Paul D Thompson

Ole J Andreassen

Alejandro D Arias-Vasquez

Premika Carrie D Bearden

S Boedhoe

Rachel D Brouwer

Randy L Buckner

Jan J Buitelaar

Kazima M Bulayeva

Dara D Cannon

Paul M Thompson

Ole A Andreassen

Carrie E Bearden

Premika S Boedhoe

Rachel M Brouwer

Jan K Buitelaar

Kazima B Bulayeva

Dara M Cannon

Ronald A Cohen

Patricia J Conrod

Anders M Dale

Ian J Deary

Emily L Dennis

Marcel A De Reus

Sylvane Desrivieres

Danai Dima

Gary Donohoe

Simon E Fisher

Jean-Paul Fouche

Clyde Francks

Sophia Frangou

Barbara Franke

Habib Ganjgahi Ac

Hugh Garavan Ad

David C Glahn

Hans J Grabe Ag,Ah

Tulio Guadalupe

Boris A Gutman

Ryota Hashimoto Aj

Derrek P Hibar

Dominic Holland

Martine Hoogman

Hilleke E Hulshoff Pol

Norbert Hosten Ak

Neda Jahanshad

Sinead Kelly

Peter Kochunov Al

William S Kremen

Phil H Lee

Scott Mackey

Nicholas G Martin

Bernard Mazoyer Ar

Colm Mcdonald

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Rajendra A Morey At

Thomas E Nichols Au,Av

ax,ay Tomas Paus Aw

Zdenka Pausova Az,Ba

Lianne Schmaal

Gunter Schumann

Li Shen

Sanjay M Sisodiya Bd

Dirk J A Smit

Jordan W Smoller Bf

Dan J Stein

Jason L Stein

Roberto Toro

Jessica A Turner Bj

Martijn P Van Den Heuvel

Odile L Van Den Heuvel

Theo G M Van Erp

Daan Van Rooij

Dick J Veltman

Henrik Walter

Yalin Wang

Joanna M Wardlaw

Christopher D Whelan

Margaret J Wright Br

Jieping Ye

ENIGMA and the individual: Predicting factors that affect the brain in 35 countries worldwide

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Here we provide an update on the progress of the ENIGMA consortium, a global alliance of over 500 scientists from over 200 institutions in 35 countries to study brain imaging data worldwide, discovering factors that modulate brain structure, integrity, connectivity, and patterns of brain differences in major brain diseases. Founded in 2009, ENIGMA's initial aims were to perform genome-wide analyses to identify common variants in the genome that are reliably associated with 1 Abbreviations: ADNI, Alzheimer's Disease Neuroimaging Initiative (http://www.adniinfo.org); CHARGE, the Cohorts for Heart and Aging Research in Genomic Epidemiology Consortium (http://www.chargeconsortium.com); IMAGEN, IMAging GENetics Consortium (http://www.imagen-europe.com).

normal variability in brain structure. Since the initial effort discovered consistent effects worldwide of genetic variants that explained less than 1% of the variance in brain measures [START_REF] Stein | The Schizophrenia Working Group of the Psychiatric Genomics Consortium[END_REF]Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication;Hibar et al., 2015a,b, in press), over 500 scientists have joined ENIGMA. ENIGMA is now (as of October 2015) a worldwide consortium, organized into over 30 working groups, studying major brain diseases (detailed at http://enigma.ini.usc.edu). The work in ENIGMA is divided into projects on (1) genetics, screening genomic data for predictors of individual variations in brain structure, function, and connectivity;

(2) disease, screening brain measures to identify patterns of differences in the major brain diseases and factors that affect them; and

(3) methods development. New "Big Data" methods are being developed and implemented around the world to perform genetic analysis of high-dimensional features that arise in neuroimagingsuch as brain networks or "connectomes" [START_REF] Sporns | The human connectome: a structural description of the human brain[END_REF], 3D or 4D maps of brain changes over time, and more complex imaging data from functional MRI and EEG/MEG.

For this issue of NeuroImage we review the work ENIGMA has done, and how it relates to making individual predictions to support the emerging discipline of precision medicinewhere personalized medical decisions are made considering an individual's genetic make-up, other risk factors, and the large body of scientific knowledge detailing genotype-phenotype relationships. ENIGMA's genetic and diseaserelated studies are discovering new factors that affect the brain throughout life, how the diseased brain differs from the healthy brain, and how patterns of brain measures differ from one disease to another. The potential to use machine learning methods in this context is vast, and we point to future opportunities and challenges, and what we have learned already about how individual genetic variants and diseases affect the brain.

One major thrust of ENIGMA's work is genomics, so we first review studies that discovered individual loci in the genome that are linked to variations in brain structure [START_REF] Vounou | Sparse reduced-rank regression detects genetic associations with voxel-wise longitudinal phenotypes in Alzheimer's disease[END_REF]; Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a, b, in press). The effect of these common genetic variants tends to be small, but the aggregate effect of thousands of them accounts for a substantial proportion of the variance in brain measures [START_REF] Toro | Genomic architecture of human neuroanatomical diversity[END_REF][START_REF] Ge | Massively expedited genome-wide heritability analysis (MEGHA[END_REF][START_REF] Chen | Pediatric Imaging, Neurocognition and Genetics Study; Alzheimer's Disease Neuroimaging Initiative[END_REF]. The relevant genes can be difficult to discover in individual cohorts, but they can be detected by metaanalyzing data across multiple sites. We discuss multivariate and machine learning methods needed to combine some of these predictors in more powerful models that can make valuable predictions about individuals, such as predicting deviations from normal lifetime aging, risk for mental illness, or recovery from trauma.

Reproducibility

There have been numerous recent surprises regarding the nature of gene effects on the brain, including surprisingly poor reproducibility of candidate gene effects on imaging measures and risk for mental illness, and the very large sample sizes needed to reliably detect any genetic associations at all. There have also been dramatic claims of poor reproducibility of findings in genetics, neuroimaging, and neuroscience studies in general [START_REF] Button | Power failure: why small sample size undermines the reliability of neuroscience[END_REF][START_REF] Ioannidis | How to make more published research true[END_REF][START_REF] Ioannidis | Publication and other reporting biases in cognitive sciences: detection, prevalence, and prevention[END_REF]. Meta-analyses, such as those conducted by ENIGMA, have been proposed as a way to screen for false positive findings. If claims of "significance chasing" and "fishing" in neuroscience studies are true [START_REF] Ioannidis | How to make more published research true[END_REF], then predictive models based on them should fail more often than models based on meta-analyzed studies of large numbers of independent cohorts, analyzed in a harmonized way [START_REF] Ware | Significance chasing in research practice: causes, consequences and possible solutions[END_REF]. ENIGMA is dedicated to replication, and a number of initiatives are underway to develop methods to replicate imaging genomics findings.

We discuss factors that affect reproducibility of models that predict specific gene effects on the brain, including technical factors of image acquisition and analysis. Low effect sizes for individual predictors make genetic effects hard to detect, so meta-analysis is valuable in demonstrating effects that no single cohort can detect on its own. Clearly, if we build a model to classify a person into a certain diagnostic group, based on a set of predictors, we also need to know how to decide if we have measured the predictors well enough, or if the context where the model was fitted is similar enough to the current situation for the prediction to make sense and be accurate. Apart from the choice of predictive model and predictors, there are many other reasons why imaging or genetic models of diagnosis or prognosis may generalize poorly or not at all, depending on the context. Factors that affect model prediction will include age and environment, and the demographic history of the populations sampled; these may affect whether or not a predictor is relevant to a new cohort or an individual. In the ENIGMA studies below, we point to examples in which predictors in the genome and image would be valuable in making individual predictions about brain volume or about a person's diagnosis, but only in certain contexts, such as in certain parts of the lifespan, or only after considering certain confounds or variables that are known to drive brain differences (duration of medication and duration of illness are often confounded, and modeling each effect independently may produce paradoxical conclusions, e.g., that medication is bad for the brain). Individual predictive models are likely to become increasingly nuanced, as we find out more about how predictors interact and contexts where different models work best.

In the course of ENIGMA's efforts, a vast quantity of normative data has been gathered and analyzed from different countries and continents of the world, allowing us to make some inferences about the normal trajectory of brain development and aging (ENIGMA-Lifespan; [START_REF] Dima | Subcortical brain volumes across the lifespan based on 10,722 people aged 2 to 92[END_REF]. We discuss the challenges and opportunities in using models based on these data to make assertions about individual and group deviations from normal, or to generate cohort, or national norms, if they exist and if their value outweighs the costs of generating them.

We also discuss several concepts that have increased the power of ENIGMA to find factors with very small effects on the brain, including how we assess their generality and extensibility to new cohorts.

ENIGMA's Genetic Studies

By December 2009, many researchers worldwide had collected genome-wide genotyping data from cohorts of subjects for whom brain imaging information such as anatomical MRI was available.

It had long been presumed that genetic and environmental factors, and the complex interactions among them, play a role in shaping brain structure. Decades of work in behavioral and medical genetics had convincingly shown that many of the major brain diseasesfrom Alzheimer's and Parkinson's disease to psychiatric illnesses such as schizophrenia and major depressionhad a strong additive genetic component. Similar genetic risks exist for neurodevelopmental disorders such as autism. Even so, studies of identical twins who share the same genome show that genetic factors do not fully account for disease risk, and discordant twin pairs provide valuable information about the impact of environmental and epigenetic factors on disease [START_REF] Munn | Amygdala volume analysis in female twins with major depression[END_REF]. Furthermore, many common disorders are likely to reflect a constellation of modest gene differences acting in concert, which smaller individual studies are unlikely to find. Instead, larger studies that capture heterogeneity have begun to unravel the influence of multiple 'low level' minor but important gene differences on disease expression [START_REF] Lopez | Genes from a translational analysis support a multifactorial nature of white matter hyperintensities[END_REF].

