Power and instrument strength requirements for Mendelian randomization studies using multiple genetic variants

Lawlor, 2008, Mendelian randomization: using genes as instruments for making causal inferences in epidemiology, Stat Med, 27, 1133, 10.1002/sim.3034

Didelez, 2007, Mendelian randomization as an instrumental variable approach to causal inference, Stat Methods Med Res, 16, 309, 10.1177/0962280206077743

Tian, 2008, Accounting for ancestry: population substructure and genome-wide association studies, Hum Mol Genet, 17, R143, 10.1093/hmg/ddn268

Wehby, 2008, 'Mendelian randomization' equals instrumental variable analysis with genetic instruments, Stat Med, 27, 2745, 10.1002/sim.3255

Aulchenko, 2009, Loci influencing lipid levels and coronary heart disease risk in 16 European population cohorts, Nat Genet, 41, 47, 10.1038/ng.269

Hegele, 2009, Plasma lipoproteins: genetic influences and clinical implications, Nat Rev Genet, 10, 109, 10.1038/nrg2481

Kathiresan, 2009, Common variants at 30 loci contribute to polygenic dyslipidemia, Nat Genet, 41, 56, 10.1038/ng.291

Reiner, 2008, Polymorphisms of the HNF1A gene encoding hepatocyte nuclear factor-1 alpha are associated with C-reactive protein, Am J Hum Genet, 82, 1193, 10.1016/j.ajhg.2008.03.017

Ridker, 2008, Loci related to metabolic-syndrome pathways including LEPR, HNF1A, IL6R, and GCKR associate with plasma C-reactive protein: the Women’s Genome Health Study, Am J Hum Genet, 82, 1185, 10.1016/j.ajhg.2008.03.015

Hazra, 2008, Common variants of FUT2 are associated with plasma vitamin B12 levels, Nat Genet, 40, 1160, 10.1038/ng.210

Tanaka, 2009, Genome-wide association study of vitamin B6, vitamin B12, folate, and homocysteine blood concentrations, Am J Hum Genet, 84, 477, 10.1016/j.ajhg.2009.02.011

Ferrucci, 2009, Common variation in the beta-carotene 15,15'-monooxygenase 1 gene affects circulating levels of carotenoids: a genome-wide association study, Am J Hum Genet, 84, 123, 10.1016/j.ajhg.2008.12.019

Meisinger, 2009, A genome-wide association study identifies three loci associated with mean platelet volume, Am J Hum Genet, 84, 66, 10.1016/j.ajhg.2008.11.015

Soranzo, 2009, A novel variant on chromosome 7q22.3 associated with mean platelet volume, counts, and function, Blood, 113, 3831, 10.1182/blood-2008-10-184234

Levy, 2009, Genome-wide association study of blood pressure and hypertension, Nat Genet, 41, 677, 10.1038/ng.384

Newton-Cheh, 2009, Genome-wide association study identifies eight loci associated with blood pressure, Nat Genet, 41, 666, 10.1038/ng.361

Bouatia-Naji, 2009, A variant near MTNR1B is associated with increased fasting plasma glucose levels and type 2 diabetes risk, Nat Genet, 41, 89, 10.1038/ng.277

Bouatia-Naji, 2008, A polymorphism within the G6PC2 gene is associated with fasting plasma glucose levels, Science, 320, 1085, 10.1126/science.1156849

Chen, 2008, Variations in the G6PC2/ABCB11 genomic region are associated with fasting glucose levels, J Clin Invest, 118, 2620

Prokopenko, 2009, Variants in MTNR1B influence fasting glucose levels, Nat Genet, 41, 77, 10.1038/ng.290

Cho, 2009, A large-scale genome-wide association study of Asian populations uncovers genetic factors influencing eight quantitative traits, Nat Genet, 41, 527, 10.1038/ng.357

Melzer, 2008, A genome-wide association study identifies protein quantitative trait loci (pQTLs), PLoS Genet, 4, e1000072, 10.1371/journal.pgen.1000072

Sabatti, 2009, Genome-wide association analysis of metabolic traits in a birth cohort from a founder population, Nat Genet, 41, 35, 10.1038/ng.271

Yuan, 2008, Population-based genome-wide association studies reveal six loci influencing plasma levels of liver enzymes, Am J Hum Genet, 83, 520, 10.1016/j.ajhg.2008.09.012

Brunner, 2008, Inflammation, insulin resistance, and diabetes–Mendelian randomization using CRP haplotypes points upstream, PLoS Med, 5, e155, 10.1371/journal.pmed.0050155

Timpson, 2005, C-reactive protein and its role in metabolic syndrome: Mendelian randomisation study, Lancet, 366, 1954, 10.1016/S0140-6736(05)67786-0

Bound, 1995, Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak, J Am Statist Assoc, 90, 443

Nelson, 1990, The distribution of the instrumental variables estimator and its t-ratio when the instrument is a poor one, J Bus, 63, S125, 10.1086/296497

Stock, 2002, Testing for Weak Instruments in Linear IV Regression, 10.3386/t0284

Stock, 2002, A survey of weak instruments and weak identification in generalized method of moments, J Bus Econ Statist, 20, 518, 10.1198/073500102288618658

