Overview

Bipolar disorder (BD) is a brain disorder characterized by shifts in mood, energy and attention/focus [1]. BD affects roughly 50 million people across the world, with a mean age of onset of 20 years and an estimated lifetime prevalence of ∼1% [2–5]. BD is also highly heritable [6], with heritability estimates of 40% or higher [7–11] and evidence of increased risk when family-members exhibit other psychiatric disorders [7, 10, 11].

There is growing consensus that BD is heterogeneous, both at the phenotypic and genetic level [12–23]. For example, diagnostic systems usually consider at least two subtypes of bipolar disorder: bipolar I and bipolar II. The diagnostic criteria for bipolar I require the presence of at least one manic episode, while those for bipolar II require at least one hypomanic and one major depressive episode [1]. Response to medication (such as lithium) is highly heterogeneous across patients, and genetic predictors of drug-response have been difficult to clearly determine and replicate [24–28].

The high degree of heterogeneity for BD at the clinical and phenotypic level may make it more difficult to identify genetic risk-factors for BD. To briefly summarize: while the overall heritability of BD is estimated at ∼40%, the overall single-nucleotide-polymorphism (SNP) heritability is only ∼ 18.6% [29], which is moderate when compared to many other psychiatric and neurological disorders [6, 30–38]. Recent genome-wide association studies (GWASs) have been used to identify several (i.e. ∼ 100) independent loci associated with BDI and BDII, with the overall variance explained by SNPs reaching ∼ 15 − 18% [29]. However, many of the loci that seem promising in one cohort fail to replicate in other cohorts [23, 39, 40]. Studies attempting to uncover gene-environment interactions in BD have also encountered challenges finding replicable signals [41–45].

Rather than focusing on small sets of loci, one can also consider collections of SNPs which individually may not be of genome-wide significance. Along this vein, Polygenic-risk-scores (PRSs), which are usually weighted sums of genetic variants, have been used to summarize the genome-wide risk for BD [46]. These PRSs may provide an estimate of overall risk and/or severity: those individuals with PRSs in the top 90% were 3.62 times more likely to be a case than those with average PRSs. These PRSs also contain information regarding multiple phenotypic traits, including the risk of other psychiatric disorders, psychopathology, educational attainment and more [47–55]. Despite these successes, to the best of our knowledge, no individual PRS has yet been able to explain a large fraction of the variation between the main bipolar subtypes.

The high degree of heterogeneity within BD poses a challenge to understanding its etiology and developing new interventions. Ultimately, a comprehensive depiction of the landscape of BD will involve clear descriptions of the heterogeneity at the phenotypic level, as well as at the genetic level.

To date, the main research efforts aimed at understanding the genetic heterogeneity underlying BD have focused on (i) increasing the power of BD meta-GWAS, (ii) running subphenotypic-specific meta-GWAS, and (iii) performing pathway-specific analyses [56–58]. These research efforts are non-trivial and in some cases require insights we do not yet have. Generally speaking, recruiting, assessing, and genotyping new subjects is expensive; there is often a trade-off between the quantity of subjects that can be recruited and the ‘quality’ or accuracy with which their data is processed. For example, one promising resource for genotyped data is 23andMe, but many of the data-sets available through this resource rely on self-reported diagnoses [59]. Consequently, any synchronization effort involves the integration and harmonization of data collected using different phenotypic instruments or genotyping methods and may inadvertently introduce non-disease-related signal. Furthermore, in many cases, the relevant subphenotypic information was not collected at all, forcing interested researchers to contact prior participants or lose those data points entirely. Finally, even when promising results are obtained, it is not always easy to find an appropriate replication sample [60]. Since we do not yet know which trait or combination of subphenotypic traits (if any) is responsible for BD genetic heterogeneity, it is not always clear how best to proceed.

Contribution

Ultimately, we seek to investigate the genetic heterogeneity of BD by using an approach which does not require the user to provide pathways or subphenotypes. As described below, we introduce a methodology which first uses the genotyped data to identify a genetic subgroup within BD, and then uses that genetic subgroup for downstream analyses (in this case risk prediction). To briefly summarize: we use a covariate-corrected biclustering algorithm to search for statistically significant biclusters comprising subsets of BD cases which exhibit disease-specific patterns of differential-expression across subsets of SNPs. In this study we find one statistically-significant disease-specific structure, which is limited to only a fraction of the case-subjects. These case-subjects collectively exhibit a shared pattern of differential-expression—i.e., a form of genetic homogeneity—which is not shared by the other BD-cases nor by the control-subjects; we refer to this bicluster as a ‘genetic subgroup’. We then demonstrate that this genetic subgroup is useful for risk-prediction.

In more detail, our analysis begins by collecting data within which to search for genetic subgroups of BD. As members of the Psychiatric Genomics Consortium (PGC), we had access to the raw genotypes of ∼ 18K BD cases and ∼ 30K controls. This data was generated by 27 studies and genotyped on a variety of platforms (OMEX, Affymetrix, Illumina). When the PGC analyzed this data [20], they synchronized the data using imputation. We were not certain how imputation might impact the potentially subtle relationships between BD cases, and therefore decided to limit our analysis to the available raw genotyped data [60]. This choice to limit ourselves to raw genotyped data placed constraints on our choices for the training and testing data sets, as the various genotyping platforms types emphasize different SNP sets (see Fig 1).

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Fig 1.

In this figure we illustrate the absolute (right) and relative (left) snp overlap between the studies available to us. The relative-overlap is calculated using the Szymkiewicz–Simpson coefficient (i.e., the overlap-coefficient between sets X and Y is |X ∩ Y|/min(|X|, |Y|)). Guided by the relative-overlap and genotyping platform used, we divided the studies into four arms (shown along the coordinate axes). The first arm contains only the single ‘BDRN’ data-set, which we use as a training/discovery set to search for heterogeneity (see Methods). We reserve the remaining studies (organized into three arms) for replication. Note that the training-set overlaps strongly with arm-2, and less strongly with arm-3 and arm-4. The magnitude of this overlap will constrain how faithfully any patterns of differential-expression found in arm-1 can possibly manifest within the other arms (see Figs 3–5).

https://doi.org/10.1371/journal.pone.0314288.g001

In order to minimize batch-effects and reduce the chances of spurious false-positives, we chose to initially focus our primary analysis on a relatively large curated study from the Bipolar Disorder Research Network (BDRN) comprising raw genotyped data collected across 2524 BD cases and 4106 controls (OMEX platform) [18]. We use this BDRN study as our training-arm, and set aside the remaining independent data for subsequent replication analyses (i.e., our replication-arms). We grouped all the BD cases in our training-arm together and searched within the training-arm for any subsets of subjects which exhibited a distinct genetic signature (i.e., differential expression) across a subset of SNPs. Any such subset of subjects along with the associated subset of differentially-expressed SNPs is referred to as a ‘bicluster’, or a ‘genetic subgroup’.

As described in [61, 62], many commonly used biclustering approaches suffer from two methodological issues. First, a bicluster that is found within the case-population may not be disease-related, as a similar signal may be found within the control-population (e.g., a bicluster representing non-disease-specific heterogeneity). Second, many biclustering algorithms proceed under the assumption that biclusters exist, often identifying ‘false-positive’ structures that are not statistically-significant.