As high-throughput genotyping methods became available, genomewide association studies (GWASs) began to reveal specific sources of risk in the genome for several major brain diseases (Fig. 1). To fully appreciate this kind of study, we need to understand that much of the genome is invariant between humans [START_REF] Rosenberg | Genetic structure of human populations[END_REF]. Many kinds of individual genetic variationscommon or rarecan occur, including polymorphisms, insertions and deletions of genetic material, loss or retention of homozygosity (LOH/ROH), or copy number variations (CNVs)where the number of copies of pieces of genomic material differs from the normal two alleles in some individuals but not others. Polymorphisms are a common marker of individual differences, where a single nucleotide polymorphism (SNP) is essentially a "single-letter" change in the genome: a change in a single base pair between individuals.

Some genomic changes interfere with the viability of the organism, leading to very low frequencies in the population. Others remain and some have a moderate or severe impact on a person's health, or their risk for disease. For example, a common variant (present in 1 in 100 in the general population) in the HFE gene impairs a person's ability to metabolize iron. Excessive iron levels can then accumulate in bodily organs, which can cause liver and kidney failure. Multiple deletions in the 22q region of the genome provide another example. Individuals with these deletions have a characteristic neurodevelopmental profile associated with mild to severe abnormalities in the face, brain, and heart, and are at heightened risk for schizophrenia and autism. 22q deletions occur frequently de novo, so they do not really remain in the (Hibar et al., Nature, 2015). This study identified five novel genetic variants associated with differences in the volumes of the putamen and caudate nucleus and stronger evidence for three previously established influences on hippocampal volume (see Stein et al., Nature Genetics, 2012) and intracranial volume (see Ikram et al., Nature Genetics, 2012). Each Manhattan plot in Part D is color-coded to match its corresponding subcortical structure, shown in the middle row. The gray dotted line represents genome-wide significance at the standard p = 5x10 -8 ; the red dotted line shows a multiple-comparison corrected threshold of p = 7.1 x 10 -9 . [Images are reproduced here with permission from MacMillan Publishers Ltd (Nature Genetics, 2012& 2013;Nature, 2014Nature, & 2015) ) and with permission from the corresponding authors.] population; rather 22q is a vulnerable spot in the genome for mutation. Even so, 22q deletion syndromeand other neurogenetic disorders such as Fragile X, Williams syndrome, and Turner syndromehave often been studied to help identify potential mechanisms that may contribute to more prevalent psychiatric conditions. ENIGMA's 22q working group has been set up to understand brain differences associated with deletions at this locus, and how they relate to those found using the same analysis protocols in ENIGMA-Schizophrenia and ENIGMA-Autism.

Genetic risk for many major psychiatric illnesses is thought to be mediated in part by common genetic variants that have persisted in human populations for thousands of years. In many cases, the adverse effects of disease risk genessuch as the Alzheimer's risk gene, APOEare not apparent until later in life (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press). Because of this, the variants tend to be preserved in the gene pool and continue to drive disease risk worldwide.

Geneticists continue to debate the relative contribution of common versus rare genetic variants to risk for various diseases, but a recent large-scale screen of schizophrenia patient cohorts worldwide implicated over 100 genetic loci in risk for the disease (Ripke et al., 2014;Fig. 1). This highly successful study pointed to several genes in the dopamine neurotransmission pathway that had long been implicated in schizophrenia and its treatmentfor example, a functional polymorphism in the DRD2 promoter region, which modulates levels of gene expression, and affects antipsychotic drug efficacy [START_REF] Zhang | Pharmacogenetics of antipsychotics: recent progress and methodological issues[END_REF]. This same genomic screen pointed to other unexpected genetic variants in immune system pathways that offer tantalizing new leads about disease mechanisms, and the role of modifiable factors in eventually treating or averting the illness. Similar efforts in bipolar illness, major depression, and ADHD uncovered genes driving risk for these disorders that overlapped to some extent with those for schizophrenia and with each other (Cross Disorders Working Group of the Psychiatric Genomics Consortium, 2013). Members of the ENIGMA Consortium have recently demonstrated the usefulness of polygenic risk scores for schizophrenia (based on the 108 loci shown in Fig. 1A) in revealing an association between early cannabis use and brain maturation during adolescencereplicated in three samples [START_REF] Franke | Is there overlap between common genetic influences on schizophrenia and subcortical brain volumes?[END_REF].

Many successful genomic screens involve over 100,000 individuals. For example, the most recent GWAS of height, educational attainment, and body mass index (BMI) identified 56 novel BMI-associated loci in a sample of up to 339,224 individuals [START_REF] Nalls | Cohorts for Health and Aging Research in Genetic Epidemiology (CHARGE), North American Brain Expression Consortium (NABEC), United Kingdom Brain Expression Consortium (UKBEC), Greek Parkinson's Disease Consortium, Alzheimer Genetic Analysis Group[END_REF][START_REF] Locke | Genetic studies of body mass index yield new insights for obesity biology[END_REF]. Similarly, the Psychiatric Genomics Consortium's discovery of genetic loci implicated in schizophrenia risk took a 'quantum leap' once the sample sizes exceeded 75,000 (Ripke et al., 2014), after less successful searches in smaller samples. Several factors may contribute towards this need for large sample sizes in genome-wide association. First, there are biological variation and ascertainment differences among cohorts. A person diagnosed with a specific illness may have other co-morbid illnesses, and diagnostic criteria may vary somewhat worldwide in terms of who is included in the groups of patients and controls.

However, the main reason GWAS needs large samples is power: a genome-wide association analysis comprises approximately a million independent tests, so a threshold of p b 5 × 10 -8 is employed to minimize false positives. Early GWAS estimated their required sample sizes based on published effect sizes of candidate genes that have since been shown to be greatly overestimated. Although the genetic architecture of each trait is unique, for most complex traits the effect sizes of individual SNPs are typically less than half a percent (Franke et al., in press). Thus, it follows from power analyses that GWAS and GWAS meta-analyses typically require data from tens of thousands of individuals.

In the imaging field, initial studies also attempted genome-wide screens of brain imaging measures, such as brain size [START_REF] Paus | KCTD8 gene and brain growth in adverse intrauterine environment: a genome-wide association study[END_REF], the volume of the temporal lobes on MRI (Stein et al., 2010a,b), in cohorts of around 800 subjects (see Medland et al., 2014, for a review). This type of analysis became feasible as large cohort studies, such as the Alzheimer's Disease Neuroimaging Initiative [START_REF] Jr | Magnetic resonance imaging in ADNI[END_REF], started to put their images and genomic data online. In line with accepted practice in genetics, it is customary to require replication of such genetic effects in independent cohorts.

While some effects appeared to replicate, most did not as the studies were underpowered, and it was unclear whether cohort factors, biological differences, or technical factors were to blame.

Endophenotype Theory and Power

As the field of imaging genetics grew, some researchers hoped that imaging might offer a more efficient approach to discover genes involved in mental illness. The reason for this optimism was based on the observation that many brain measures are consistently reported as affected in psychiatric cohort studies (see later, under ENIGMA Disease Studies), so they could maybe serve as quantitative traits, or markers, correlated with the illness.

There was also some hope that the biological signals in imagesmeasures of neurotransmitters, receptors or metabolite levels, blood flow, the volume of specialized brain areas such as the hippocampus, or its chemical contentmight be influenced by genetic variants because of their proximity to primary gene action. Likewise, it was argued that brain-derived measures may have a simpler genetic architectureperhaps with fewer individual genes or pathways influencing themcompared to the multitude of factors driving a person's overall risk for developing a disease [START_REF] Saykin | Genetic studies of quantitative MCI and AD phenotypes in ADNI: progress, opportunities, and plans[END_REF]. Brain measures may also offer a more precise or reproducible diagnostic scale. [START_REF] Potkin | Genome-wide strategies for discovering genetic influences on cognition and cognitive disorders: methodological considerations[END_REF] noted that GWAS can be more efficient when researchers analyze continuous measures (such as brain volumes) rather than binary traits, such as diagnosis, which may also disguise complexities such as co-morbidity, etc.

This endophenotype theory2 led to confidence that genomewide screening of brain measures would yield "hits"genetic loci consistently associated with brain measuresrelatively efficiently and, some believed, in much smaller samples. Several countervailing arguments should also be considered. The genetics of brain traits may reveal common pathways involved in a number of mental illnesses, but one loses some specificity when moving from a psychiatric disorder to brain measuresdifferent disorders may have very similar brain abnormalities. For this reason, ENIGMA's Disease Working groups have analyzed tens of thousands of brain scans to see which measures best distinguish patients from controls, across a range of 12 diseases, with a view to understanding similarities and differences. Collecting brain imaging data is more expensive than diagnostic testing. Also, genes that affect brain measures may be of less interest to a patient or physician unless they are also connected to disease risk or prognosis. In ENIGMA, however, the costs of collecting the imaging data had already been incurred, making the feasibility of a large-scale analysis the main consideration. Others voiced a muted optimism: [START_REF] Munafò | The genetic architecture of psychophysiological phenotypes[END_REF] noted that effect sizes for gene effects on neuroimaging data were not likely to be any greater than for any other trait, but the value in studying them came from the ability of brain measures to help understand mechanisms that might underlie associations between genes and more conventional traits (see also [START_REF] Flint | Assessing the utility of intermediate phenotypes for genetic mapping of psychiatric disease[END_REF]). Yet, the potential to find genetic factors that jointly influence risk for mental illness and a neuroimaging trait could dramatically improve statistical power and provide an important link between the genome and the behavioral symptoms used to diagnose psychiatric and neurological illnesses [START_REF] Glahn | Arguments for the sake of endophenotypes: examining common misconceptions about the use of endophenotypes in psychiatric genetics[END_REF].

