Testing for association based on excess allele sharing in a sample of related cases and controlsAbstractIntroductionMethodsMatching statisticObserved IBSExpected IBSSex-linked lociFrequency based statisticsHellinger DistanceEstimating allele frequenciesDetermining significanceSimulationsResultsType I error ratePowerCorrelationsLinked STR allele frequencyDiscussionAcknowledgmentsAppendix I. Derivation of probabilities needed for calculating expected IBSReferencesORIGINAL INVESTIGATIONTesting for association based on excess allele sharing in a sampleof related cases and controlsLambertus Klei Æ Kathyrn RoederReceived: 21 November 2006 / Accepted: 12 February 2007 / Published online: 7 March 2007 Springer-Verlag 2007Abstract Samples consisting of a mix of unrelated casesand controls, small pedigrees, and much larger pedigreespresent a unique challenge for association studies. Fewmethods are available for efficient analysis of such a broadspectrum of data structures. In this paper we introduce anew matching statistic that is well suited to complex datastructures and compare it with frequency-based methodsavailable in the literature. To investigate and compare thepower of these methods we simulate datasets based oncomplex pedigrees. We examine the influence of variouslevels of linkage disequilibrium (LD) of the disease allelewith a marker allele (or equivalently a haplotype). For lowfrequency marker alleles/haplotypes, frequency-based sta-tistics are more powerful in detecting association. In con-trast, for high frequency marker alleles, the matchingstatistic has greater power. The highest power for fre-quency-based statistics occurs when the disease allele fre-quency closely matches the frequency of the linked markerallele. In contrast maximum power of the matching statisticalways occurs for intermediate marker allele frequencyregardless of the disease allele frequency. Moreover, thematching and frequency-based statistics exhibit little cor-relation. We conclude that these two approaches can beviewed as complementary in finding possible associationbetween a disease and a marker for many different situa-tions.IntroductionSubjects originally recruited for linkage analysis of a bin-ary trait are often available for follow up associationstudies. Frequently these samples are supplemented withunrelated cases and controls drawn from the same popu-lation to increase the power of the study. Although con-venient to collect, few analysis methods are available forsamples of complex structure, potentially including a mixof small pedigrees, much larger pedigrees, and unrelatedsubjects (Go¨ring and Terwilliger 2000, Gordon et al. 2004).When too few closely-related individuals are sampled, thesample structure inhibits effective application of a trans-mission disequilibrium tests. In particular the unrelatedsubjects have little utility in this framework. On the otherhand, most population-based tests for association expectthe subjects to be unrelated. Ignoring family structure canlead to spurious associations (Newman et al. 2001; Abneyet al. 2002). Of the few methods of analysis that can ana-lyze disparate samples (e.g., Risch and Teng 1998; Slagerand Schaid 2001; Bourgain et al. 2003), it remains an openquestion how well they work under a variety of conditions.In addition, the field of methods becomes even narrowerwhen the pedigrees are composed of numerous distantlyrelated subjects and pedigrees with inbreeding loops.For unrelated samples, many tests for association can begrouped under the label ‘‘frequency-based’’ because theyare based on assessing the difference in allele frequenciesbetween affected and unaffected individuals. For conve-nience we call the affected individuals ‘cases’ and theunaffected individuals ‘internal controls’ or simply ‘con-trols’. Building on the structure of these tests, Bourgainet al. (2003) developed two frequency-based methods, thecorrected chi-square method, and the case-control quasi-likelihood (CC-QLS) method, that account for arbitrarilyL. KleiWestern Psychiatric Institute and Clinic,University of Pittsburgh Medical Center,Pittsburgh, PA 15213, USAK. Roeder (&)Department of Statistics, Carnegie Mellon University,Pittsburgh 15213, USAe-mail: [email protected] Genet (2007) 121:549–557DOI 10.1007/s00439-007-0345-zcomplex, but known, relatedness among subjects. Weinvestigate a method similar to the corrected chi-squarethat is based on the Hellinger distance between case andcontrol allele frequencies. Our method adjusts for complexrelatedness among subjects through allele dropping simu-lations and takes into account pedigree structure whenestimating allele frequencies.Other statistical procedures have been developed thatare based on detecting an excess of matching alleles orhaplotypes among cases. Unlike the frequency-basedmethods, these statistics are based on pairwise comparisonsof subjects. Like frequency-based methods, these tests havebeen developed either for unrelated subjects (te Meermanand van der Meulen 1997; Tzeng et al. 2003) or for pedi-grees suitable for a transmission disequilibrium tests(Bourgain et al. 2000, 2001). Here we extend the matchingapproach to permit samples drawn from complex pedigreesand/or unrelated subjects. When restricted to a single largepedigree, the proposed test is similar to the linkage testknown as the affected-pedigree-member method by Weeksand Lange (1988).In what follows we describe this new matching methodfor association analysis and conduct a simulation study toassess its performance when the data consists of cases andcontrols drawn from complex pedigrees. The methods ofBourgain et al. (2003) are also evaluated in the simulations.The structure of the simulations is motivated by a study ofthe genetics of schizophrenia in the Oceanic population ofPalau (Klei et al. 2005; Devlin et al. 2007), but the resultsshould be relevant for many other complex sample struc-tures and diseases.MethodsMatching statisticThe matching statistic is based on the observation thatwhen a disease allele is in linkage disequilibrium with amarker allele, one expects to observe individuals withmatching marker alleles more often than predicted underthe null hypothesis of no linkage. To detect this effect wepropose to use the difference between the observed andexpected identity by state (IBS) for each pair of cases as thetest statistic. This matching test statistic, Mkfor locus k, canbe written as:Mk¼1ncase2Xi\jO