, Guiducci C, Burtt NP, Surti A, Gonzalez E, Purcell S, Gabriel S, Marrugat J, Peden J, Erdmann J, Diemert P, Willenborg C, König IR, Fischer M, Hengstenberg C, Ziegler A, Buysschaert I, Lambrechts D, Van de Werf F, Fox KA, El Mokhtari NE, Rubin D, Schrezenmeir J, Schreiber S, Schäfer A, Danesh J, Blankenberg S, Roberts R, McPherson R, Watkins H, Hall AS, Overvad K, Rimm E, Boerwinkle E, Tybjaerg-Hansen A, Cupples LA, Reilly MP, Melander O, Mannucci PM, Ardissino D, Siscovick D, Elosua R, Stefansson K, O'Donnell CJ, Salomaa V, Rader DJ, Peltonen L, Schwartz SM, Altshuler D, Kathiresan S. Plasma HDL cholesterol and risk of myocardial infarction: a Mendelian randomisation study. Lancet 2012; 380(9841):572-580.
5. Nordestgaard BG, Palmer TM, Benn M, Zacho J, Tybjærg-Hansen A, Davey Smith G, Timpson NJ. The effect of elevated body mass index on ischemic heart disease risk: causal estimates from a Mendelian randomisation approach. PLoS Medicine 2012; 9(5):e1001212.
6. Brunner EJ, Kivimäki M, Witte DR, Lawlor DA, Davey Smith G, Cooper JA, Miller M, O Lowe GD, Rumley A, Casas JP, Shah T, Humphries SE, Hingorani AD, Marmot MG, Timpson NJ, Kumari M. Inflammation, insulin resistance, and diabetes - Mendelian randomization using CRP haplotypes points upstream. PLoS Medicine 2008; 5(8):e155.
7. Lawlor DA, Harbord RM, Sterne JA, Timpson N, Davey Smith G. Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. Statistics in Medicine 2008; 27(8):1133-1363.
8. Davey Smith G, Lawlor DA, Harbord R, Timpson N, Day I, Ebrahim S. Clustered environments and randomized genes: a fundamental distinction between conventional and genetic epidemiology. PLoS Medicine 2007; 4(12):e352.
9. Davey Smith G, Hemani G. Mendelian randomization: genetic anchors for causal inference in epidemiological studies. Human Molecular Genetics 2014; 23:R89-R98.
10. Bound J, Jaeger D, Baker R. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association 1995; 90(430):443-450.
11. Hernán MA, Robins J. Instruments for causal inference: an epidemiologist's dream? Epidemiology 2006; 17(4):360-372.
12. Staiger D, Stock J. Instrumental variables regression with weak instruments. Econometrica 1997; 65(3):557-586.
13. Burgess S, Thompson SG. Bias in causal estimates from Mendelian randomization studies with weak instruments. Statistics in Medicine 2011; 30(11):1312-1323.
14. Pierce BL, Ahsan H, VanderWeele TJ. Power and instrument strength requirements for Mendelian randomization studies using multiple genetic variants. International Journal of Epidemiology 2010; 40(3):740-752.
15. Burgess S, Thompson SG, CRP CHD Genetics Collaboration. Avoiding bias from weak instruments in Mendelian randomization studies. International Journal of Epidemiology 2011; 40(3):755-764.
16. Palmer TM, Lawlor DA, Harbord RM, Sheehan NA, Tobias JH, Timpson NJ, Davey Smith G, Sterne JA. Using multiple genetic variants as instrumental variables for modifiable risk factors. Statistics Methods Medicine Research 2012; 21(3):223-242.
17. Hansen C, Hausman J, Newey W. Estimation with many instrumental variables. Journal of Business and Economic Statistics 2008; 26(4):398-422.
18. Newey W, Windmeijer F. GMM with many weak moment conditions. Econometrica 2009; 77(3):687-719.
19. Burgess S, Thompson SG. Use of allele scores as instrumental variables for Mendelian randomization. International Journal of Epidemiology 2013; 42(4):1134-1144.
20. Palmer TM, Lawlor DA, Harbord RM, Sheehan NA, Tobias JH, Timpson NJ, Davey Smith G, Sterne JAC. Using multiple genetic variants as instrumental variables for modifiable risk factors. Statistical Methods Medical Research 2012; 21(3):223-242.
21. Clarke PS, Palmer TM, Windmeijer F. Estimating structural mean models with multiple instrumental variables using the generalised method of moments. The Centre for Market and Public Organisation, 2011.