In ENIGMA's first paper in Nature Genetics, Stein and 158 authors (2012), including 4 existing consortia (SYS, EPIGEN, ADNI, and IMAGEN3 ), meta-analyzed GWAS data from cohorts worldwide and found genetic loci consistently associated with the size of the human hippocampus and total intracranial volume. Notably, in a partnership with another consortium, CHARGE (Bis et al., 2012), the top "hits"the genetic variants with greatest effect sizeswere anonymously exchanged and found to be the same, supporting the replicability of the findings in completely independently designed efforts.

In a follow-up study in a larger sample (N = 21,151 individuals; Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; called "ENIGMA2"), eight genetic loci were discovered that were reliably associated with the size (volume) of several subcortical structures, including the putamen, caudate, and pallidum. With the increased sample size, earlier findings regarding the hippocampus and intracranial volume were replicated and reinforced; new genetic loci were also discovered. Several of the SNPs implicated lie within or close to genes involved in cell migration, axon guidance, or apoptosisall cellular processes likely to lead to observable differences in the size of cellular nuclei in the brain. Parallel work in mice by the Williams lab in Memphis began to study mouse homologs of these variants [START_REF] Ashbrook | Joint genetic analysis of hippocampal size in mouse and human identifies a novel gene linked to neurodegenerative disease[END_REF]; recent data suggest that variation of the top putamen gene, KTN1, can predict putamen volume and cell counts in outbred mice (R. Williams, pers. commun.).

Several lessons were learned from the first two ENIGMA genetic studies, in addition to a third pair of papers currently in submission, involving an even larger sample (N N 31,000; Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a, b, in press; Adams and the CHARGE and ENIGMA2 Consortia, submitted for publication). First, through meta-analyses, it was possible to detect factors (here, SNPs) that accounted for less than 1% of the variance in brain measures. This was despite the fact that the participating studies were designed with different goals in mind, and many used scanners of different field strengths, processed by researchers who had not all met, and communicated through email and teleconference calls.

Much of the consistency in brain measures capitalized on the ongoing refinement of standardized protocols for analyzing images and genomes; in turn, those protocols relied on decades of work by developers of widely used and extensively tested analysis packages such as FreeSurfer [START_REF] Dale | Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction: a linear approach[END_REF]Fischl, 2012), and FSL (Jenkinson et al., 2012). The supplement of the first ENIGMA paper [START_REF] Vounou | Sparse reduced-rank regression detects genetic associations with voxel-wise longitudinal phenotypes in Alzheimer's disease[END_REF] contained 104 pages of ancillary tests supporting the validity and reliability of the data, including tests comparing different imaging software for brain volume quantification.

On the genomic side, the ability to compare genomic data in a common reference frame depended on the availability of the HapMap3 (The International HapMap3 Consortium, 2010) and later the 1000 Genomes reference datasets [START_REF] Project | A map of human genome variation from population-scale sequencing[END_REF]. These reference panels are continually updated and refined, and allow genotyping data collected with one kind of genotyping array ("chip") to be imputed to match data collected using others, and pooled in the same overall study.

A second issue is whether these findings could have been detected more efficiently using only some of the samples. In a sense, this is a "meta-question"how might the study have been designed more efficiently after seeing the results?

As in any meta-analysis, the weight assigned to each cohort in the final statistics can be made to depend on its total sample size, or on the standard error of the regression coefficients (which is in fact what ENIGMA does). As such, it is not vital for every cohort to reject the null hypothesis on its own. In fact, any cohort study, however small, can partner with other sites to contribute to the discovery of effects that it cannot detect alone. In ENIGMA1 [START_REF] Vounou | Sparse reduced-rank regression detects genetic associations with voxel-wise longitudinal phenotypes in Alzheimer's disease[END_REF], only 5 of the 21 cohort studies were able to detect the effect of the SNPs on the brain in their cohort alone, at the nominal significance level of p = 0.05. By the time of ENIGMA2, 20 of the 38 Caucasian European (CEU) cohort studies could detect the effects of the top SNP. Even so, the aggregate support of the discovery and replication samples was crucial to making sure the effects were credible and unlikely to be false positives.

Relevance to Disease Risk

The quest to identify genetic variants associated with brain measures is partly motivated by finding variants that affect our individual risk for disease. Any modulators of health outcomes in populations may have a vast impact on society, even if they are not the main factors explaining risk for any one individual. As well as affecting risk for disease, genetic differences may also affect symptom severity, treatment response, and prognosis.

As such, several clinical trials for Alzheimer's disease drugs already stratify their cohorts by APOE genotypea major risk gene for AD that may have a bearing on treatment response as well as disease risk (see Riedel et al., submitted for publication, for a review of APOE effects, which are remarkably complex). At the time of writing, several manuscripts are under review addressing the overlap between ENIGMA's genomic findings and accepted or emerging markers of disease risk (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press; Adams and the CHARGE and ENIG-MA2 Consortia, submitted for publication; Franke et al., in press). Here we simply review their overall design. Some initial reports have appeared in abstract form, relating brain-related SNPs to risk for Parkinson's disease (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press), obsessive compulsive disorder (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press), schizophrenia [START_REF] Stein | The Schizophrenia Working Group of the Psychiatric Genomics Consortium[END_REF]Franke et al., in press), and multiple sclerosis (Rinker et al., submitted for publication). An initial negative report has appeared for epilepsy [START_REF] Whelan | Polygenic contributions of ENIGMA2 hippocampal SNPs in 8,835 epilepsy patients and 29,037 controls[END_REF]. Even so, given the low fraction of heritability explained by the SNPs discovered, the studies so far are widely accepted as underpowered.

One method to assess an individual's relative risk for disease, based on genome-wide genotyping data, involves computing a polygenic risk score (PRS) for each individual. In Alzheimer's disease, for example, carrying one copy of the APOE4 genotype boosts lifetime risk for AD by a factor of 3, and carrying two copies may boost risk by 15 times. These odds ratios are not constant across human populations and even vary by ethnicity, or circumstances, so some caution is needed when extrapolating them to new data; but as AD GWAS data accumulate, over 20 common genetic variants have been found to affect AD risk -3 of them, in the genes CLU, PICALM, and CR1, appear to be associated with a difference in disease risk of over 10% per allele. If an individual's genotype is known for these loci, it is possible to create a polygenic risk score in a number of different ways, depending on whether the goal is to predict diagnosis, outcome, or brain measures. The simplest approach is to count risk loci, although that clearly ignores the vastly different odds ratios from each locus. It is more common to weight the loci based on their odds ratio for disease, or by their regression coefficients. APOE4, for example, is just a single genotype that might contribute to calculation of a polygenic risk score together with other risk loci. As shown by the PGC analyses, the predictive accuracy of PRS scores increases as the number of variants included increases. Calculation of these scores does not need to be restricted to genome-wide significant loci.

Recent efforts to predict disease status based on polygenic risk scores have had varied success, but the reasons are quite well understood. First, for the most prevalent neurological or psychiatric diseases, we do not yet have a set of common variants that account for more than a small fraction of disease risk (except for APOE4, where a single copy may triple a person's risk for AD, other factors being equal). In AD, there are rare mutations in genes related to AD pathologysuch as presenilin and APPthat invariably produce earlyonset AD. Carriers of these genetic variants are the targets of major neuroimaging initiatives [START_REF] Benzinger | Regional variability of imaging biomarkers in autosomal dominant Alzheimer's disease[END_REF]. A very important aspect of thisrelevant to the field of personalized medicineis that the person's genotype in conjunction with amyloid imaging can accurately predict the age of onset for the disease and the symptoms [START_REF] Benzinger | Regional variability of imaging biomarkers in autosomal dominant Alzheimer's disease[END_REF].

Another cause for optimism is the efforts of the Psychiatric Genomics Consortium (PGC). When the PGC Schizophrenia Working Group increased their sample size to 36,989 cases and 113,075 controls, they discovered over 100 loci associated with risk for schizophrenia, suggesting that other GWAS may experience similar boosts, depending on where they are in the arc of discovery. The rate of success of these efforts, and yield on the efforts invested, also depends on the polygenicity of each disease, and the distribution of risk loci across the genome. Holland et al. (submitted for publication) used recent data from the ENIGMA study and the PGC to estimate what sample sizes are needed for a GWAS to discover enough SNPs to account for, say 50% or 80% of the chip-based heritability, i.e., the amount of the population variance predictable from genotyped SNPs. They argued that some traits are more polygenic than others, and that, relative to some brain measures, GWAS studies of schizophrenia and major depressive disorder may require much larger sample sizes to discover enough SNPs to account for high levels of the chip-based heritability. If that is true, then imaging genetics may be well on the way to a significantly higher rate of discovery, and a more complete understanding of common variants driving individual differences in brain measures.

How much individual variance is explainable by GWAS and common genetic variants?