To address these issues we searched for biclusters using the ‘half-loop’ algorithm of [63, 64]. As described in [64], this algorithm ensures that the pattern of differential-expression within the bicluster is not similarly present within the control-population, reducing the likelihood that we highlight structures unrelated to disease status. Second, the half-loop algorithm uses a permutation-test to estimate the p-value of each bicluster found, allowing us to test against the null hypothesis that no bicluster exists. Finally, the half-loop algorithm also allows us to correct for other covariates, such as proxies for genetic-ancestry (see Methods). While our approach is much simpler than some of the more recent machine-learning approaches, our biclusters are directly associated with subject- and SNP-subsets, which can be directly interpreted and assessed for homogeneity and/or used in downstream analyses.

Using the relatively conservative half-loop method mentioned above, we found strong evidence for genetic heterogeneity. We discovered one bicluster which is statistically significant and which replicates in all three other data-sets. This primary bicluster was enriched for (but not completely driven by) BDI over BDII. After removing this bicluster we saw further evidence of residual heterogeneity, but our training data-set was not sufficiently powered to clearly identify a secondary bicluster.

We then assessed the role of our bicluster in risk-prediction. We found that the subset of case-subjects highlighted by the bicluster can be used to improve the performance of a PRS. This advantage was more pronounced when (i) the SNPs included in the PRS were limited to those of high estimated significance, and (ii) the case-population was limited to those diagnosed with BDI. These observations suggest that focusing on genetically identifiable subgroups of BD-subjects might improve overall risk-prediction and enhance replication across the top SNPs.

Finally, we also ran a simple gene-set over-representation analysis, revealing that the genetic subgroup identified above (i.e., the bicluster) is significantly enriched for many pathways associated with neuronal development and maintenance.

In summary, we find strong evidence for the genetic-heterogeneity of BD in the form of a bicluster. Notably, BD subphenotype information was not required to identify this signature, nor were rare-variants (i.e., we relied only on common SNPs with maf greater than 25% within the training-arm). The signature of this bicluster has the potential to refine downstream analyses (e.g., improving genome-wide risk-prediction), and the associated gene-enrichment suggests an association with certain mechanisms of neuronal development.

Data

We make use of data from 27 of the cohorts described in [20]. These cohorts have been curated as described in [20] and its supplementary information, and include de-identified subjects from several countries in Europe, North America and Australia, totaling over 18000 cases and 29000 controls of European descent. Case-subjects were required to meet international consensus criteria (DSM-IV, ICD-9, or ICD-10) for a lifetime diagnosis of BD established using structured diagnostic instruments from assessments by trained interviewers, clinician-administered checklists, or medical record review. Control-subjects in most samples were screened for the absence of lifetime psychiatric disorders, as indicated. For each of the 27 cohorts, we had access to both the raw genotypes and the imputed data generated by Stahl et al. using the 1000 Genomes (1KG) European reference-panel (see [20]).

Due to the details of our heterogeneity analysis (described further below), we make three additional choices. First, for our primary analysis we use only the raw genotyped data within each cohort, but not the imputed data. This is because we want to avoid any concerns of spurious correlations that might arise from imputation [60]. Second, when running our biclustering algorithm we do not explicitly correct for linkage-disequilibrium (LD) between genotyped SNPs at the level of the data-set itself (e.g., by eliminating SNPs in strong LD with other SNPs). Instead, we implicitly correct for LD within our biclustering algorithm by contrasting cases against controls. Third, it is typically quite difficult to reliably detect signal associated with rare variants (i.e., SNPs with a low minor-allele-frequency, a.k.a. ‘maf’), especially when the power of the data-set is low. This difficulty is compounded when searching for heterogeneity, as the effective sample-size (e.g., the number of subjects in a bicluster) is further reduced—often only a fraction of the total subject-population [64]. Thus, in order to avoid spurious results associated with rare-variants, we limit our analysis to common variants (i.e., SNPs with maf greater than 25%). This high maf-threshold has the added benefit that the signals that we do find are described in terms of common variants, which will hopefully be easier to access in future studies.

As shown in Fig 1, the common genotyped SNP-overlap between the cohorts varies significantly. Cohorts that were genotyped using similar platforms tend to have large SNP-overlaps, while those genotyped on different platforms tend to have smaller SNP-overlaps. After clustering the cohorts by platform (and removing any duplicate subjects across cohorts) we defined four ‘arms’, as shown along the axes in Fig 1. Arm-1 consists of the single cohort labeled ‘BDRN’ (2524 cases, 4106 controls, OMEX). Arm-2 includes cohorts ‘may1’ through ‘rom3’ (5781 cases, 8289 controls, OMEX). Arm-3 includes cohorts ‘bonn’ through ‘bmpo’ (3581 cases, 7591 controls, Illumina). Arm-4 includes cohorts ‘dub1’ through ‘gain’ (6825 cases, 9752 controls, Affymetrix).

The first arm (comprising the single cohort ‘BDRN’) is relatively large and collected within the UK, comprising case-subjects of European descent over the age of 17 (see [18, 65, 66] for details). As a result, we expect this cohort to be less susceptible to spurious heterogeneity associated with batch-effects, and we use this cohort as a ‘training’ or ‘discovery’ arm, reserving the other three independent data-sets for validation (i.e., ‘replication’ arms). This training-arm has a large SNP-overlap of ∼ 85% with arm-2, and a smaller SNP-overlap with arms 3 and 4 (i.e., ∼ 50% and ∼ 30%, respectively). Correspondingly, we expect that any signal involving a multi-SNP-pattern found in arm-1 will only have an opportunity to replicate strongly in arm-2, and will not have the opportunity to replicate as strongly in arms 3 and 4 (as we will have fewer SNPs to use for validation).

Correcting for ancestry

We use the genome-wide principal-components calculated by Stahl et al. to assess relatedness and correct for ancestry. Of the first 20 principal-components, denoted {U₁, …, U₂₀}, Stahl et al. determined that the first six principal-components (U₁-U₆) and U₁₉ showed significant correlation with the main phenotype across the studies considered in [20].

In the discovery phase of our analysis we are restricted to the training-arm (arm-1). For this sample we use an F-test applied to a nested logistic model, which selects only the first two principal-components (i.e., U₁ and U₂) as significantly related to case-control status in arm-1. Therefore, to mimic the analyses one might conduct with access only to arm-1, we correct our biclustering algorithm for these two principal-components, under the assumption that they are a proxy for ancestry.

In all but this initial biclustering analysis on arm-1, we remain consistent with [20] and correct for principal-components U₁ through U₆, as well as U₁₉. This includes both the calculation of A U C in the subsequent replication studies (e.g., A(i) and A′(i) in Fig 3) as well as the PRS-analysis described below.