Staiger, 1994, Instrumental Variables Regression with Weak Instruments, 10.3386/t0151

Draper, 1998, Applied Regression Analysis, 10.1002/9781118625590

Donald, 2001, Choosing the number of instruments, Econometrica, 69, 1161, 10.1111/1468-0262.00238

Gilad, 2008, Revealing the architecture of gene regulation: the promise of eQTL studies, Trends Genet, 24, 408, 10.1016/j.tig.2008.06.001

Dehghan, 2008, Association of three genetic loci with uric acid concentration and risk of gout: a genome-wide association study, Lancet, 372, 1953, 10.1016/S0140-6736(08)61343-4

Doring, 2008, SLC2A9 influences uric acid concentrations with pronounced sex-specific effects, Nat Genet, 40, 430, 10.1038/ng.107

Vitart, 2008, SLC2A9 is a newly identified urate transporter influencing serum urate concentration, urate excretion and gout, Nat Genet, 40, 437, 10.1038/ng.106

Wallace, 2008, Genome-wide association study identifies genes for biomarkers of cardiovascular disease: serum urate and dyslipidemia, Am J Hum Genet, 82, 139, 10.1016/j.ajhg.2007.11.001

Li, 2007, The GLUT9 gene is associated with serum uric acid levels in Sardinia and Chianti cohorts, PLoS Genet, 3, e194, 10.1371/journal.pgen.0030194

Meyre, 2009, Genome-wide association study for early-onset and morbid adult obesity identifies three new risk loci in European populations, Nat Genet, 41, 157, 10.1038/ng.301

Thorleifsson, 2009, Genome-wide association yields new sequence variants at seven loci that associate with measures of obesity, Nat Genet, 41, 18, 10.1038/ng.274

Willer, 2009, Six new loci associated with body mass index highlight a neuronal influence on body weight regulation, Nat Genet, 41, 25, 10.1038/ng.287

He, 2009, Genome-wide association studies identify loci associated with age at menarche and age at natural menopause, Nat Genet, 41, 724, 10.1038/ng.385

Liu, 2009, Genome-wide association analyses identify SPOCK as a key novel gene underlying age at menarche, PLoS Genet, 5, e1000420, 10.1371/journal.pgen.1000420

Ong, 2009, Genetic variation in LIN28B is associated with the timing of puberty, Nat Genet, 41, 729, 10.1038/ng.382

Perry, 2009, Meta-analysis of genome-wide association data identifies two loci influencing age at menarche, Nat Genet, 41, 648, 10.1038/ng.386

Sulem, 2009, Genome-wide association study identifies sequence variants on 6q21 associated with age at menarche, Nat Genet, 41, 634, 10.1038/ng.383

Stolk, 2009, Loci at chromosomes 13, 19 and 20 influence age at natural menopause, Nat Genet, 41, 645, 10.1038/ng.387

Thomas, 2004, Commentary: the concept of ‘Mendelian Randomization’, Int J Epidemiol, 33, 21, 10.1093/ije/dyh048

Baum, 2003, Instrumental variables and GMM: estimation and testing, Stata J, 3, 1, 10.1177/1536867X0300300101

Little, 2003, Mendelian randomisation: a new spin or real progress?, Lancet, 362, 930, 10.1016/S0140-6736(03)14396-6

Angrist, 1995, Two-stage least squares estimation of average causal effects in models with variable treatment intensity, J Am Statist Assoc, 90, 431, 10.1080/01621459.1995.10476535

Heckman, 2005, Structural equations, treatment effects, and econometric policy evaluation, Econometrica, 73, 669, 10.1111/j.1468-0262.2005.00594.x

Imbens, 1994, Identification and estimation of local average treatment effects, Econometrica, 62, 467, 10.2307/2951620

Tan, 2006, Regression and weighting methods for causal inference using instrumental variables, J Am Statist Assoc, 101, 1607, 10.1198/016214505000001366

Greene, 2003, Econometric Analysis, 5th

Rassen, 2009, Instrumental variable analysis for estimation of treatment effects with dichotomous outcomes, Am J Epidemiol, 169, 273, 10.1093/aje/kwn299

Palmer, 2008, Adjusting for bias and unmeasured confounding in Mendelian randomization studies with binary responses, Int J Epidemiol, 37, 1161, 10.1093/ije/dyn080

Robins, 2004, Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models, Biometrika, 91, 763, 10.1093/biomet/91.4.763

van der Laan, 2007, Estimation of treatment effects in randomized trials with noncompliance and a dichotomous outcome, J R Stat Soc B, 69, 442, 10.1111/j.1467-9868.2007.00598.x

Vansteelandt, 2003, Causal inference with generalized structural mean models, J R Stat Soc B, 65, 817, 10.1046/j.1369-7412.2003.00417.x

Shinohara, 2008, Estimating Effects by Combining Instrumental Variables with Case-control Designs: the Role of Principal Stratification

Van der Laan, 2008, Estimation based on case-control designs with known prevalence probability, Int J Biostat, 4, Article 17, 10.2202/1557-4679.1114