In recent years, a number of powerful methods emerged to estimate what fraction of the population variance in a trait could be predicted, in principle, from all the SNPs on the genotyping chip, even if the exact genes and SNPs were not yet known. 4 Predictions can be made from the full set of association statistics: models (linear or Gaussian) are first fitted to the observed effect sizes of all the SNPs, even if most SNP effects fail to reach the accepted standard for genome-wide significance. In much the same way as FDR (the false discovery rate method) is used in imaging to confirm evidence for a distributed signalspread out across the brain, the overall effect of genome-wide SNPs on a trait can be estimated without having to pinpoint which exact regionsof the image or the genomecontribute unequivocally to the effect. [START_REF] Hibar | Boosting power to detect Parkinson's disease genetic risk variants by conditioning on genetic determinants of brain structure[END_REF] used genome-wide summary statistics to estimate heritability [START_REF] So | Uncovering the total heritability explained by all true susceptibility variants in a genome-wide association study[END_REF] and found that common variants across the genome explained around 19% of the variance in hippocampal volume, which is comparable to SNP-based estimates of heritability for many psychiatric disorders and other biological traits. More recently, B.K. Bulik-Sullivan et al., 2015 introduced a similar method based on linkage disequilibrium5 (LD) scores that is also able to recover heritability from summary statistics. The LD score method assigns an LD score to each SNPthe sum of its squared correlations (r 2 ) with all other SNPs in a 1 centimorgan window. One then regresses the chi-squared statistics from a GWAS against the LD score for each SNP. The slope of the resulting regression line depends on the sample size and the SNPheritabilitythe proportion of trait variance accounted for by all the genotyped SNPs (see B. Bulik-Sullivan et al. (2015), B.K. Bulik-Sullivan et al., 2015, for derivations).

A related method, GCTA (genome-wide complex trait analysis; [START_REF] Yang | GCTA: a tool for genome-wide complex trait analysis[END_REF] suggested that a still higher proportion of population variance in brain volumetric measures may be accounted for based on all genotyped SNPs, even in cases where we do not know which SNPs help as predictors of the trait. Members of the ENIGMA Consortium have applied this method to estimate SNP-based heritability for structural [START_REF] Toro | Genomic architecture of human neuroanatomical diversity[END_REF] and functional [START_REF] Dickie | Global genetic variations predict brain response to faces[END_REF] brain measures. A working group in ENIGMA, ENIGMA-GCTA, is now comparing the GCTA and LD score methods to better estimate how much brain variation is explainable by genotyped SNPs, at least for the brain measures that are most readily computed from MRI. SNP-based heritability estimates of cortical surface area for different cortical subdivisions calculated by GCTA were recently published [START_REF] Chen | Pediatric Imaging, Neurocognition and Genetics Study; Alzheimer's Disease Neuroimaging Initiative[END_REF]. These cortical subdivisions were defined by a genetically based cortical parcellation scheme [START_REF] Chen | Hierarchical genetic organization of human cortical surface area[END_REF].

The reason ENIGMA and other GWAS researchers are interested in measuring heritabilityand ideally the fraction of heritability explained by common genetic variantsis that it should be possible to prioritize brain measures for deeper genetic analysis based on their heritability, reliability, polygenicity, and relevance to disease. Such rankings or "Bayesian priors" would help in prioritizing research, making studies more efficient and better powered [START_REF] Schork | All SNPs are not created equal: genome-wide association studies reveal a consistent pattern of enrichment among functionally annotated SNPs[END_REF]Becker et al., submitted for publication; Holland et al., submitted for publication; Wang et al., submitted for publication). Even so, there is no evidence that phenotypes with higher heritability show stronger associations with SNPs. One such example is white matter hyperintensitiesa brain measure with high heritability, for which specific genomic risk factors have been hard to find. The main benefit of focusing on highly heritable phenotypes comes from the fact that measurement error is typically lower, and prioritizing brain measures is important as there are so many ways to quantify brain structure and function.

A recurring caveat in this work is that the SNP effects are not expected to be constant in all cohorts. They may depend on a person's age, environment, or other circumstances. We now know from ENIGMA2 that the top 8 loci associated with the volumes of subcortical structures were detectable consistently worldwide, even though each one accounts for b 1% of the variance. A later screen for age × SNP effects suggested that some genes have a greater effect on brain measures later in life (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press), perhaps because they interact adversely with other biological processes or environmental stressors. In other words, although ENIGMA primarily uses metaanalysis to assess evidence, we do not assume that the effect size is always the same. Heterogeneity of effects is also assesseda SNP effect important late in life may not be replicated in younger samples. Conversely, since most psychiatric disorders occur at a young age, one may expect to find associations that link genetic vulnerability, brain structure and disease at a younger age, with effects that may diminish later. Moreover, for certain disorders such as addiction, the psychological, neurobiological and genetic factors most relevant at one age (e.g., impulsivity or sensation-seeking in adolescents experimenting with drugs) may be quite different from the factors when dependent (e.g., compulsivity or habit-based behavior) or when recovering (e.g., stress regulation or cognitive control). Even so, ENIGMA's genomic screens so far are only well-powered to detect SNP effects that are consistentthere may also be SNP effects, so far undetected, that depend on the demographics of the cohort assessed, or disease status, or other circumstantial factors. This is a reminder that predictive models work best in cohorts similar to those where discoveries were made. Because of this concern, which to some extent affects all brain imaging studiesand all human studies -ENIGMA has diversified to over 33 countries. Recently, ENIGMA partnered with other consortia such as the Japanese consortium, COCORO (Okada et al., in press); encouragingly, effects of psychiatric illness on brain structural measures were replicated in Western and Eastern populations, not just in the structures affected the most, but in their rank order, showing congruence between independent studies [START_REF] Van Erp | Subcortical brain volume abnormalities in 2028 individuals with schizophrenia and 2540 healthy controls via the ENIGMA consortium[END_REF]Okada et al., in press).

ENIGMA's Disease Studies

After the initial success of the genetic analyses [START_REF] Stein | The Schizophrenia Working Group of the Psychiatric Genomics Consortium[END_REF] Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press), ENIGMA investigators had analyzed brain MRI data from well over 30,000 individualsaround a third of the data came from patients with a range of psychiatric conditions. In the primary GWAS studies, analyses were run with and without patients, and excluding patients did not affect the main findings; of course the possibility remains that some SNP effects may be easier to detect in some patient cohorts, but ENIGMA's overall results were not driven by the presence of patients.

In 2012, ENIGMA formed working groups on schizophrenia [START_REF] Van Erp | Subcortical brain volume abnormalities in 2028 individuals with schizophrenia and 2540 healthy controls via the ENIGMA consortium[END_REF], bipolar disorder (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press), major depression [START_REF] Schmaal | Subcortical brain alterations in major depressive disorder: findings from the ENIGMA major depressive disorder working group[END_REF], and ADHD [START_REF] Hoogman | Subcortical volumes across the life span in ADHD: an ENIGMA collaboration[END_REF]; groups meta-analyzing data on 8 additional disorders have been formed since, with current sample sizes detailed in Table 1; a map of participating sites is shown in Fig. 2. In the summer of 2015, additional working groups were formed on anorexia nervosa, recovery after stroke, and Parkinson's diseasethe current "roadmap" showing relationships between ENIGMA's working groups is shown in Fig. 3 (also see http://enigma.ini.usc.edu for the latest status). The diseases surveyed include many where controversy exists on the nature and scope of disease effects on the brain. Given this controversy, the main benefit of meta-analysis is to discover which effects are strongest or most reliably found, and which depend on known or unknown factors of the cohorts assessed.

The initial goal of ENIGMA's Disease working groups has been to meta-analyze effects of these disorders on the subcortical brain measures studied in the GWAS study. As scans had already been analyzed with a harmonized protocol, and subtle genomic effects had been discovered, there was some interest in ranking brain measures in terms of disease effects (i.e., differences between patients and controls).

A secondary goal was to find factors that might moderate how these diseases impact the brain, such as a person's age, the duration or severity of illness, comorbidities, or treatment-related effects, such as which medications the patients had been treated with, and for how long. Clearly, treatment effects on the disease or the brain depend on many factors. ENIGMA's multiple cohorts, in some cases, offered the opportunity to gauge their generality or consistency. At the same time, many groups joined ENIGMA and provided only brain measures as their initial case-control analyses did not require genome-wide genotyping data on their cohorts. As such, truly vast samples began to be analyzed (N = 8,927, in the published ENIGMA-Depression study; N = 10,194 in the ENIGMA-Lifespan study; see Table 1).

At the time of writing, ENIGMA's first studies of schizophrenia and major depression have been published; results are compared in Fig. 4. Some caveats are needed in showing these data side by side: the schizophrenia and major depression patients were not ascertained at the same sites, so site or geographic effects may be present.

Among the subcortical structures so far assessed, the hippocampus shows the greatest differences in each disorder in terms of statistical effect sizesbut in major depression, it is the only structure showing differences, of those assessed so far [START_REF] Schmaal | Subcortical brain alterations in major depressive disorder: findings from the ENIGMA major depressive disorder working group[END_REF]. Many other structures show volume deficits or even hypertrophy in schizophrenia; basal ganglia enlargement has been widely noted in prior studies of patients taking second-generation antipsychotics. In people with schizophrenia, abnormal ventricular enlargement has long been reported (as far back as [START_REF] Johnstone | Cerebral ventricular size and cognitive impairment in chronic schizophrenia[END_REF], but the natural variations in ventricular size make the effect size smaller for this structure, even though the absolute volume difference, on average, is greater than for other structures assessed. In major depression, the hippocampal volume difference was greater in patients who experienced more depressive episodes, and in those diagnosed before the age of 21 years, which were at least partly independent effects. This is in line with many prior reports of greater brain differences in those with an earlier onset of the disease. Studies of cortical measures are now underway across all ENIGMA disease working groups; many cortical regions are commonly implicated in psychiatric illness, so these analyses may offer a more complete picture relating brain structural differences to clinical measures, medications, and outcomes. At the same time, diffusion imaging studies are also underway; initial reports reveal consistent deficits in fractional anisotropya measure of white matter microstructurefor major white matter tracts in schizophrenia [START_REF] Bora | Neuroanatomical abnormalities in schizophrenia: a multimodal voxelwise meta-analysis and meta-regression analysis[END_REF][START_REF] Holleran | Altered interhemispheric and temporal lobe white matter microstructural organization in severe chronic schizophrenia[END_REF][START_REF] Ellison-Wright | Distribution of tract deficits in schizophrenia[END_REF][START_REF] Kelly | The ENIGMA-Schizophrenia DTI working group[END_REF]; an interesting question is whether antipsychotic medications affect white matter (Ahmed et al., 2015) and brain connectivity [START_REF] O'donoghue | Applying neuroimaging to detect neuroanatomical dysconnectivity in psychosis[END_REF] in a way that fits with their known effects on structural anatomy.