Biclustering

For our initial biclustering of arm-1 we use the half-loop method of [64]. To briefly summarize the method, we first introduce some notation. Assume that the data-set contains M_D case-subjects, and M_X control-subjects, each measured across N allele-combinations (note, each SNP is associated with three allele combinations: heterozygous and homozygous dominant and recessive). We denote the array of case-subjects by D, with D(j_D, k) referring to allele-combination-k in case-subject-j_D. Similarly, we denote the array of control-subjects by X, with X(j_X, k) referring to allele-combination-k in control-subject-j_X. We’ll use the generic subject-index j to refer to both the j_D and the j_X.

In its most basic form, the half-loop algorithm proceeds as follows:

1. Step-0 First we load/initialize the data-arrays D and X.
2. Step-1 For each case j_D and allele-combination k, we measure the fraction of other cases in D which share that allele-combination, denoted by [D ← D](j_D, k). Similarly, we measure the fraction of controls in X which share that allele-combination, denoted by [D ← X](j_D, k). The difference between these two values, denoted by Q(j_D, k) = [D ← D](j_D, k) − [D ← X](j_D, k) is a measure of differential-expression.
3. Step-2 After calculating Q(j_D, k), we form the ‘row-scores’ Q^row(j_D) = ∑_k Q(j_D, k), as well as the ‘column-scores’ and the ‘trace’ . The row- and column-scores measure how strongly each case-subject and allele-combination contribute to the trace, which is itself a measure of the overall differential-expression exhibited between D and X.
4. Step-3 We remove a small fraction of case-subjects and allele-combinations from D with the lowest row- and column-scores.
5. Step-4 We return to Step-1, iterating until there are no more case-subjects within D.

The algorithm proceeds iteratively; at each iteration i we remove a small fraction γ of the remaining case-subjects and allele-combinations. In this analysis we choose γ = 0.5⁸ ∼ 0.004, which is sufficiently small that we expect statistical convergence of the algorithm’s accuracy (see Fig 32 in supplementary section 7.3 in [64]). After each iteration i, a subset comprising M(i) case-subjects and a subset comprising N(i) allele-combinations remain, together forming an M(i) × N(i) sub-array D(i) of the original D. If the case-array D were to contain a bicluster with a sufficiently strong signal, then the rows and columns of that bicluster would be retained until the end, with the other rows and columns eliminated earlier.

This half-loop method has detection-thresholds similar to spectral-clustering and message-passing [67, 68], but has several additional useful features. First, the half-loop method allows us to search for disease-specific heterogeneity by directly correcting for control-subjects. This case-control correction also motivates the null-hypothesis H0 described below; the permutation-test allows us to avoid spurious structures that are unrelated to the disease-label. Second, the half-loop scores in Step-1 allow us to (implicitly) correct for linkage-disequilibrium (LD). More specifically, subsets of SNPs which are in equally strong LD in both the case- and control-populations will be excluded as the algorithm proceeds, unless some of those SNPs are involved in a pattern of differential-expression specific to the remaining case-subjects, in which case they will be retained (as desired). Third, the method also allows us to correct for continuous covariates. This covariate-correction is described in detail in [64], but essentially amounts to a reweighting of the Q(j, k) in Step-1 to reduce the overall level of differential-expression contributed by structures which are not evenly distributed in covariate-space. Finally, the method itself is rather straightforward and does not require the fine-tuning of parameters.

As mentioned in Step-2, the overall level of differential-expression between D(i) and X at each iteration is recorded as the trace . The significance-level of is determined with respect to a null hypothesis (H0) which assumes that the heterogeneity is independent of case- and control-labels. Samples from H0 are drawn by randomly permuting the case- and control-labels in arm-1 (i.e., randomly interchanging rows of D and X) while respecting proximity in covariate-space. By comparing the values of the from the original data to the distribution of associated with the null-hypothesis, we assign an (empirical) training-p-value to the individual for each iteration i. Similarly, we calculate an overall empirical training-p-value (across all iterations), which estimates the probability that the trace from the original data-set could be drawn from the null-hypothesis.

Within this context, the detection of a disease-specific bicluster corresponds to an elevated (i.e., statistically-significant) value of . The case-subjects and allele-combinations comprising the bicluster can then be approximated by the subsets and for those i.

Replication

When discussing any particular replication-arm (e.g., arm-2), we will use primed indices (e.g., cases and controls will be indexed via and ). To assess replication we first consider the set of allele-combinations available within the replication-arm. This subset will limit the alleles we can use from within the original training-arm (i.e., arm-1). For any iteration i, we select the allele-subset from the training-data-set, and then construct the intersection . For the replication-arm arm-2 the allele set will have a size N′(i), which is typically around 85% of N(i) (i.e., 85% of the full size of ). For the other replication-arms (i.e., arms 3 and 4) the overlap will be lower. Using as well as the case-subject subset , we define the M(i) × N′(i) submatrix D′(i) within the training data (note D′(i) is a submatrix of the M(i) × N(i) submatrix D(i) defined above). We then calculate the dominant SNP-wise principal-component of D′(i).

We project each subject within the training-data-set onto v(i), producing a ‘bicluster-score’ (i.e., a single number) for each case-subject in the training-data-set, and for each control-subject in the training-data-set (recall that j_D and j_X index the case- and control-subjects in the training-data-set). Based on the definition of the bicluster, we expect that the typical values of will be larger than the typical values of . We measure this difference by calculating the area under the receiver-operator-characteristic curve (A U C) between the sets and ; we refer to this A U C as A(i). When calculating A(i) we correct for the same ancestry-related covariates as in [20] (see Methods and [60]).

We also project each subject in the replication-arm onto the same vector v(i), producing bicluster-scores for each case-subject in the replication-arm, and for each control-subject in the replication-arm. Once again, we expect that the typical values of will be larger than the typical values of in the replication-arm. We measure this difference by calculating the A U C A′(i), once again correcting for the ancestry-related covariates.

We assess the overall significance of the replication by considering a null-hypothesis where the structure of the replication-arm is independent of disease-status. We can draw a sample from this null-hypothesis (H0’) by randomly permuting the case- and control-labels within the replication-arm (while respecting proximity in covariate-space). In this manner we compare the original replication A U C A′(⋅) (as a function of i) to the distribution of A′(⋅) obtained under H0’.

Later on below (e.g., Fig 3) we calculate the average of A′(⋅) over a range of iterations, and then compare to the distribution of obtained under this label-shuffled null-hypothesis. We define the range of iterations by taking an interval which is significant for both the trace and the A U C A(i) defined using only the training-arm. For example, in Fig 3 we consider the range of iterations i ∈ [175, 350].

Polygenic-Risk-Scores (PRSs)

We calculate PRSs using the general strategy from [20], and further described in page 60 of the S1 Text within that paper. To briefly summarize: We use the genotype-level data from [20], which was imputed using the 1KG reference-panel. We then run a GWAS on this genotype-level data. This GWAS produces summary-statistics defined by contrasting cases and controls from the training-arm, while correcting for ancestry-related covariates. Once we have the summary-statistics defined by the GWAS, we run Plink’s ‘clump’ function to account for LD. We perform this clumping step using the same parameters as in [20] (e.g., info-score threshold of 0.9, R²-threshold of 0.1, genomic window of 500Kb, and minor-allele-frequency threshold of 0.05.) As a technical note: our ultimate goal is to analyze these PRS scores in the context of our heterogeneity analysis, which can be influenced by subtle relationships between SNPs. Consequently, we wanted to use the most accurate available information regarding LD. After the initial data-sets described in [20] were published, the Haplotype Reference Consortium European Reference Panel (HRC EUR panel) became available through the Wellcome Trust Sanger Institute [69]. This HRC EUR panel dramatically increased the amount of information available for approximating LD, and we use this panel when clumping our summary statistics. Finally, after clumping, we use the assigned weights for each SNP to form a PRS. We test the performance of this PRS on our replication-arms.

