title: Accounting for selection and correlation in the analysis of two-stage genome-wide association studies.
abstract: The problem of selection bias has long been recognized in the analysis of two-stage trials, where promising candidates are selected in stage 1 for confirmatory analysis in stage 2. To efficiently correct for bias, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been proposed for a wide variety of trial settings, but where the population parameter estimates are assumed to be independent. We relax this assumption and derive the UMVCUE in the multivariate normal setting with an arbitrary known covariance structure. One area of application is the estimation of odds ratios (ORs) when combining a genome-wide scan with a replication study. Our framework explicitly accounts for correlated single nucleotide polymorphisms, as might occur due to linkage disequilibrium. We illustrate our approach on the measurement of the association between 11 genetic variants and the risk of Crohn's disease, as reported in Parkes and others (2007. Sequence variants in the autophagy gene IRGM and multiple other replicating loci contribute to Crohn's disease susceptibility. Nat. Gen. 39: (7), 830-832.), and show that the estimated ORs can vary substantially if both selection and correlation are taken into account.
authors.affiliation: MRC Biostatistics Unit, IPH Forvie Site, Robinson Way, Cambridge CB2 0SR, UK david.robertson@mrc-bsu.cam.ac.uk.
authors.forename: David S
authors.initials: DS
authors.lastname: Robertson
authors.affiliation: Imperial College London, 1st Floor, Stadium House, 68 Wood Lane, London W12 7RH, UK.
authors.forename: A Toby
authors.initials: AT
authors.lastname: Prevost
authors.affiliation: MRC Integrative Epidemiology Unit, University of Bristol, Oakfield House, Bristol BS8 2BN, UK and MRC Biostatistics Unit, IPH Forvie Site, Robinson Way, Cambridge CB2 0SR, UK.
authors.forename: Jack
authors.initials: J
authors.lastname: Bowden
mesh_terms: D003424:Crohn Disease / Q000235:genetics; D055106:Genome-Wide Association Study / Q000592:standards*; D006801:Humans; D020641:Polymorphism, Single Nucleotide; D015983:Selection Bias
keywords: Correlated outcomes; Genome-wide scan; Selection bias; Two-stage sample; Uniformly minimum variance conditionally unbiased estimator