Extensions and Refinements

Because of the worldwide scope of the ENIGMA studies, only the brain measures that were most readily measured have so far been examined. Clearly, there are measures that may be more relevant to each disease or closer to the action of disease-causing genes, but if they are difficult to harmonize and measure in a standard way, the available sample sizes will lag behind those available for the simpler measures. Because of decades of work on shape analysis of anatomy, several of the ENIGMA disease groups have begun to analyze and meta-analyze subcortical shape (Gutman et al., 2015a,b,c), to map the profile of volumetric effects with more spatial precision. These efforts will also determine whether shape metrics offer additional predictive value over and above standard metrics, and in which situations.

The ENIGMA-Laterality group is studying global trends in the profile of left-right differences in brain structure, and whether they relate to handedness, sex, and disease status, in over 15,000 people (Guadalupe et al., 2015, submitted for publication). Reduced or abnormal brain asymmetry has been reported in many brain disorders (Okada et al., in press), but the scope and generality of these differences is not yet understood. Also, many important aspects of human brain function show lateralization in terms of the underlying processing networks, but the biology of this specialization is poorly understood, as are factors that influence it. Whether brain asymmetry measures add value as diagnostic predictors, will be testable across ENIGMA.

ENIGMA-EEG is studying the influence of genetic variants on brain functional activity measured with scalp recorded electrical signals, in a combined dataset from 10,155 individuals, ranging from 5 to 74 years of age. EEG metrics of brain function mature rapidly with age, and relate to aspects of cognition such as the brain's processing efficiency; they also show abnormalities across many neurodevelopmental and psychiatric disorders. Combining data from several large twin and family datasets, the ENIGMA-EEG working group is performing a genomewide association analysis of brain oscillatory powera highly heritable traitbefore proceeding to in-depth analyses of lateralized activity, brain connectivity, and network properties.

Brain-Wide Genome-Wide Association Studies

Voxel-based mapping methods are complementary to approaches that measure the volumes of specific regions of the brain, and they allow comprehensive and unbiased searches for effects of disease or genetic variations across the brain. "Brain-wide" genome-wide searches, Table 1 ENIGMA working groups, showing the number of independent participating samples, and the total sample size analyzed to date. A range of recruitment methods are represented. Some ENIGMA working groups, such as ENIGMA-Lifespan, ask questions that can be answered in healthy cohortsoften participants are controls from psychiatric studies, or population based samples, in which people with a current psychiatric diagnosis may be excluded altogether. Members of ENIGMA disease working groups have contributed their controls to several ongoing studies, leading to normative samples of unprecedented size (over 10,000 in the Lifespan and 15,000 in the Lateralization groups). Some working groups study clinic-based samples of cases and controls, and others study samples enriched for certain risk factors: over half of the people enrolled in ADNI, for example, have mild cognitive impairment, which puts them at heightened risk for developing Alzheimer's disease. In ENIGMA-Lateralization, one participating cohort (BIL&GIN) enrolls left-handers at a higher frequency than found in the general population, to boost power to understand handedness effects. Study designs, enrolment and sampling approaches vary widely across cohorts taking part in ENIGMA, so several ENIGMA studies assess how much difference it makes to restrict or broaden analyses in certain ways, such as pooling or separating certain categories of patients. Genetic analyses, for example, are typically run twice, first including patients and then excluding them. Disease group analyses may assess brain differences in different patient subgroupschronically ill versus firstepisode patients, at-risk siblings versus the general population, or people with different symptom profiles, or with distinct etiologies (e.g., negative symptoms, whose origin may differ in schizophrenia, addiction, or PTSD). Abbreviations: SWEDD = scans without evidence of dopaminergic deficit. or "voxelwise GWAS" [START_REF] Shen | Whole genome association study of brain-wide imaging phenotypes for identifying quantitative trait loci in MCI and AD: A study of the ADNI cohort[END_REF]Stein et al., 2010a,b) can involve over a trillion statistical tests. However, once we account for the covariance within the image and genomic data, the number of independent tests being conducted drops to less than 15,000 x 1,000,000. Given the extremely low p-values of some genetic associations in ENIGMA (p ~10 -23 in Hibar and the CHARGE and ENIGMA2 Fig. 3. ENIGMA Roadmap. The current organization of ENIGMA's Working Groups is shown here. Several groups relate brain measures to variation in the genome, and specialized groups are dedicated to helping members run analyses of genome-wide SNP data, copy number variants, and epigenetic markers on the genome. In parallel, there are psychiatric and neurology working groups dedicated to the study of worldwide data from a range of diseases. As shown here in detail for the schizophrenia working group, there are secondary projects, to relate brain variation to specific symptoms or clinical measures. In parallel, support groups coordinate large scale efforts to harmonize DTI (diffusion tensor imaging) and related brain data [START_REF] Jahanshad | Combining meta-and mega-analytic approaches for multi-site diffusion imaging based genetic studies: From the ENIGMA-DTI working group[END_REF]. Partnerships between the DTI and Genomics groups are leading to genome-wide screens of DTI measures in over 13,000 people; cross-disorder partnerships study brain features that may relate to diagnostic boundaries, or common co-morbidities, allowing factors driving brain variations to be disentangled.

ENIGMA working groups

Consortia, submitted for publication; Hibar et al., 2015a,b, in press), several effects can still survive a "double" Bonferroni correction for multiple testing across both the image and the genome [START_REF] Medland | Whole-genome analyses of whole-brain data: working within an expanded search space[END_REF].

As a result, several recent approaches have been developed to perform brain-wide genome-wide association studies to identify "spatial" features associated with genetic variants, such as specific WM pathways and their components, patterns of cortical thickness, or even activation patterns, rather than "global" measures such as brain or subcortical structure volumes. These approaches may be broadly divided into (1) "brute force" methods, that use mass-univariate testing to test every SNP for associations at each voxel in the image, and (2) data reduction methods, that attempt to reduce the search space by reducing the number of features in the image, or the genome, or both [START_REF] Vounou | Discovering genetic associations with high-dimensional neuroimaging phenotypes: a sparse reduced-rank regression approach[END_REF][START_REF] Vounou | Sparse reduced-rank regression detects genetic associations with voxel-wise longitudinal phenotypes in Alzheimer's disease[END_REF][START_REF] Ge | Increasing power for voxel-wise genome-wide association studies: the random field theory, least square kernel machines and fast permutation procedures[END_REF]. Data reduction methods may include classical methods, such as canonical covariates analysis, or independent components analysis [START_REF] Gupta | Genetic markers of white matter integrity in schizophrenia revealed by parallel ICA[END_REF][START_REF] Calhoun | Comparison of PCA approaches for very large group ICA[END_REF], or modern variants such as sparse coding, compressive sensing, or "deep learning" for feature discovery (see [START_REF] Thompson | Genetics of the connectome, invited review paper for the special issue on the connectome[END_REF] for a review of multivariate imaging genomics methods). Among the "brute force" methods, Jahanshad et al. (2015a,b) detail a practical method whereby several sites run a voxel-based morphometric analysis independently, using a GWAS or other covariate-based analysis at each voxel, and later communicate their findings to a central site for meta-analysis (see Fig. 5). This approach was able to map out in the brain and metaanalyze the effects of the top SNP from the ENIGMA2 study, which screened the genome for variants associated with the size of subcortical structures (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press). To avoid re-computing everything when a new site joins, this "meta-morphometry" approach allows cohorts to align their data to their own brain templates, which are later aligned to an overall mean template for meta-analysis. Such a distributed effort offers many advantages for imaging genomics, due to the vast number of predictors: as new cohorts join, each site's computational hardware can be leveraged by all the others. Such an approach allows cooperative computation on data without requiring all the data to be shared or ever transferred. This is an interesting area of cooperative machine learning that can also increase "buy-in"opening up participation to countries with stricter data transfer laws.

As part of ENIGMA3, a genome-wide screen of the cortex, one subproject will adopt "genetic clustering" methods to identify coherent patterns of gene effects in the brain [START_REF] Chen | Genetic topography of brain morphology[END_REF][START_REF] Chen | Pediatric Imaging, Neurocognition and Genetics Study; Alzheimer's Disease Neuroimaging Initiative[END_REF]. Based on the notion of genetic correlation, brain regions or sets of voxels can be grouped into clusters with similar genetic determination. The standard decomposition of the brain into regions may be adapted to include genetic clusters, or new regions where genome-wide association may be more efficient [START_REF] Chiang | Gene network effects on brain microstructure and intellectual performance identified in 472 twins[END_REF]. This approach has already been applied to create genetic partitions of the cortex; initial work in ENIGMA will overlay pre-made partitions on the cortical data from each site. Genetic correlations can now be computed rapidly from GWAS summary statistics (B. Bulik-Sullivan et al., 2015;[START_REF] Bulik-Sullivan | LD Score regression distinguishes confounding from polygenicity in genome-wide association studies[END_REF] making it feasible to compute and perform clustering on matrices of "genetic connectivity" whose entries are genetic correlations. The ENIGMA-GCTA Working Group is currently studying these methods, in multisite data.