For any subject j′ within a particular replication-arm, we denote by PRS_wide(j′) the ‘population-wide’ PRS defined by contrasting all the cases in the training-arm with the controls in the training-arm (when generating the summary-statistics). We further denote by the population-wide PRS constructed after restricting the SNP-weight-vector to include only those SNPs with individual GWAS p-values that are more significant than the threshold (when forming the PRS).

We also define a ‘bicluster-informed’ PRS, denoted by PRS_bicl(j′;i), by contrasting only the cases in D(i) with the controls from the training-arm (when generating the summary-statistics). We further denote by the bicluster-informed PRS constructed after restricting the SNP-weight-vector to include only those SNPs with individual GWAS p-values that are more significant than the threshold (when forming the PRS). With this notation PRS_wide(j′) and are equivalent to PRS_bicl(j′;1) and , respectively. However, we will typically consider PRS_bicl for iterations i ∈ [175, 350]; in this range and will differ.

We measure the performance of the population-wide PRS_wide(j′) by calculating the AUC_wide between the case-values and the control-values , once again correcting for the ancestry-related covariates. Similarly, we measure the performance of , PRS_bicl(j′;i) and by calculating the associated AUCs, denoted by , AUC_bicl(i) and , respectively.

Gene-enrichment analysis

We perform a simple over-representation analysis using the go_bp ontology from Seek [70]. We restrict our attention to the 132 neuronally-related pathways (i.e., those referencing neurons, synapses or axons). For any given iteration i we consider the remaining allele-combinations within , retaining those genes which have more than half their originally associated alleles remaining. These retained genes form a gene-set which we then overlap with each pathway to obtain the intersection . From this intersection we obtain the gene-count for pathway l at iteration i.

We assess the significance of the gene-counts by considering the same null-hypothesis H0 used when biclustering. We compare each of the κ(i, l) to the distribution of κ(i, l) obtained under the label-shuffled null-hypothesis. Later on below we calculate the average z-score of the κ(i, l) over a range of iterations and all the neuronally-related pathways, and then compare that to the distribution of obtained under H0.

Interaction with covariates

Given the observations above, it is natural to ask what might be driving the signal associated with this bicluster. We first checked to see if the bicluster was driven by the ancestry-related covariates in our data-set. As shown in Figs 15 and 16 in S1 Text, the subjects in the bicluster have a distribution of ancestries similar to the remainder of arm-1 (recall that we corrected for ancestry as a covariate). By considering the subjects remaining in D(i), we also determined that the bicluster does not seem to be associated with sex (see Fig 17 in S1 Text).

Interaction with BD subtype

We then checked to see if the bicluster was associated with bipolar subtype. We measured the fraction of subjects classified as bipolar-type-1 versus bipolar-type-2 as our algorithm proceeded. Specifically, we measured the fraction of case-subjects in that were classified as BDI and BDII. If the bicluster were driven by BDII subjects, then we would expect the proportion of remaining BDII case-subjects to increase with the iteration-index i. Conversely, if the bicluster were driven by BDI subjects, then we would expect the proportion of remaining BDI case-subjects to increase with iteration-index. As shown in Fig 6, we found that this latter scenario holds; the bicluster was significantly enriched for BDI relative to BDII. This enrichment for BDI also impacts our risk-prediction results (see below). Note that, when determining this enrichment, we compare the proportion of BDI and BDII case-subjects at each iteration to the proportion at iteration i = 1 (i.e., across all case-subjects in arm-1). In this manner our enrichment is defined relative to the starting proportion of BDI and BDII subjects in our training-arm, and is not influenced by the recruitment rates for BDI and BDII (which can differ across studies).

While significant, this BDI-enrichment was not completely overwhelming: the initial fraction of BDII participants in arm-1 was ∼ 31%, which dropped to ∼ 26% at iteration i = 240. Thus, while the majority of the case-subjects in the bicluster are classified as BDI, those classified with BDII do still contribute to the overall signal. It is possible that this BDI-enrichment is due to a true difference between the BD-subtypes at the genetic level. However, it is also possible that this enrichment is partially driven by inaccuracies associated with classification [14].

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Fig 6.

This figure plots the ratio of BDI to BDII subjects within (light-green, left y-axis) as a function of the iteration i (left) and the number of removed case-subjects (right). The dark-green line corresponds to the negative-log-probability (right y-axis) of observing a ratio at least as large by chance. The dashed and dotted horizontal lines indicate 0.05 and 0.01 significance values, respectively. Note that the BDI population is over-represented across a range of iterations including i ∈ [175, 350], implying that the bicluster we observe is significantly enriched for BDI subjects.

https://doi.org/10.1371/journal.pone.0314288.g006

Bicluster-informed PRS performance

As described in the Methods section, we calculated the population-wide and the bicluster-informed across a variety of iterations i and -thresholds. We compared the bicluster-informed performance to the one generated by the population-wide across a variety of -thresholds. Results for arm-2 are shown in Fig 7. Results for arm-3 and arm-4 are shown alongside arm-2 in Fig 8, and individually in Figs 23 and 24 in S1 Text.

Note that, when constructing , we restrict ourselves to a subset of case-subjects within the training-arm determined by . In this case, when i ∈ [175, 350] the case-subset retains only ∼ 50% − 20% of the original case-subjects in arm-1. Typically, one might expect a reduction in the number of case-subjects to yield a corresponding reduction in power, giving rise to a reduced discriminability in the testing-arms 2,3 and 4. However, as we see in Fig 8, the discriminability for is typically higher than when i ∈ [175, 350]. This suggests that the case-subjects in identified by the bicluster correspond to a stronger genetic signal, likely arising from the increased homogeneity within .

Note that PRS_bicl and PRS_wide are not capturing identical signals (see the Nagelkerke R² analysis in the S1 Text). It is useful to compare the performance of PRS_bicl with PRS_wide as there are features of PRS_bicl which indicate that it is more robust than PRS_wide. As one example, we point out that is markedly higher than when the number of SNPs used (denoted by N_SNP) is fewer; one begins to see the effect between 1K and 10K. This suggests that the bicluster-informed is not only outperforming the population-wide , but also correctly attributing the largest PRS-weights to those SNPs that truly carry the signal (and which are most important for replication). As one illustration, by comparing the values of AUC_bicl to AUC_wide in Fig 8, we can directly see that the bicluster-informed PRS would replicate across arms 2,3 and 4 for values of i = 225 and N_SNP ∈ [10³, 10⁴], while the population-wide PRS would not.

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Fig 7. In each subplot we show in yellow the (vertical) for arm-2 as a function of the number of SNPs corresponding to each -threshold (horizontal, log-scale).

