title: Power and instrument strength requirements for Mendelian randomization studies using multiple genetic variants.
abstract: BACKGROUND
  Mendelian Randomization (MR) studies assess the causality of an exposure-disease association using genetic determinants [i.e. instrumental variables (IVs)] of the exposure. Power and IV strength requirements for MR studies using multiple genetic variants have not been explored.
  
  
  METHODS
  We simulated cohort data sets consisting of a normally distributed disease trait, a normally distributed exposure, which affects this trait and a biallelic genetic variant that affects the exposure. We estimated power to detect an effect of exposure on disease for varying allele frequencies, effect sizes and samples sizes (using two-stage least squares regression on 10,000 data sets-Stage 1 is a regression of exposure on the variant. Stage 2 is a regression of disease on the fitted exposure). Similar analyses were conducted using multiple genetic variants (5, 10, 20) as independent or combined IVs. We assessed IV strength using the first-stage F statistic.
  
  
  RESULTS
  Simulations of realistic scenarios indicate that MR studies will require large (n > 1000), often very large (n > 10,000), sample sizes. In many cases, so-called 'weak IV' problems arise when using multiple variants as independent IVs (even with as few as five), resulting in biased effect estimates. Combining genetic factors into fewer IVs results in modest power decreases, but alleviates weak IV problems. Ideal methods for combining genetic factors depend upon knowledge of the genetic architecture underlying the exposure.
  
  
  CONCLUSIONS
  The feasibility of well-powered, unbiased MR studies will depend upon the amount of variance in the exposure that can be explained by known genetic factors and the 'strength' of the IV set derived from these genetic factors.
authors.affiliation: Department of Health Studies, University of Chicago, Chicago, IL, USA. bpierce@health.bsd.uchicago.edu
authors.forename: Brandon L
authors.initials: BL
authors.lastname: Pierce
authors.forename: Habibul
authors.initials: H
authors.lastname: Ahsan
authors.forename: Tyler J
authors.initials: TJ
authors.lastname: Vanderweele
mesh_terms: D015982:Bias; D005240:Feasibility Studies; D005260:Female; D020022:Genetic Predisposition to Disease / Q000453:epidemiology*; D014644:Genetic Variation; D055106:Genome-Wide Association Study; D006801:Humans; D008297:Male; D057182:Mendelian Randomization Analysis; D017720:Molecular Epidemiology; D018570:Risk Assessment; D012680:Sensitivity and Specificity
references.citation: Am J Hum Genet. 2009 Apr;84(4):477-82
references.pmid: 19303062
references.citation: J Clin Invest. 2008 Jul;118(7):2620-8
references.pmid: 18521185
references.citation: Am J Hum Genet. 2009 Feb;84(2):123-33
references.pmid: 19185284
references.citation: Nat Genet. 2008 Apr;40(4):437-42
references.pmid: 18327257
references.citation: Nat Genet. 2009 Jun;41(6):648-50
references.pmid: 19448620
references.citation: Nat Genet. 2009 Jun;41(6):724-8
references.pmid: 19448621
references.citation: Stat Med. 2008 Jul 10;27(15):2745-9
references.pmid: 18344186
references.citation: Am J Hum Genet. 2008 May;82(5):1193-201
references.pmid: 18439552
references.citation: Nat Genet. 2009 Jan;41(1):89-94
references.pmid: 19060909
references.citation: Trends Genet. 2008 Aug;24(8):408-15
references.pmid: 18597885
references.citation: Nat Genet. 2009 Jun;41(6):729-33
references.pmid: 19448623
references.citation: Nat Genet. 2008 Apr;40(4):430-6
references.pmid: 18327256
references.citation: Am J Hum Genet. 2008 Oct;83(4):520-8
references.pmid: 18940312
references.citation: Lancet. 2003 Sep 20;362(9388):930-1
references.pmid: 14511923
references.citation: Blood. 2009 Apr 16;113(16):3831-7
references.pmid: 19221038
references.citation: Stat Methods Med Res. 2007 Aug;16(4):309-30
references.pmid: 17715159
references.citation: Am J Hum Genet. 2008 Jan;82(1):139-49
references.pmid: 18179892
references.citation: Nat Genet. 2009 Jan;41(1):56-65
references.pmid: 19060906
references.citation: Nat Genet. 2009 Jan;41(1):77-81
references.pmid: 19060907
references.citation: Nat Genet. 2008 Oct;40(10):1160-2
references.pmid: 18776911
references.citation: Nat Genet. 2009 Jun;41(6):677-87
references.pmid: 19430479
references.citation: Nat Genet. 2009 Jun;41(6):734-8
references.pmid: 19448622
references.citation: Hum Mol Genet. 2008 Oct 15;17(R2):R143-50
references.pmid: 18852203
references.citation: Am J Epidemiol. 2009 Feb 1;169(3):273-84
references.pmid: 19033525
references.citation: Nat Genet. 2009 Jan;41(1):25-34
references.pmid: 19079261
references.citation: Nat Genet. 2009 Feb;41(2):157-9
references.pmid: 19151714
references.citation: PLoS Genet. 2008 May 09;4(5):e1000072
references.pmid: 18464913
references.citation: Nat Genet. 2009 May;41(5):527-34
references.pmid: 19396169
references.citation: Am J Hum Genet. 2008 May;82(5):1185-92
references.pmid: 18439548
references.citation: Stat Med. 2008 Apr 15;27(8):1133-63
references.pmid: 17886233
references.citation: PLoS Genet. 2007 Nov;3(11):e194
references.pmid: 17997608
references.citation: Nat Genet. 2009 Jan;41(1):35-46
references.pmid: 19060910
references.citation: Lancet. 2005 Dec 3;366(9501):1954-9
references.pmid: 16325697
references.citation: Int J Epidemiol. 2004 Feb;33(1):21-5
references.pmid: 15075141
references.citation: Nat Rev Genet. 2009 Feb;10(2):109-21
references.pmid: 19139765
references.citation: Nat Genet. 2009 Jan;41(1):47-55
references.pmid: 19060911
references.citation: Science. 2008 May 23;320(5879):1085-8
references.pmid: 18451265
references.citation: Am J Hum Genet. 2009 Jan;84(1):66-71
references.pmid: 19110211
references.citation: PLoS Med. 2008 Aug 12;5(8):e155
references.pmid: 18700811
references.citation: Int J Epidemiol. 2008 Oct;37(5):1161-8
references.pmid: 18463132
references.citation: Nat Genet. 2009 Jun;41(6):666-76
references.pmid: 19430483
references.citation: Int J Biostat. 2008;4(1):Article 17
references.pmid: 22462152
references.citation: Lancet. 2008 Dec 6;372(9654):1953-61
references.pmid: 18834626
references.citation: PLoS Genet. 2009 Mar;5(3):e1000420
references.pmid: 19282985
references.citation: Nat Genet. 2009 Jun;41(6):645-7
references.pmid: 19448619
references.citation: Nat Genet. 2009 Jan;41(1):18-24
references.pmid: 19079260