22. Farbmacher H. GMM with many weak moment conditions: replication and application of Newey and Windmeijer (2009). Journal of Applied Econometrics 2012; 27(2):343-346.
23. Angrist JD, Krueger A. Does compulsory school attendance affect schooling and earnings? The Quarterly Journal of Economics 1991; 106(4):979-1014.
24. Hansen LP. Large sample properties of generalized method of moments estimators. Econometrica: Journal of the Econometric Society 1982; 50(4):1029-1054.
25. Hansen LP, Heaton J, Yaron A. Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics 1996; 14(3):262-280.
26. Bun MJG, Windmeijer F. A comparison of bias approximations for the two-stage least squares (2SLS) estimator. Economics Letters 2011; 113(1):76-79.
27. Nagar AL. The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations. Econometrica 1959; 27(4):575-595.
28. Rothenberg TJ. Chapter 15 Approximating the Distributions of Econometric Estimators and Test Statistics, Handbook of Econometrics[Internet]. Elsevier: Amsterdam, 1984. Available from: http://linkinghub.elsevier.com/retrieve/pii/S1573441284020079. DOI: 10.1016/S1573-4412(84)02007-9.
29. Newey W, Smith RJ. Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 2004; 72(1):219-255.
30. Newey WK, Smith RJ. Asymptotic Bias and Equivalence of GMM and GEL Estimators [Internet]. Citeseer. Available from: http://economics.mit.edu/files/1097.
31. Bekker PA. Alternative approximations to the distributions of instrumental variable estimators. Econometrica 1994; 62(3):657-681.
32. Baum CF, Schaffer ME, Stillman S. Enhanced routines for instrumental variables/GMM estimation and testing. Stata Journal 2007; 7(4):465-506.
33. Hausman JA, Newey WK, Woutersen T, Chao JC, Swanson NR. Instrumental variable estimation with heteroskedasticity and many instruments: instrumental variable estimation. Quantitative Economics 2012; 3(2):211-255.
34. Stock J, Wright J, Yogo M. A survey of weak instruments and weak identification in generalized method of moments. Journal of Business & Economic Statistics 2002; 20(4):518-529.
35. Boyd A, Golding J, Macleod J, Lawlor DA, Fraser A, Henderson J, Molloy L, Ness A, Ring S, Davey Smith G. Cohort profile: the "Children of the 90s" - the index offspring of the Avon Longitudinal Study of Parents and Children. International Journal of Epidemiology 2012; 42(1):111-127.
36. Fraser A, Macdonald-Wallis C, Tilling K, Boyd A, Golding J, Davey Smith G, Henderson J, J Macleod, Molloy L, Ness A, Ring S, Nelson SM, Lawlor DA. Cohort profile: the Avon Longitudinal Study of Parents and Children: ALSPAC mothers cohort. International Journal of Epidemiology 2012; 42(1):97-110.
37. Bristol U of. Data dictionary, ALSPAC, Bristol University [Internet]. Available from: http://www.bristol.ac.uk/alspac/researchers/data-access/data-dictionary/ [Accessed on 13 May 2013].
38. Kotecha SJ, Watkins WJ, Paranjothy S, Dunstan FD, Henderson AJ, Kotecha S. Effect of late preterm birth on longitudinal lung spirometry in school age children and adolescents. Thorax 2011; 67(1):54-61.
39. Kotecha SJ, Watkins WJ, Heron J, Henderson J, Dunstan FD, Kotecha S. Spirometric lung function in school-age children: effect of intrauterine growth retardation and catch-up growth. American Journal of Respiratory and Critical Care Medicine 2010; 181(9):969-974.
40. Howe LD, Matijasevich A, Tilling K, Brion M-J, Leary SD, Davey Smith G, Lawlor DA. Maternal smoking during pregnancy and offspring trajectories of height and adiposity: comparing maternal and paternal associations. International Journal of Epidemiology 2012; 41(3):722-732.
41. von Hinke Kessler Scholder S, Davey Smith G, Lawlor DA, Propper C, Windmeijer F. Child height, health and human capital: evidence using genetic markers. European Economic Review 2013; 57:1-22.