Many disorders affect the brain's white matter and connectivity. Using diffusion tensor imaging (DTI), ENIGMA's disease working groups have begun to compile evidence across cohorts for differences in a range of DTI measures, which reflect white matter integrity and microstructure [START_REF] Kelly | The ENIGMA-Schizophrenia DTI working group[END_REF]. Several years of work went into harmonizing ENIGMA's DTI analysis protocols, to study which metrics are consistently heritable and reproducible across multiple twin and family cohorts worldwide (Jahanshad et al., 2013a,b;[START_REF] Jahanshad | Combining meta-and mega-analytic approaches for multi-site diffusion imaging based genetic studies: From the ENIGMA-DTI working group[END_REF][START_REF] Kochunov | Heritability of fractional anisotropy in human white matter: a comparison of human connectome project and ENIGMA-DTI data[END_REF]. These DTI protocols have been carried forward into ongoing GWAS and disease studies, and initial genome-wide screens of the structural connectome (Jahanshad et al., 2013a,b;[START_REF] De Reus | Towards an ENIGMA connectome atlas: comparing connection prevalence across sites[END_REF]. On the genetic side, ENIGMA working groups have also formed to assess other kinds of genetic variation, including copy number variants (CNVs), where abnormalities have been reported in autism, schizophrenia, and learning disabilities. The ENIGMA CNV helpdesk is now supervising supervising an initial analysis of CNV data in 13,057 people from 24 cohorts worldwide, after developing harmonized protocols for CNV "calling" and quality control. Participating cohorts include groups from Japan, Mexican-Americans, and people of Western European, Nordic or Swedish ancestry. Initial efforts are evaluating known "psychiatric" CNVs as predictors of MRI and DTI phenotypes computed in other ENIGMA projects. Challenges include the pooling of data from genotyping chips with different coverage; some have sparse coverage of SNPs in regions with segmental duplications or complex CNVs.

In a complementary initiative, the ENIGMA-Epigenetics working group is studying epigenetic processes such as methylation, which is an index of biological aging and lifecourse 'stress' that may explain an important proportion of the gene-environment contribution to expression of many common diseases such as stroke and dementia. The group is now performing epigenome-wide association studies (EWAS), across Here we show the effect sizes (Cohen's d), for the mean volume difference between patients and matched controls, for a range of brain structures measured from MRI. After meta-analysis of all cohorts, in schizophrenia, a range of subcortical structures showed volumetric differences, including hypertrophy, which may be due in part to antipsychotic treatment. In major depression, the hippocampus is smaller in the depressed groups. Such data, for these and other brain measures, is now being compiled and analyzed across 12 disorders in ENIGMA (see Table 1 for a summary), and may be useful for classification, so long as relevant confounds, site effects, and co-morbidities are appropriately modeled and understood.

14 cohorts from Asia, Australia, North America, and Western Europe, to test associations between DNA methylation and brain measures, initially focusing on total brain volume, subcortical volumes and cortical thickness and surface areas. The working group is analyzing methylation data from 9,000 people, of whom 5,000 have both methylation data and MRI. In addition, the ENIGMA-Epigenetics group is prioritizing the analysis of DNA methylation sites based on their effects on gene expression or association with stress-and anxiety-related phenotypes. There is some evidence of early life changes in stress response genes through methylation [START_REF] Backhouse | Early life risk factors for stroke and cognitive impairment[END_REF], just as early life events influence later life disease expressionnotably stroke, white matter hyperintensities, and cognitive impairment. Of great interest are epigenetic changes throughout the life span, and with aging, which may predict mortality from all causes, as well as physical and cognitive performance. Associations are being tested first for brain phenotypes that are known to change the most across the lifespan, based on incoming information from ENIGMA's Lifespan study in over 10,000 individuals [START_REF] Dima | Subcortical brain volumes across the lifespan based on 10,722 people aged 2 to 92[END_REF].

Relevance to Individual Evaluation, and Longitudinal Assessment

ENIGMA was not designed to make predictions about individuals based on their scans and genomic data. As in most epidemiological studies, the power lies in aggregating so much individual data that subtle effects on the brain can be detected, including findings that each cohort's data were insufficient to detect. In other words, its primary goal has been to relate brain measures to disease and treatment effects, and to variants in the genome. With the aggregated data, it has been possible to determine how reproducible these patterns are worldwide. Also, for the study of treatment effects, ENIGMA does not have the ideal design. Ideally, one would prefer to have pre-post treatment longitudinal designs instead of the cross-sectional comparisons in ENIGMA, where medication status is often confounded by age, disease duration, comorbidity and disease severity.

Even if a large data sample is needed to discover a factor that influences the brain, it does not mean that it is irrelevant to individuals; APOE is one such example, discovered in 1993 by linkage analysis in pedigrees. More recently, a rare variant in the TREM2 gene [START_REF] Jonsson | Variant of TREM2 associated with the risk of Alzheimer's disease[END_REF][START_REF] Rajagopalan | TREM2 risk variant and loss of brain tissue[END_REF] was found to affect Alzheimer's disease risk and accelerate brain tissue loss as we ageperhaps doubling loss rates in old age and increasing AD risk by a factor of 2-4. This gene variant is undoubtedly important for those who carry it: it is found in a little under 1% of controls and a little over 1% of AD patients.

How Does it Help to Predict Risk for Decline?

In current clinical practice, it is not recommended to notify a research participant of their APOE status, and most ethics boards clearly define the circumstances in which incidental findings or health-relevant information is communicated back to a research participant. In the case of APOE, participants are not typically informed of their genetic status, as there are no effective treatments for late-onset Alzheimer's disease. Still, discovering predictors of more rapid decline is useful for the pharmaceutical industry for understanding the behavior of participants in clinical trials, and can greatly improve drug trial design, reducing costs. Enrichment approaches use some characteristic of a patient to select them for a clinical trialthis may be prior response to a certain drug, or it also may be a prediction that they are more likely to decline (FDA, 2013). In the AD field, some clinical trials now select patients based on having a PiB-positive PET scan [START_REF] Ikonomovic | Post-mortem correlates of in vivo PiB-PET amyloid imaging in a typical case of Alzheimer's disease[END_REF] as evidence of incipient AD pathologyand the APOE4 risk genotype, as carriers are more likely to develop AD. This selective enrolment allows faster, less costly, and more well powered clinical trials, with demonstrable reductions in the number of patients needed to show treatment effects (Hua et al., submitted for publication).

ENIGMA's disease working groups are likely to broaden the set of known factors that help predict recovery or decline. In ENIGMA-HIV, for example, a key goal is to understand predictors of resiliencefactors that might forecast healthy brain development after the use of antiretroviral treatment [START_REF] Fouche | A meta-analysis by the ENIGMA-HIV working group: CD4 counts predict subcortical volume loss in HIVpositive individuals[END_REF]. Crucially, it is important (2015a,b,c) proposed a method whereby each site aligns data to their own brain template (mean deformation template, or MDT). Statistics from each site are meta-analyzed at each voxel, after a second round of registration to an overall mean template (computed here from 4 cohorts representing different parts of the lifespan). Analyses proceed in parallel, using computational resources across all sites; analyses are updated when a new site joins. This approach applies equally to voxel-based maps of function, and the ENIGMA-Shape working group has modified it to work with surface-based coordinates (Gutman et al., 2015a,b,c). If structural labels are used to drive the multi-channel registration (top panels), in conjunction with an approach such as tensor-based morphometry, the resulting local volumetric measures should closely mirror volumetric findings for specific regions of interest. As such, some results of brain-wide genome-wide searches can be checked by consulting genome-wide association results for specific regions of interest (Hibar et al., 2015a,b;Adams and the CHARGE and ENIGMA2 Consortia, submitted for publication).

to know if a predictor of decline is specific to one cohort or likely to generalize to others, or if it is applicable in a limited set of situations. Understanding how APOE4 and other major risk genes shift the lifetime trajectory of brain measures will also help determine how much they will help when used for clinical trial stratification. This is a goal of the ENIGMA-Lifespan group [START_REF] Dima | Subcortical brain volumes across the lifespan based on 10,722 people aged 2 to 92[END_REF]. Clearly, any predictors of suicidal behavior would be very important in the management and follow-up of patients with psychiatric disorders [START_REF] Mathews | Neurobiological aspects of suicide and suicide attempts in bipolar disorder[END_REF], and a secondary project on suicidality was started within the ENIGMA-Depression working group (Rentería et al., submitted for publication). Similarly, factors that predict whether ADHD in a child will persist into adulthood, will have clinical utility [START_REF] Hoogman | Subcortical volumes across the life span in ADHD: an ENIGMA collaboration[END_REF]. Ultimately, the stratification or clustering of ENIGMA cohort data into subtypes, based on imaging, clinical or behavioral data, may point to distinctions that help us understand the heterogeneity of these disorders. This heterogeneity, without models to disentangle it, makes individual patient predictions harder to make.