Additionally, we show for a particular iteration i (with i varying across subplots). The color-code used for ranges from blue to pink, corresponding to the iteration index i. Note that, by using the bicluster to inform the PRS, the performance typically improves. This improvement in performance becomes marked when the number of SNPs is limited to a relatively small fraction of the total (e.g., ∼ 1% of the total, corresponding to a log₁₀(#) of ∼ 3).

https://doi.org/10.1371/journal.pone.0314288.g007

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Fig 8. This figure uses circles to displays the same information as Fig 7 (corresponding to replication arm-2).

In this figure we use an algebraic-scale for the horizontal-axis (rather than a log-scale) in order to better emphasize the interval where the number of SNPs used is between 1K and 10K. The results for replication arm-3 and arm-4 are shown using squares and triangles, respectively.

https://doi.org/10.1371/journal.pone.0314288.g008

Motivated by the significant BDI-enrichment seen within the training-arm (see Fig 6), we repeated these assessments for the BDI- and BDII-populations within the testing-arms. More specifically, recall that, for any particular testing-arm, the and values shown in Figs 7 and 8 are defined using the values of across all case- and control-subjects j′ for that testing-arm. We can now use the same values of and , but only compare the BDI-case-subjects to the control-subjects in the testing-arm. This produces ‘restricted’ AUC-values, which we denote by and , respectively. In a similar fashion we can restrict the case-subjects in the testing-arm to the BDII-case-subjects, and calculate and .

The results are shown in Figs 9 and 10, respectively. Note that the improvement to risk-prediction persists for the BDI-population, but is not as robust for the BDII-population. The performance of is particularly poor for the BDII-population in arm-3, for which there were only M = 435 BDII-subjects (i.e., the fewest out of all the arms). It is possible that the variation in the performance of for the BDII-population across the replication-arms has to do with these differences in power. It is also possible that there are other systematic issues affecting the BDII-population, including variation in the life history of the subjects or the metrics used for their clinical diagnosis [14].

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Fig 9. This figure is similar to Fig 8, except that we limit ourselves only to those case-subjects in the replication-arms which are classified as BDI.

This subset corresponded to 66% (M = 3834), 84% (M = 2995) and 75% (M = 5107) of the case-population for arms 2, 3 and 4, respectively. The corresponding AUC-values are denoted by and in the main text. For reference the training-arm had M = 1645 BDI case-subjects, corresponding to 65% of the case-population in arm-1.

https://doi.org/10.1371/journal.pone.0314288.g009

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Fig 10. This figure is similar to Fig 8, except that we limit ourselves only to those case-subjects in the replication-arms which are classified as BDII.

This subset corresponded to 19% (M = 1082), 12% (M = 435) and 16% (M = 1060) of the case-population for arms 2, 3 and 4, respectively. The corresponding AUC-values are denoted by and in the main text. For reference the training-arm had M = 788 BDII case-subjects, corresponding to 31% of the case-population in arm-1.

https://doi.org/10.1371/journal.pone.0314288.g010

To summarize the overall relationship between BD-subtype, the bicluster-informed PRS and the population-wide PRS, we pool the subjects across the replication-arms and convert the combined AUC-values into R²-values on a liability-scale [71] using prevalences of 2% for BD, and 1% for BDI and BDII [72]. Using notation analogous to the AUC-values, we denote these liability-scores as , and , as well as , and , respectively. The resulting liability-scores are shown in Fig 11.

We believe that Fig 11 hints at the potential our methodology offers to researchers of complex disease. By limiting our definition of a case to those with a more genetically homogeneous BD signature, we were able to generate a PRS_bicl which outperforms PRS_wide in the following ways:

• The maximum is 20–40% higher than the maximum , depending on the iteration-index i.
• This increase in liability-score occurs despite the fact that the PRS_bicl is generated using ∼ 50% to 80% fewer cases than the PRS_wide. For example, we considered only between 1191–526 cases in arm-1 to generate the values for i = [175, 350], whereas 2524 cases were used to generate the values.
• The p-values assigned to the SNPs via the bicluster-informed GWAS were less noisy than those p-values assigned using the population-wide GWAS. For example, Fig 11 indicates that the first 10K SNPs of highest significance from the population-wide GWAS contained almost no disease-related information. By contrast, the first 10K SNPs of highest significance from the bicluster-informed GWAS typically contain most of the available disease-related information. The bicluster-informed GWAS produces a with only ∼ 5K to 10K SNPs that surpasses the maximum of (e.g., within the i = 225 subplot the value of at 5K SNPs is comparable to the value of at ∼ 150K SNPs).
• Furthermore, the values of typically plateau somewhere between 10K–35K SNPs (corresponding to ). Meanwhile, the values of continue to increase until (including all ∼ 150K SNPs).

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Fig 11. This figure is similar to Fig 8, and uses the data from Figs 8, 9 and 10.

This time we combine the information across all three replication-arms, and calculate replication AUC-values for this combined data-set. We then convert these AUC-values into liability-scores (see [71]). The results for all the cases ( and ) are shown with an asterisk ‘*’, whereas the results for only the BD1-cases ( and ) are shown with an ‘×’, and the results for only the BD2-cases ( and ) are shown with a diamond. In each case the yellow curves correspond to the liability-scores derived from the population-wide PRS, whereas the cyan-magenta curves correspond to the liability-scores derived from the bicluster-informed PRS. Note that our overall results are closely matched by the BD1-cases, but not by the BD2-cases.

https://doi.org/10.1371/journal.pone.0314288.g011

To summarize: The PRS_bicl outperforms PRS_wide overall, and when restricted to either BDI and BDII, achieving a higher maximum for each subtype. The PRS_bicl also achieves its peak performance with far fewer SNPs, consistent with a far less noisy signal. Put another way, the values of , and all plateau earlier than , and , indicating that the SNPs which are most relevant to the bicluster-informed PRS performance have indeed been identified by the bicluster-informed GWAS as having low individual p-values.

Additionally, we note that there is a close relationship between and , but a discrepancy between and . The values of indicate that some subset of BDII cases share the bicluster signature, but the maximum for is only 50% of the maximum for . This could imply that the bicluster has focused on a signature that is associated with BDI, perhaps serving as a risk factor for manic episodes in the presence of the necessary epigenetic or environmental influences.

Gene-enrichment

We also perform a simple over-representation analysis, measuring the overlap κ(i, l) between the bicluster D(i) at iteration i and the various neuronally-related pathways from the go_bp ontology (see Methods). The average z-score for the enrichment-values κ(i, l), averaged over the interval i ∈ [175, 350] and all neuronally-related pathways, is quite significant, with p ≲ 1e − 4 (as determined by a permutation-test). Examples of some of the more significantly over-represented pathways are shown in Table 1.

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Table 1. Here we list some of the pathways from the go_bp ontology.

