ORIGINAL INVESTIGATION Bayesian latent trait modeling of migraine symptom data Carla Chia Ming Chen �� Jonathan M. Keith �� Dale R. Nyholt �� Nicholas G. Martin �� Kerrie L. Mengersen Received: 19 January 2009 / Accepted: 12 April 2009 / Published online: 24 April 2009 �� Springer-Verlag 2009 Abstract Definition of disease phenotype is a necessary preliminary to research into genetic causes of a complex disease. Clinical diagnosis of migraine is currently based on diagnostic criteria developed by the International Headache Society. Previously, we examined the natural clustering of these diagnostic symptoms using latent class analysis (LCA) and found that a four-class model was preferred. However, the classes can be ordered such that all symptoms progressively intensify, suggesting that a single continuous variable representing disease severity may provide a better model. Here, we compare two models: item response theory and LCA, each constructed within a Bayesian context. A deviance information criterion is used to assess model fit. We phenotyped our population sample using these models, estimated heritability and conducted genome-wide linkage analysis using Merlin-qtl. LCA with four classes was again preferred. After transformation, phenotypic trait values derived from both models are highly correlated (correlation = 0.99) and consequently results from subsequent genetic analyses were similar. Heritability was estimated at 0.37, while multipoint linkage analysis produced genome-wide significant linkage to chromosome 7q31-q33 and suggestive linkage to chromo- somes 1 and 2. We argue that such continuous measures are a powerful tool for identifying genes contributing to migraine susceptibility. Introduction Research into the genetics of complex diseases often involves the identification of genes associated with groups of patients who exhibit different combinations of disease symptoms or phenotypes. This analysis depends crucially on the careful classification of patients. Commonly, the clustering of patients depends on the criteria established by medical societies, such as the International Headache Society (Headache Classification Committee of the Inter- national Headache Society 1988 Olesen and Steiner 2004 Silberstein et al. 2005) for migraine. Without doubt, these criteria are valuable for the diagnosis of diseases, but their effectiveness for genetic research is debatable (Hallmayer et al. 2003 Wessman et al. 2007) as discussed below. Migraine is a hereditary disorder with estimated heri- tability between 34 and 57% (Ziegler et al. 1998 Mulder et al. 2003 Svensson et al. 2003, 2004 Nyholt et al. 2004, 2005). The two most common forms of migraine are C. C. M. Chen (&) J. M. Keith K. L. Mengersen School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia e-mail: carla.chen@qut.edu.au J. M. Keith e-mail: j.keith@qut.edu.au K. L. Mengersen e-mail: k.mengersen@qut.edu.au D. R. Nyholt Neurogenetics Laboratory, Queensland Institute of Medical Research, PO Royal Brisbane Hospital, Brisbane, QLD 4029, Australia e-mail: daleN@qimr.edu.au D. R. Nyholt N. G. Martin Genetic Epidemiology Laboratory, Queensland Institute of Medical Research, PO Royal Brisbane Hospital, Brisbane, QLD 4029, Australia N. G. Martin e-mail: Nick.Martin@qimr.edu.au 123 Hum Genet (2009) 126:277���288 DOI 10.1007/s00439-009-0671-4

migraine without aura (MO) and migraine with aura (MA), where aura typically concerns a visual disturbance. The genetic research of migraine is mainly focused on these two subgroups. To date, except for CACNA1A, ATP1A2 and SCN1A���genes that contribute to a rare mendelian form of MA, familial hemiplegic migraine (FHM), no gene has been convincingly implicated in migraine (Table 1). This may be due to clinical and genetic heterogeneity of the disease. The phenotype defined by IHS criteria may oversimplify the complex variability among sufferers of this complex disease (Anttila et al. 2006 Wessman et al. 2007). Furthermore, there is overlap in the symptoms of MO and MA. Clinically, the symptoms of MA are a super- set of the symptoms of MO. The work of Nyholt et al. 2004 and Ligthart et al. (2006) provides further support for the argument that MA and MO are not separate entities. Therefore, the development of an endophenotype or an alternative phenotype may give better insight into the genetics of common migraine. There are currently two main types of method for investigating the phenotypic structure of symptom survey results, one based on the use of statistical methodologies to convert the symptoms to a unidimensional value and the other based on trait component analysis (TCA), which treats each individual symptom as a response variable for the purpose of linkage analyses. Nyholt et al. (2004) pio- neered the use of latent class analysis (LCA) of the pheno- type for migraine. The authors applied LCA to migraine symptomatic data in an Australian twin population sample and found that the best fit to the data was obtained using a model with three symptomatic latent classes these corre- spond to a mild form of recurrent non-migrainous head- aches, a moderately severe form of migraine and a severe form. Moreover, the estimated heritability using LCA was found to be slightly higher than the heritability estimated using IHS criteria. Nyholt et al. (2005) then applied this method for genome-wide linkage analysis and identified linkage to chromosome 5q21. They also replicated previ- ously reported susceptibility loci on chromosomes 6p12.2- p21.1 and 1q21-q23. Since migraine is a suite of symptoms and the sub- phenotype analysis in Nyholt et al. (2005) found that individual symptoms are associated with specific linkage peaks in their data, there have been several attempts to identify gene loci linked to individual symptoms (Anttila et al. 2006, 2008). This method is referred to as trait component analysis. Anttila et al. (2006) applied TCA to dissect the genetic susceptibility of migraine in a Finnish cohort. They found strong evidence that various migraine symptoms are linked to chromosome 4q24, including photophobia, phonophobia, intensity, unilaterality, nausea, vomiting and attack length. They also found that pulsation is linked to chromosome 17p3 and reported some sugges- tive linkage of the phonophobia trait to chromosome 10q22 and the ������aggravation by physical exercise������ trait to chro- mosomes 12q21, 15q14 and Xp21. Besides LCA, other clustering methods have been applied to genetic research of diseases with complex aetiology. These include grade of membership (GoM), used to analyze schizophrenia (Hallmayer et al. 2003), mania (Cassidy et al. 2001) and Alzheimer���s (Fillenbaum 1998 Corder and Woodbury 1993) model-based clustering, used to analyze anorexia nervosa (Devlin et al. 2002) and fuzzy clustering, used to analyze anxiety disorder (Kaabi et al. 2006). All these algorithms aim to identify homogenous classes/com- ponents in the data, based on specified traits of interest, and estimate the parameters associated with each class. For some diseases composed of many individual symptoms, the data may be better modeled using a con- tinuous representation. Indeed, in earlier analyses of multi- symptom migraine data using LCA and GoM (Chen et al. 2009 Nyholt et al. 2004, 2005 Ligthart et al. 2006, 2008), the classes could be ordered in such a way that there was a gradual reduction in all symptoms, suggesting that there is a single latent continuous trait underlying the observed pattern of symptoms. It is therefore reasonable to hypo- thesize that the data may be modeled using a single conti- nuous variable representing severity of the disease instead of classes. Item response theory (IRT), which is also known as latent trait analysis, is a popular statistical method for modeling psychological and educational survey responses. It assumes an underlying continuous latent value which has direct influence on the responses to items. Indeed, items are Table 1 The chromosome regions associated with the common forms of migraine Phenotype Cohort Chromosome References MO Icelandic 4q21 Bjornsson �� et al. (2003) MO Italian 14q21.2-q22.3 Soragna et al. (2003) MA Canadian 11q24 Cader et al. (2003) MA Finnish 4q24 Wessman et al.(2002) MA North American Caucasians 19q13 Jones et al.(2001) TCA and LCA Finnish and Australian 10q22-10q23 Anttila et al.(2008) 278 Hum Genet (2009) 126:277���288 123