Normative Data Across the Human Lifespan

One effort where ENIGMA may contribute to individual prediction and evaluationalbeit with some caveatsis the ENIGMA-Lifespan project [START_REF] Dima | Subcortical brain volumes across the lifespan based on 10,722 people aged 2 to 92[END_REF]. In this work, ENIGMA cohorts are invited to contribute volumetric measures from normal individuals in their samples, which span the age range from 2 to 92 years of age. Although some cohort studies focus on children or the elderly, many scan people across the lifespan, allowing the computation of age-trajectories for several key brain measures; the results show a remarkable difference in the maturational trajectory of different structures, supporting many earlier neurodevelopmental reports on the sequence of brain development [START_REF] Gogtay | Dynamic mapping of human cortical development during childhood through early adulthood[END_REF][START_REF] Sowell | Mapping changes in the human cortex throughout the span of life[END_REF]. To cope with the nonuniform sampling density of the cohorts, these overall trajectories must be interpreted cautiously; clearly some parts of the lifespan are better sampled than others, and unmodeled effects of scan site, demographics, and even cultural or environmental differences may drive some of the effects. Clearly, disentangling the driving factors is statistically complex, but the potential is there, to derive normative measures and models of our path through life, in cohort studies as diverse as ENIGMA. The life span analyses (and normative curves) are also highly relevant for neurodevelopmental disorders such as OCD, ADHD, autism, etc.for early detection, and secondary prevention in at-risk populations. Eventually, there may even be efforts to train individuals in specific domains, to stimulate the maturation of specific brain areas that appear to be deviant from the norm curves.

Such normative data have possible applications for individual assessment, if used judiciously. In pediatrics, growth charts for height and weight offer metrics of where a child stands relative to others of the same age, as a Z-score for example. Similar metrics for brain structure, among others, may help in studies of neurodevelopment where interventions and treatments are used to promote healthy maturation, or recovery, as in the case of brain trauma, for example. Similarly, better trajectories to chart loss of brain volume with advancing age help in routine diagnosis of the individual with possible cognitive problems, by indicating first if their brain is within normal limits for age, and secondly the precise centile on which it lies [START_REF] Farrell | Development and initial testing of normal reference MR images for the brain at ages 65-70 and 75-80 years[END_REF]Dickie et al., 2013, in press)much more data is needed to populate these graphs, but (much like child growth charts) they have the potential to be highly valuable in routine clinical practice as well as research. Original scan data are being collected to expand these templates (e.g., www. brainsimagebank.ac.uk).

Norming of brain measures also has commercial applications [START_REF] Ochs | Comparison of automated brain volume measures obtained with NeuroQuant® and FreeSurfer[END_REF]. ENIGMA relies heavily on developments in software for imaging and genotype acquisition, quality control, and analysis, that make standardized assessment possible. In some regions of the world, such as Thailand and Cambodia, ENIGMA has contributors who are interested in whether it makes sense to use brain development norms from Western cohorts, or build their own (Jahanshad et al., 2015a,b,c;[START_REF] Fouche | A meta-analysis by the ENIGMA-HIV working group: CD4 counts predict subcortical volume loss in HIVpositive individuals[END_REF]. By comparing developmental trajectories across very diverse multi-cohort data, better answers to these and other practical questions are within reach.

Machine Learning, Big Data, and Individual Prediction

With the advent of very large neuroimaging datasets, we can fit predictive models to the data and test them for their robustness. Our models of how diseases and genes affect the brain are constantly being tested and improved, especially in situations where statistical effects have previously been too small to discover, or have been confounded by factors that cannot be adjusted for. In GWAS for example, there are known genetic differences in allele frequencies across populations, and if these are not accurately modeled based on much larger datasets, and adjusted for using multidimensional scaling, they will confound the analysis and lead to spurious results -many more SNPs will show "effects" on the brain, ultimately turning out to be false positives. Years of "false alarms" [START_REF] Farrell | Evaluating historical candidate genes for schizophrenia[END_REF] led the genomics community to adopt strict standards for reporting effects, including a standard genome-wide significance threshold (described above). In addition, independent replication of effects is required. In imaging, a somewhat more flexible approach has been used, with approaches from FDR to random field theory and permutation all co-existing in the literature; the use of candidate brain regions or prior hypotheses in functional imaging studies is encouraged, but the use of candidate regions in genomics is sometimes hotly debated as leading to many false positive effects [START_REF] Collins | Hypothesis-driven candidate genes for schizophrenia compared to genome-wide association results[END_REF][START_REF] Farrell | Evaluating historical candidate genes for schizophrenia[END_REF]ENIGMA-DTI Working Group, 2014). [START_REF] Munafò | Has analytical flexibility increased in imaging studies of bipolar disorder and major depression?[END_REF] argued that the growing flexibility in analyses used in neuroimaging is increasing the reporting of false positive results, and meta-analyses may offer better estimates of the validity of claims regarding brain differences in major depression and bipolar illness, fields for which they meta-analyzed the neuroimaging literature.

Given the sample sizes attained, ENIGMA offers a framework not only for unrestricted searches, but also to test more focused hypotheses and provide internal replication using, for example, cross-validation methods. So far, the Working Groups have over 30 "secondary proposals": many study clinical measures, disease subtypes, and patterns of behavior such as suicidality or negative symptoms, or other differences that might contribute to the heterogeneity of brain disease and outcomes. One such project, in the ENIGMA-Major Depression group, assesses the effects of childhood trauma on depression-related brain measures, a factor that may be modeled effectively by comparisons with data from the ENIGMA-PTSD group, where childhood trauma is also a major predictive factor. Partnerships between ENIGMA groups may resolve some sources of brain differences that are difficult to disentangle. In HIV+ people who abuse stimulant drugs, for example, white matter inflammation is commonly reported, while patterns of accelerated atrophy are often seen in HIV + people who do not use intravenous drugs, especially in those carrying the APOE4 genotype. These and other predictors can be assessed in partnerships between the ENIGMA-Addictions and ENIGMA-HIV groups, by determining a common core of predictor variables that can be harmonized.

More refined models are also needed: we now know that the profile and extent of brain differences in disease may depend critically on a patient's age, duration of illness and course of treatment, as well as adherence to the treatment, polypharmacy and other unmeasured factors. Differences in ancestral background, as determined based on genotype, are strongly related to systematic differences in brain shape [START_REF] Bakken | A geographic cline of skull and brain morphology among individuals of European Ancestry[END_REF][START_REF] Fan | Pediatric imaging, neurocognition, and genetics study. Modeling the 3D geometry of the cortical surface with genetic ancestry[END_REF]. Any realistic understanding of the brain imaging measures must take all these into account, as well as acknowledge the existence of causal factors perhaps not yet known or even imagined. The quest to identify individual predictors is therefore more likely to succeed in finding factors that affect aggregate risk and outcome in groups of individuals, rather than offer firm predictions regarding an individual.

A more immediately achievable goal, for ENIGMA, is to rank brain measures in terms of how well they do predict individual decline, or diagnosis. Predictors of imminent brain decline are already used to boost the power for clinical trials in Alzheimer's disease, by overenrolling, or separately analyzing patients whose brain measures, or clinical and genomic measures, suggest that they will decline faster. In ENIGMA, the ENIGMA-Plasticity group is evaluating the genetic influences on measures of brain change, in a meta-analytic setting [START_REF] Brouwer | Genetic influences on longitudinal changes in subcortical volumes: results of the ENIGMA Plasticity Working Group[END_REF]. If reproducible drivers of brain decline could be found by screening brain data worldwide, they would help in planning enrichment approaches for drug trials. Several major initiatives have this goal (e.g., ADNI;[START_REF] Jr | Magnetic resonance imaging in ADNI[END_REF]. Currently, the only genetic marker used for enrichment is APOE, but this may change as more information accumulates (see Lupton et al., submitted for publication). The complex pattern of association between brain measures and SNPs across the APOE gene (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press) suggests that future polygenic predictors based on machine learning may better predict clinical decline, and decline in brain measures, than the standard APOE genetic test, which is based on just 2 SNPs.

Machine Learning

Innovations in machine learning make it possible to build robust predictive models from millions of predictors, often using dimension reduction techniques to home in on more efficient sets of variables that explain the most variance in the data; this vast field, including sparse learning and compressive sensing, is especially valuable in imaging genomics, with millions of predictors in both the images and the genome. Several machine learning developments have been applied to connect genomic and imaging measures, using methods such as parallel ICA [START_REF] Gupta | Genetic markers of white matter integrity in schizophrenia revealed by parallel ICA[END_REF][START_REF] Calhoun | Comparison of PCA approaches for very large group ICA[END_REF], elastic net [START_REF] Wan | Hippocampal surface mapping of genetic risk factors in AD via sparse learning models[END_REF], sparse reduced rank regression (sRRR; [START_REF] Vounou | Discovering genetic associations with high-dimensional neuroimaging phenotypes: a sparse reduced-rank regression approach[END_REF], among others. ENIGMA is beginning to test some of these models, specifically in the disease working groups, for case-control differentiation and differential diagnosis. Past efforts to combine imaging and genomic data for outcome prediction suggest that imaging measures may be much more predictive of future clinical decline than genomic measures, but both are complementary (Peters and the Alzheimer's Disease DREAM Challenge, submitted for publication). Predictive models should improve as they draw on more data, and the larger ENIGMA GWAS studies are now discovering more genetic markers that can be used in predictive models for brain measures (Hibar and the CHARGE and ENIGMA2 Consortia, submitted for publication; Hibar et al., 2015a,b, in press; Adams and the CHARGE and ENIG-MA2 Consortia, submitted for publication). However, compelling as these approaches are and not wishing to dampen the enthusiasm for these very promising techniques, the image measurements being predicted generally require a human check and correction if necessary, particularly in datasets with complex imaging features such as occur in older patients with strokemachine learning analysis algorithms still cannot reliably separate the hyperintensity due to a small cortical infarct from that due to a white matter hyperintensity or artifact, reliably. Also, the variants driving the heritability of disease risk are only just beginning to be discovered for many of the major brain diseases studied within and outside of ENIGMA. Unsupervised learning is also relevant for understanding the heterogeneity of diseases, which has made it harder to discover their causes and mechanisms. [START_REF] Brodersen | Dissecting psychiatric spectrum disorders by generative embedding[END_REF] argued that one could use unsupervised learning on imaging, clinical and genetic data to see whether subtypes (or clusters) can be identified within a disease, and whether these data cluster together in agreement (or disagreement) with current diagnostic classifications.