Shown here are only the 32 most significant pathways as determined by κ(175, l). Each pathway is listed alongside approximations to its individual over-representation p-value (estimated using the hypergeometric-distribution). The −log₁₀(p)-values are listed for iterations 175–350 (see top row). Those annotations with an individual over-representation p-value smaller than 0.05 are in bold.

https://doi.org/10.1371/journal.pone.0314288.t001

Secondary bicluster

After discovering and analyzing the primary bicluster within arm-1 (described above), we searched for a secondary bicluster. We first eliminated the structure associated with the primary bicluster by scrambling the entries of the submatrix D(175) (see [64] for details). We then reran our half-loop algorithm on this scrambled version of arm-1. While we did find a secondary trace that was indicative of heterogeneity, the overall level of differential-expression was far lower than for the first bicluster (see Fig 25 in S1 Text). Moreover, the structure associated with this secondary trace did not significantly replicate (see Figs 26–28 in S1 Text). It is possible that a secondary bicluster exists, but that we could not pinpoint it due to a lack of power in our training-arm. It is also possible that the scrambled version of arm-1 is heterogeneous, but not in a way that can be described by a bicluster (see [64] for examples along these lines). In either case, a larger sample size will be required to further probe this residual heterogeneity.

Control biclusters

Up to this point we have only considered biclusters within the case-population; i.e., subsets of case-subjects which exhibit a genetic-signature that is not shared by the control-subjects. It is natural to ask if there are also biclusters that exist within the control-population (i.e., whether or not the control-population is homogeneous). Such ‘control-biclusters’ might be induced by batch effects or issues associated with recruitment; e.g., many of the BD controls may be drawn from another disease study (such as cancer), thus being more likely to share certain genetic features. It might also be the case that some of the control-biclusters are biologically significant, corresponding to mechanisms which protect against the disease. In either scenario, a better understanding of the heterogeneity within the control-population can assist in designing homogeneous populations of controls for future studies.

We can easily carry out this analysis simply by reversing the labels within our biclustering algorithm (i.e., swapping D and X). This reversed search will find biclusters that are driven by genetic-signatures which are more prevalent within the controls than within the cases. As mentioned above, we find that the control-population within arm-1 is quite homogeneous: the trace decays monotonically with no distinguished peaks (see Fig 29 in S1 Text). This homogeneity can be viewed as a validation of our initial choice of arm-1 as a training- or discovery-arm.

On the other hand, we find strong evidence for heterogeneity within the control-populations of arms 2, 3 and 4 (see Figs 30—32 in S1 Text). In each case the trace has a significant distinguished maximum involving only a fraction of the control-subjects (i.e,. 13%, 28% and 15% of the controls, respectively).

The heterogeneity observed in the control-populations of arms 2, 3 and 4 might be expected; each of these arms comprises multiple smaller studies. Notably however, the ‘control-biclusters’ within these arms cannot all be easily dismissed as batch-effects. Indeed, each of the dominant control-biclusters is also quite significant, while also usually well balanced across the ancestry-related covariates and individual cohorts within each arm. Each of these dominant control-biclusters also replicates across the majority of other arms.

Thus, while a portion of these control-biclusters might be driven by batch-effects or other idiosyncrasies in the control-population, it is possible that some of these signals have biological relevance, perhaps involving mechanisms which protect against BD (as the control-biclusters were identified specifically because they involved genetic patterns not as prevalent across the cases). Consequently, we would recommend considering this heterogeneity when performing other kinds of analysis. For example, one should not necessarily assume that the controls are homogeneous, as small subgroups of controls can likely exhibit genetic-signatures that are distinct from the rest.