42. Lango Allen H, Estrada K, Lettre G, Berndt SI, Weedon MN, Rivadeneira F, Willer CJ, Jackson AU, Vedantam S, Raychaudhuri S, Ferreira T, Wood AR, Weyant RJ, Segrè AV, Speliotes EK, Wheeler E, Soranzo N, Park J-H, Yang J, Gudbjartsson D, Heard-Costa NL, Randall JC, Qi L, Vernon Smith A, Mägi R, Pastinen T, Liang L, Heid IM, Luan J, Thorleifsson G, Winkler TW, Goddard ME, Sin Lo K, Palmer C, Workalemahu T, Aulchenko YS, Johansson Å, Carola Zillikens M, Feitosa MF, Esko T, Johnson T, Ketkar S, Kraft P, Mangino M, Prokopenko I, Absher D, Albrecht E, Ernst F, Glazer NL, Hayward C, Hottenga J-J, Jacobs KB, Knowles JW, Kutalik Z, Monda KL, Polasek O, Preuss M, Rayner NW, Robertson NR, Steinthorsdottir V, Tyrer JP, Voight BF, Wiklund F, Xu J, Hua Zhao J, Nyholt DR, Pellikka N, Perola M, Perry JRB, Surakka I, Tammesoo M-L, Altmaier EL, Amin N, Aspelund T, Bhangale T, Boucher G, Chasman DI, Chen C, Coin L, Cooper MN, Dixon AL, Gibson Q, Grundberg E, Hao K, Juhani Junttila M, Kaplan LM, Kettunen J, König IR, Kwan T, Lawrence RW, Levinson DF, Lorentzon M, McKnight B, Morris AP, Müller M, Suh Ngwa J, Purcell S, Rafelt S, Salem RM, Salvi E, Sanna S, Shi J, Sovio U, Thompson JR, Turchin MC, Vandenput L, Verlaan DJ, Vitart V, White CC, Ziegler A, Almgren P, Balmforth AJ, Campbell H, Citterio L, De Grandi A, Dominiczak A, Duan J, Elliott P, Elosua R, Eriksson JG, Freimer NB, Geus EJC, Glorioso N, Haiqing S, Hartikainen A-L, Havulinna AS, Hicks AA, Hui J, Igl W, Illig T, Jula A, Kajantie E, Kilpeläinen TO, Koiranen M, Kolcic I, Koskinen S, Kovacs P, Laitinen J, Liu J, Lokki M-L, Marusic A, Maschio A, Meitinger T, Mulas A, Paré G, Parker AN, Peden JF, Petersmann A, Pichler I, Pietiläinen KH, Pouta A, Ridderstråle M, Rotter JI, Sambrook JG, Sanders AR, Oliver Schmidt C, Sinisalo J, Smit JH, Stringham HM, Bragi Walters G, Widen E, Wild SH, Willemsen G, Zagato L, Zgaga L, Zitting P, Alavere H, Farrall M, McArdle WL, Nelis M, Peters MJ, Ripatti S, van Meurs JBJ, Aben KK, Ardlie KG, Beckmann JS, Beilby JP, Bergman RN, Bergmann S, Collins FS, Cusi D, den Heijer M, Eiriksdottir G, Gejman PV, Hall AS, Hamsten A, Huikuri HV, Iribarren C, Kähönen M, Kaprio J, Kathiresan S, Kiemeney L, Kocher T, Launer LJ, Lehtimäki T, Melander O, Mosley Jr TH, Musk AW, Nieminen MS, O'Donnell CJ, Ohlsson C, Oostra B, Palmer LJ, Raitakari O, Ridker PM, Rioux JD, Rissanen A, Rivolta C, Schunkert H, Shuldiner AR, Siscovick DS, Stumvoll M, Tönjes A, Tuomilehto J, van Ommen G-J, Viikari J, Heath AC, Martin NG, Montgomery GW, Province MA, Kayser M, Arnold AM, Atwood LD, Boerwinkle E, Chanock SJ, Deloukas P, Gieger C, Grönberg H, Hall P, Hattersley AT, Hengstenberg C, Hoffman W, Mark Lathrop G, Salomaa V, Schreiber S, Uda M, Waterworth D, Wright AF, Assimes TL, Barroso I, Hofman A, Mohlke KL, Boomsma DI, Caulfield MJ, Adrienne Cupples L, Erdmann J, Fox CS, Gudnason V, Gyllensten U, Harris TB, Hayes RB, Jarvelin M-R, V Mooser, Munroe PB, Ouwehand WH, Penninx BW, Pramstaller PP, Quertermous T, Rudan I, Samani NJ, Spector TD, Völzke H, H Watkins, Wilson JF, Groop LC, Haritunians T, Hu FB, Kaplan RC, Metspalu A, North KE, Schlessinger D, Wareham NJ, Hunter DJ, O'Connell JR, Strachan DP, Wichmann H-E, Borecki IB, van Duijn CM, Schadt EE, Thorsteinsdottir U, Peltonen L, Uitterlinden AG, Visscher PM, Chatterjee N, Loos RJF, Boehnke M, McCarthy MI, Ingelsson E, Lindgren CM, Abecasis GR, Stefansson K, Frayling TM, Hirschhorn JN. Hundreds of variants clustered in genomic loci and biological pathways affect human height. Nature 2010; 467(7317):832-838.