In conclusion, we have reviewed current work by the ENIGMA Consortium. ENIGMA began in 2009, and is now a distributed effort, with over 30 working groups (see Table 1), coordinated from many centers worldwide. As we noted, ENIGMA's main goals have been to detect effects of disease and genetic variants on the brain, to see how consistent these effects are worldwide, and to study what modulates these effects. On the genetic side, it may soon be possible for polygenic scoring to produce predictors that are routinely used in brain imaging studies, explaining some of the observed variance. This may make other effects easier to detect. On the disease side, we are beginning to identify and confirm distinctive patterns of brain differences in each of a range of brain diseases, along with a better understanding of which patterns are specific to given disorders, which patterns tend to generalize, and what factors account for the heterogeneity across cohorts. This will help us understand the situations where predictive models can be used, for diagnostic classification, outcome prediction, and norming of individual data against appropriate reference populations.

We end with a note in praise of small studies. Like any consortium, ENIGMA would be impossible without the cohort studies and all the individuals who contribute; most of the data analyzed in ENIGMA came from cohorts with relatively modest sample sizes. Inevitably, many hypotheses are not addressable on a large scale, and some questions -especially causal questions -involve targeted interventions or phenotypic assessments with a depth or sophistication not likely to be attained at every site. As Aristotle said, "Nobody has the ability to work everything out, but everyone has something useful to say; working together, the whole vast world of science is within our reach." (ἐκ πάντων δὲ συναθροιζομένων γίγνεσθαί τι μέγεθος; Aristotle, Metaphysics α, c. 350 BCE). This is the ENIGMA motto: http:// enigma.ini.usc.edu/about-2/.

Fig. 1 .

 1 Fig. 1. Recent genome-wide association studies (GWAS) of brain disorders and brain structure. Part A shows the Manhattan plot from a 2014 Nature meta-analysis conducted by the Psychiatric Genomics Consortium. The genetic variants are presented on the x-axis, and the height of the dots shows the strength of association between each genetic variant and schizophrenia. A negative log p-value scale is used: higher points denote stronger associations. The group identified 108 schizophrenia-associated genetic loci in a sample of 34,241 cases and 45,604 controls (red line = genome-wide significance level, conventionally set at p = 5x10 -8 ; green SNPs = polymorphisms in linkage disequilibrium with index SNPs (diamonds), which indicate independent genome-wide significant signals). Part B 26 loci significantly associated with risk of Parkinson's Disease (Nalls et al., 2015), in 13,708 cases and 95,282 controls (red SNPs = genome-wide significant signals). Part C 19 loci significantly associated with risk of AD, in a sample of 17,008 cases and 37,154 controls (Lambert et al., Nature Genetics, 2013; genes identified by previous GWAS are shown in black; newly associated genes in red; red diamonds indicate SNPs with the smallest overall p-values in the analysis). Part D shows genome-wide associations for eight subcortical structures, conducted by the ENIGMA consortium in 30,717 individuals from 50 cohorts worldwide(Hibar et al., Nature, 2015). This study identified five novel genetic variants associated with differences in the volumes of the putamen and caudate nucleus and stronger evidence for three previously established influences on hippocampal volume (seeStein et al., Nature Genetics, 2012) and intracranial volume (seeIkram et al., Nature Genetics, 2012). Each Manhattan plot in Part D is color-coded to match its corresponding subcortical structure, shown in the middle row. The gray dotted line represents genome-wide significance at the standard p = 5x10 -8 ; the red dotted line shows a multiple-comparison corrected threshold of p = 7.1 x 10 -9 . [Images are reproduced here with permission from MacMillan Publishers Ltd(Nature Genetics, 2012 & 2013; Nature, 2014 Nature, & 2015) ) and with permission from the corresponding authors.]

Fig. 2 .

 2 Fig. 2. ENIGMA Map. The ENIGMA consortium now consists of over 30 Working Groups made up of 500 scientists from over 200 institutions and 35 countries; several of these Working Groups have several ongoing secondary projects, led by different investigators. Here we show 12 of the working groups, focusing on specific diseases and methodologies, including ADHD, autism, addiction, bipolar disorder, diffusion tensor imaging, epilepsy, HIV, major depressive disorder, OCD, PTSD and schizophrenia. Centers where individuals are scanned and genotyped are denoted with color-coded pins (legend, bottom left).

Fig. 4 .

 4 Fig. 4. ENIGMA's studies of brain differences in disease revealed consistent patterns of subcortical volume differences across multiple cohorts with schizophrenia and major depression (data reproduced, with permission, from van Erp et al., 2015; Schmaal et al., 2015, Molecular Psychiatry).Here we show the effect sizes (Cohen's d), for the mean volume difference between patients and matched controls, for a range of brain structures measured from MRI. After meta-analysis of all cohorts, in schizophrenia, a range of subcortical structures showed volumetric differences, including hypertrophy, which may be due in part to antipsychotic treatment. In major depression, the hippocampus is smaller in the depressed groups. Such data, for these and other brain measures, is now being compiled and analyzed across 12 disorders in ENIGMA (see Table1for a summary), and may be useful for classification, so long as relevant confounds, site effects, and co-morbidities are appropriately modeled and understood.

Fig. 5 .

 5 Fig. 5. Meta-Analyzing Statistical Brain Maps. As in other fields of brain mapping, voxelbased statistical analyses can map statistical associations between predictors and brain signals. To meta-analyze maps of statistical associations across sites, Jahanshad et al. (2015a,b,c) proposed a method whereby each site aligns data to their own brain template (mean deformation template, or MDT). Statistics from each site are meta-analyzed at each voxel, after a second round of registration to an overall mean template (computed here from 4 cohorts representing different parts of the lifespan). Analyses proceed in parallel, using computational resources across all sites; analyses are updated when a new site joins. This approach applies equally to voxel-based maps of function, and the ENIGMA-Shape working group has modified it to work with surface-based coordinates(Gutman et al., 2015a,b,c). If structural labels are used to drive the multi-channel registration (top panels), in conjunction with an approach such as tensor-based morphometry, the resulting local volumetric measures should closely mirror volumetric findings for specific regions of interest. As such, some results of brain-wide genome-wide searches can be checked by consulting genome-wide association results for specific regions of interest(Hibar et al., 2015a,b; Adams and the CHARGE and ENIGMA2 Consortia, submitted for publication).

Please cite this article as: Thompson, P.M., et al., ENIGMA and the individual: Predicting factors that affect the brain in 35 countries worldwide, NeuroImage (2016), http://dx.doi.org/10.1016/j.neuroimage.2015.11.057

The term "endophenotype" was coined by[START_REF] John | Chromosome variability and geographic distribution in insects[END_REF]; in psychiatric genetics, it is used to denote a biomarker that fulfills several criteria[START_REF] Gottesman | The endophenotype concept in psychiatry: etymology and strategic intentions[END_REF][START_REF] Glahn | Arguments for the sake of endophenotypes: examining common misconceptions about the use of endophenotypes in psychiatric genetics[END_REF], including heritability, reproducible measurement, segregation with illness in families and in the general population, and state-independenceit must remain stable when a patient's illness is active or in remission. Others used the term "intermediate phenotype" for the brain measures studied in imaging genetics, as the endophenotype refers to the characteristics that are shared by both patients and their unaffected first-degree family members.

Abbreviations: SYS, Saguenay Youth Study, http://www.saguenay-youth-study.org; EPIGEN, The Epilepsy Genetics (EPIGEN) Consortium[START_REF] Cavalleri | Multicentre search for genetic susceptibility loci in sporadic epilepsy syndrome and seizure types: a case-control study[END_REF]; ADNI, Alzheimer's Disease Neuroimaging Initiative (http://www.adni-info.org); IMAGEN, IMAging GENetics Consortium (http://www.imagen-europe.com).

Obviously the SNPs are "known" in the sense that they are on the genotyping chip. The issue is that we do not know exactly which specific sets of SNPs or genes are truly contributing to a trait.

5 Linkage disequilibrium is the presence of statistical associations between alleles (genomic variants) at different loci in the genome, which arise because nearby regions on the genome tend to be inherited together. Maps of the level of LD between adjacent SNPs on the genome have been compiled for multiple ethnic groups. In imaging, LD leads to peaks of association with brain measures, and these LD maps can be used analytically to estimate SNP-based measures of heritability or genetic correlations from GWAS summary statistics.

P.M. Thompson et al. / NeuroImage xxx (2016) xxx-xxx Please cite this article as: Thompson, P.M., et al., ENIGMA and the individual: Predicting factors that affect the brain in 35 countries worldwide, NeuroImage (2016), http://dx.doi.org/10.1016/j.neuroimage.2015.11.057

(healthy only) 21-85 de Reus et al., 2015

Acknowledgments

This work was supported in part by a Consortium grant (U54 EB 020403) from the NIH Institutes contributing to the Big Data to Knowledge (BD2K) Initiative, including the NIBIB. Funding for individual consortium authors is listed in Hibar et al., Nature, 2015 and in other papers cited here. This paper was collaboratively written on Google Docs by all authors, over a period of several weeks. We thank Josh Faskowitz for making Fig. 3, the ENIGMA "roadmap". P.M. Thompson et al. / NeuroImage xxx (2016) xxx-xxx Please cite this article as: Thompson, P.M., et al., ENIGMA and the individual: Predicting factors that affect the brain in 35 countries worldwide, NeuroImage (2016), http://dx.doi.org/10.1016/j.neuroimage.2015.11.057