Bipolar Disorder Working Group of the Psychiatric Genomics Consortium

Eli A Stahl^1,2,3, Gerome Breen^4,5, Andreas J Forstner^6,7,8,9,10, Andrew McQuillin¹¹, Stephan Ripke^12,13,14, Vassily Trubetskoy¹³, Manuel Mattheisen^{15,16,17,18,19}, Yunpeng Wang^20,21, Jonathan R I Coleman^4,5, Héléna A Gaspar^4,5, Christiaan A de Leeuw²², Stacy Steinberg²³, Jennifer M Whitehead Pavlides²⁴, Maciej Trzaskowski²⁵, Enda M Byrne²⁵, Tune H Pers^3,26, Peter A Holmans²⁷, Alexander L Richards²⁷, Liam Abbott¹², Esben Agerbo^19,28,29, Huda Akil³⁰, Diego Albani³¹, Ney Alliey-Rodriguez³², Thomas D Als^15,16,19, Adebayo Anjorin³³, Verneri Antilla¹⁴, Swapnil Awasthi¹³, Judith A Badner³⁴, Marie Bækvad-Hansen^19,35, Jack D Barchas³⁶, Nicholas Bass¹¹, Michael Bauer³⁷, Richard Belliveau¹², Sarah E Bergen³⁸, Carsten Bøcker Pedersen^19,28,29, Erlend Bøen³⁹, Marco P. Boks⁴⁰, James Boocock⁴¹, Monika Budde⁴², William Bunney⁴³, Margit Burmeister⁴⁴, Jonas Bybjerg-Grauholm^19,35, William Byerley⁴⁵, Miquel Casas^46,47,48,49, Felecia Cerrato¹², Pablo Cervantes⁵⁰, Kimberly Chambert¹², Alexander W Charney², Danfeng Chen¹², Claire Churchhouse^12,14, Toni-Kim Clarke⁵¹, William Coryell⁵², David W Craig⁵³, Cristiana Cruceanu^50,54, David Curtis^55,56, Piotr M Czerski⁵⁷, Anders M Dale^58,59,60,61, Simone de Jong^4,5, Franziska Degenhardt⁸, Jurgen Del-Favero⁶², J Raymond DePaulo⁶³, Srdjan Djurovic^64,65, Amanda L Dobbyn^1,2, Ashley Dumont¹², Torbjørn Elvsåshagen^66,67, Valentina Escott-Price²⁷, Chun Chieh Fan⁶¹, Sascha B Fischer^6,10, Matthew Flickinger⁶⁸, Tatiana M Foroud⁶⁹, Liz Forty²⁷, Josef Frank⁷⁰, Christine Fraser²⁷, Nelson B Freimer⁷¹, Louise Frisén^72,73,74, Katrin Gade^42,75, Diane Gage¹², Julie Garnham⁷⁶, Claudia Giambartolomei²⁰⁶, Marianne Giørtz Pedersen^19,28,29, Jaqueline Goldstein¹², Scott D Gordon⁷⁷, Katherine Gordon-Smith⁷⁸, Elaine K Green⁷⁹, Melissa J Green^80,133, Tiffany A Greenwood⁶⁰, Jakob Grove^15,16,19,81, Weihua Guan⁸², José Guzman-Parra⁸³, Marian L Hamshere²⁷, Martin Hautzinger⁸⁴, Urs Heilbronner⁴², Stefan Herms^6,8,10, Maria Hipolito⁸⁵, Per Hoffmann^6,8,10, Dominic Holland^58,86, Laura Huckins^1,2, Stéphane Jamain^87,88, Jessica S Johnson^1,2, Radhika Kandaswamy⁴, Robert Karlsson³⁸, James L Kennedy^89,90,91,92, Sarah Kittel-Schneider⁹³, James A Knowles^94,95, Manolis Kogevinas⁹⁶, Anna C Koller⁸, Ralph Kupka^97,98,99, Catharina Lavebratt⁷², Jacob Lawrence¹⁰⁰, William B Lawson⁸⁵, Markus Leber¹⁰¹, Phil H Lee^12,14,102, Shawn E Levy¹⁰³, Jun Z Li¹⁰⁴, Chunyu Liu¹⁰⁵, Susanne Lucae¹⁰⁶, Anna Maaser⁸, Donald J MacIntyre^107,108, Pamela B Mahon^63,109, Wolfgang Maier¹¹⁰, Lina Martinsson⁷³, Steve McCarroll^12,111, Peter McGuffin⁴, Melvin G McInnis¹¹², James D McKay¹¹³, Helena Medeiros⁹⁵, Sarah E Medland⁷⁷, Fan Meng^30,112, Lili Milani¹¹⁴, Grant W Montgomery²⁵, Derek W Morris^115,116, Thomas W Mühleisen^6,117, Niamh Mullins⁴, Hoang Nguyen^1,2, Caroline M Nievergelt^60,118, Annelie Nordin Adolfsson¹¹⁹, Evaristus A Nwulia⁸⁵, Claire O’Donovan⁷⁶, Loes M Olde Loohuis⁷¹, Anil P S Ori⁷¹, Lilijana Oruc¹²⁰, Urban Ösby¹²¹, Roy H Perlis^122,123, Amy Perry⁷⁸, Andrea Pfennig³⁷, James B Potash⁶³, Shaun M Purcell^2,109, Eline J Regeer¹²⁴, Andreas Reif⁹³, Céline S Reinbold^6,10, John P Rice¹²⁵, Fabio Rivas⁸³, Margarita Rivera^4,126, Panos Roussos^1,2,127, Douglas M Ruderfer¹²⁸, Euijung Ryu¹²⁹, Cristina Sánchez-Mora^46,47,49, Alan F Schatzberg¹³⁰, William A Scheftner¹³¹, Nicholas J Schork¹³², Cynthia Shannon Weickert^80,133, Tatyana Shehktman⁶⁰, Paul D Shilling⁶⁰, Engilbert Sigurdsson¹³⁴, Claire Slaney⁷⁶, Olav B Smeland^135,136, Janet L Sobell¹³⁷, Christine Søholm Hansen^19,35, Anne T Spijker¹³⁸, David St Clair¹³⁹, Michael Steffens¹⁴⁰, John S Strauss^91,141, Fabian Streit⁷⁰, Jana Strohmaier⁷⁰, Szabolcs Szelinger¹⁴², Robert C Thompson¹¹², Thorgeir E Thorgeirsson²³, Jens Treutlein⁷⁰, Helmut Vedder¹⁴³, Weiqing Wang^1,2, Stanley J Watson¹¹², Thomas W Weickert^80,133, Stephanie H Witt⁷⁰, Simon Xi¹⁴⁴, Wei Xu^145,146, Allan H Young¹⁴⁷, Peter Zandi¹⁴⁸, Peng Zhang¹⁴⁹, Sebastian Zöllner¹¹², eQTLGen Consortium, BIOS Consortium, Rolf Adolfsson¹¹⁹, Ingrid Agartz^17,39,150, Martin Alda^76,151, Lena Backlund⁷³, Bernhard T Baune^152,158, Frank Bellivier^{153,154,155,156}, Wade H Berrettini¹⁵⁷, Joanna M Biernacka¹²⁹, Douglas H R Blackwood⁵¹, Michael Boehnke⁶⁸, Anders D Børglum^15,16,19, Aiden Corvin¹¹⁶, Nicholas Craddock²⁷, Mark J Daly^12,14, Udo Dannlowski¹⁵⁸, Tõnu Esko^{3,111,114,159}, Bruno Etain^{153,155,156,160}, Mark Frye¹⁶¹, Janice M Fullerton^133,162, Elliot S Gershon^32,163, Michael Gill¹¹⁶, Fernando Goes⁶³, Maria Grigoroiu-Serbanescu¹⁶⁴, Joanna Hauser⁵⁷, David M Hougaard^19,35, Christina M Hultman³⁸, Ian Jones²⁷, Lisa A Jones⁷⁸, René S Kahn^2,40, George Kirov²⁷, Mikael Landén^38,165, Marion Leboyer^88,153,166, Cathryn M Lewis^4,5,167, Qingqin S Li¹⁶⁸, Jolanta Lissowska¹⁶⁹, Nicholas G Martin^77,170, Fermin Mayoral⁸³, Susan L McElroy¹⁷¹, Andrew M McIntosh^51,172, Francis J McMahon¹⁷³, Ingrid Melle^174,175, Andres Metspalu^114,176, Philip B Mitchell⁸⁰, Gunnar Morken^177,178, Ole Mors^19,179, Preben Bo Mortensen^15,19,28,29, Bertram Müller-Myhsok^54,180,181, Richard M Myers¹⁰³, Benjamin M Neale^3,12,14, Vishwajit Nimgaonkar¹⁸², Merete Nordentoft^19,183, Markus M Nöthen⁸, Michael C O’Donovan²⁷, Ketil J Oedegaard^184,185, Michael J Owen²⁷, Sara A Paciga¹⁸⁶, Carlos Pato^95,187, Michele T Pato⁹⁵, Danielle Posthuma^22,188, Josep Antoni Ramos-Quiroga^46,47,48,49, Marta Ribasés^46,47,49, Marcella Rietschel⁷⁰, Guy A Rouleau^189,190, Martin Schalling⁷², Peter R Schofield^133,162, Thomas G Schulze^{42,63,70,75,173}, Alessandro Serretti¹⁹¹, Jordan W Smoller^12,192,193, Hreinn Stefansson²³, Kari Stefansson^23,194, Eystein Stordal^195,196, Patrick F Sullivan^38,197,198, Gustavo Turecki¹⁹⁹, Arne E Vaaler²⁰⁰, Eduard Vieta²⁰¹, John B Vincent¹⁴¹, Thomas Werge^19,202,203, John I Nurnberger²⁰⁴, Naomi R Wray^24,25, Arianna Di Florio^27,198, Howard J Edenberg²⁰⁵, Sven Cichon^6,8,10,117, Roel A Ophoff^40,41,71, Laura J Scott⁶⁸, Ole A Andreassen^135,136, John Kelsoe⁶⁰, Pamela Sklar^1,2,†