43. Paternoster L, Zhurov AI, Toma AM, Kemp JP, St. Pourcain B, Timpson NJ, McMahon G, McArdle W, Ring SM, Davey Smith G, Richmond S, Evans DM. Genome-wide association study of three-dimensional facial morphology identifies a variant in PAX3 associated with nasion position. The American Journal of Human Genetics 2012; 90(3):478-485.
44. Fatemifar G, Hoggart CJ, Paternoster L, Kemp JP, Prokopenko I, Horikoshi M, Wright VJ, Tobias JH, Richmond S, Zhurov AI, Toma AM, Pouta A, Taanila A, Sipila K, Lähdesmäki R, Pillas D, Geller F, Feenstra B, Melbye M, Nohr EA, Ring SM, St Pourcain B, Timpson NJ, Davey Smith G, Jarvelin M-R, Evans DM. Genome-wide association study of primary tooth eruption identifies pleiotropic loci associated with height and craniofacial distances. Human Molecular Genetics 2013; 22(18):3807-3817.
45. Royston P. Multiple imputation of missing values: further update of ice, with an emphasis on categorical variables. Stata Journal 2009; 9(3):466-477.
46. Royston P. Multiple imputation of missing values. Stata Journal 2004; 4:227-241.
47. Hausman JA. Specification tests in econometrics. Econometrica 1978; 46(6):1251-1271.
48. Wu DM. Alternative tests of independence between stochastic regressors and disturbances. Econometrica 1973; 41(4):733-750.
49. Wooldridge J. Econometric Analysis of Cross Section and Panel Data. The MIT press: Cambridge, Massachusetts, 2002.
50. Angrist JD, Pischke JS. Mostly Harmless Econometrics: An Empiricist's Companion. Princeton Univirsity Press: Princeton, 2009.
51. Breusch TS, Pagan AR. The Lagrange multiplier test and its applications to model specification in econometrics. The Review of Economic Studies 1980; 47(1):239-253.
52. Sargan J. The estimation of economic relationships using instrumental variables. Econometrica 1958; 26(3):393-415.
53. Baum C, Schaffer M, Stillman S. IVREG2: Stata module for extended instrumental variables/2SLS and GMM estimation. Statistical Software Components 2002. Available from: http://ideas.repec.org/c/boc/bocode/s425401.html.
54. StataCorp. Stata Statistical Software: Release 13. StataCorp LP: College Station, TX, 2013. Available from: http://www.stata.com/support/faqs/resources/citing-software-documentation-faqs/.
55. Von Hinke Kessler Scholder S, Wehby GL, Lewis S, Zuccolo L. Alcohol exposure in utero and child academic achievement. The Economic Journal 2014; 124(576):634-667.
56. Granell R, Henderson AJ, Evans DM, Davey Smith G, Ness AR, Lewis S, Palmer TM, Sterne JAC. Effects of BMI, fat mass, and lean mass on asthma in childhood: a Mendelian randomization study. PLoS Medicine 2014; 11(7):e1001669.
57. Davies NM, Davey Smith G, Windmeijer F, Martin RM. COX-2 selective nonsteroidal anti-inflammatory drugs and risk of gastrointestinal tract complications and myocardial infarction: an instrumental variable analysis. Epidemiology 2013; 24(3):352-362.
58. Davies NM, Gunnell D, Thomas KH, Metcalfe C, Windmeijer F, Martin RM. Physicians' prescribing preferences were a potential instrument for patients' actual prescriptions of antidepressants. Journal of Clinical Epidemiology 2013; 66:1386-1396.
59. Rassen JA, Brookhart MA, Glynn R, Mittleman M, Schneeweiss S. Instrumental variables II: instrumental variable application - in 25 variations, the physician prescribing preference generally was strong and reduced covariate imbalance. Journal of Clinical Epidemiology 2009; 62(12):1233-1241.