¹Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, US. ²Department of Psychiatry, Icahn School of Medicine at Mount Sinai, New York, NY, US. ³Medical and Population Genetics, Broad Institute, Cambridge, MA, US. ⁴MRC Social, Genetic and Developmental Psychiatry Centre, King’s College London, London, GB. ⁵NIHR BRC for Mental Health, King’s College London, London, GB. ⁶Department of Biomedicine, University of Basel, Basel, CH. ⁷Department of Psychiatry (UPK), University of Basel, Basel, CH. ⁸Institute of Human Genetics, University of Bonn, School of Medicine & University Hospital Bonn, Bonn, DE. ⁹Centre for Human Genetics, University of Marburg, Marburg, DE. ¹⁰Institute of Medical Genetics and Pathology, University Hospital Basel, Basel, CH. ¹¹Division of Psychiatry, University College London, London, GB. ¹²Stanley Center for Psychiatric Research, Broad Institute, Cambridge, MA, US. ¹³Department of Psychiatry and Psychotherapy, Charité—Universitätsmedizin, Berlin, DE. ¹⁴Analytic and Translational Genetics Unit, Massachusetts General Hospital, Boston, MA, US. ¹⁵iSEQ, Center for Integrative Sequencing, Aarhus University, Aarhus, DK. ¹⁶Department of Biomedicine—Human Genetics, Aarhus University, Aarhus, DK. ¹⁷Department of Clinical Neuroscience, Centre for Psychiatry Research, Karolinska Institutet, Stockholm, SE. ¹⁸Department of Psychiatry, Psychosomatics and Psychotherapy, Center of Mental Health, University Hospital Würzburg, Würzburg, DE. ¹⁹iPSYCH, The Lundbeck Foundation Initiative for Integrative Psychiatric Research, DK. ²⁰Institute of Biological Psychiatry, Mental Health Centre Sct. Hans, Copenhagen, DK. ²¹Institute of Clinical Medicine, University of Oslo, Oslo, NO. ²²Department of Complex Trait Genetics, Center for Neurogenomics and Cognitive Research, Amsterdam Neuroscience, Vrije Universiteit Amsterdam, Amsterdam, NL. ²³deCODE Genetics / Amgen, Reykjavik, IS. ²⁴Queensland Brain Institute, The University of Queensland, Brisbane, QLD, AU. ²⁵Institute for Molecular Bioscience, The University of Queensland, Brisbane, QLD, AU. ²⁶Division of Endocrinology and Center for Basic and Translational Obesity Research, Boston Children’s Hospital, Boston, MA, US. ²⁷Medical Research Council Centre for Neuropsychiatric Genetics and Genomics, Division of Psychological Medicine and Clinical Neurosciences, Cardiff University, Cardiff, GB. ²⁸National Centre for Register-Based Research, Aarhus University, Aarhus, DK. ²⁹Centre for Integrated Register-based Research, Aarhus University, Aarhus, DK. ³⁰Molecular & Behavioral Neuroscience Institute, University of Michigan, Ann Arbor, MI, US. ³¹Department of Neuroscience, IRCCS—Istituto Di Ricerche Farmacologiche Mario Negri, Milan, IT. ³²Department of Psychiatry and Behavioral Neuroscience, University of Chicago, Chicago, IL, US. ³³Psychiatry, Berkshire Healthcare NHS Foundation Trust, Bracknell, GB. ³⁴Psychiatry, Rush University Medical Center, Chicago, IL, US. ³⁵Center for Neonatal Screening, Department for Congenital Disorders, Statens Serum Institut, Copenhagen, DK. ³⁶Department of Psychiatry, Weill Cornell Medical College, New York, NY, US. ³⁷Department of Psychiatry and Psychotherapy, University Hospital Carl Gustav Carus, Technische Universität Dresden, Dresden, DE. ³⁸Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, SE. ³⁹Department of Psychiatric Research, Diakonhjemmet Hospital, Oslo, NO. ⁴⁰Psychiatry, UMC Utrecht Brain Center Rudolf Magnus, Utrecht, NL. ⁴¹Human Genetics, University of California Los Angeles, Los Angeles, CA, US. ⁴²Institute of Psychiatric Phenomics and Genomics (IPPG), University Hospital, LMU Munich, Munich, DE. ⁴³Department of Psychiatry and Human Behavior, University of California, Irvine, Irvine, CA, US. ⁴⁴Molecular & Behavioral Neuroscience Institute and Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, MI, US. ⁴⁵Psychiatry, University of California San Francisco, San Francisco, CA, US. ⁴⁶Instituto de Salud Carlos III, Biomedical Network Research Centre on Mental Health (CIBERSAM), Madrid, ES. ⁴⁷Department of Psychiatry, Hospital Universitari Vall d´Hebron, Barcelona, ES. ⁴⁸Department of Psychiatry and Forensic Medicine, Universitat Autònoma de Barcelona, Barcelona, ES. ⁴⁹Psychiatric Genetics Unit, Group of Psychiatry Mental Health and Addictions, Vall d´Hebron Research Institut (VHIR), Universitat Autònoma de Barcelona, Barcelona, ES. ⁵⁰Department of Psychiatry, Mood Disorders Program, McGill University Health Center, Montreal, QC, CA. ⁵¹Division of Psychiatry, University of Edinburgh, Edinburgh, GB. ⁵²University of Iowa Hospitals and Clinics, Iowa City, IA, US. ⁵³Translational Genomics, USC, Phoenix, AZ, US. ⁵⁴Department of Translational Research in Psychiatry, Max Planck Institute of Psychiatry, Munich, DE. ⁵⁵Centre for Psychiatry, Queen Mary University of London, London, GB. ⁵⁶UCL Genetics Institute, University College London, London, GB. ⁵⁷Department of Psychiatry, Laboratory of Psychiatric Genetics, Poznan University of Medical Sciences, Poznan, PL. ⁵⁸Department of Neurosciences, University of California San Diego, La Jolla, CA, US. ⁵⁹Department of Radiology, University of California San Diego, La Jolla, CA, US. ⁶⁰Department of Psychiatry, University of California San Diego, La Jolla, CA, US. ⁶¹Department of Cognitive Science, University of California San Diego, La Jolla, CA, US. ⁶²Applied Molecular Genomics Unit, VIB Department of Molecular Genetics, University of Antwerp, Antwerp, Belgium. ⁶³Department of Psychiatry and Behavioral Sciences, Johns Hopkins University School of Medicine, Baltimore, MD, US. ⁶⁴Department of Medical Genetics, Oslo University Hospital Ullevål, Oslo, NO. ⁶⁵NORMENT, KG Jebsen Centre for Psychosis Research, Department of Clinical Science, University of Bergen, Bergen, NO. ⁶⁶Department of Neurology, Oslo University Hospital, Oslo, NO. ⁶⁷NORMENT, KG Jebsen Centre for Psychosis Research, Oslo University Hospital, Oslo, NO. ⁶⁸Center for Statistical Genetics and Department of Biostatistics, University of Michigan, Ann Arbor, MI, US. ⁶⁹Department of Medical & Molecular Genetics, Indiana University, Indianapolis, IN, US. ⁷⁰Department of Genetic Epidemiology in Psychiatry, Central Institute of Mental Health, Medical Faculty Mannheim, Heidelberg University, Mannheim, DE. ⁷¹Center for Neurobehavioral Genetics, University of California Los Angeles, Los Angeles, CA, US. ⁷²Department of Molecular Medicine and Surgery, Karolinska Institutet and Center for Molecular Medicine, Karolinska University Hospital, Stockholm, SE. ⁷³Department of Clinical Neuroscience, Karolinska Institutet and Center for Molecular Medicine, Karolinska University Hospital, Stockholm, SE. ⁷⁴Child and Adolescent Psychiatry Research Center, Stockholm, SE. ⁷⁵Department of Psychiatry and Psychotherapy, University Medical Center Göttingen, Göttingen, DE. ⁷⁶Department of Psychiatry, Dalhousie University, Halifax, NS, CA. ⁷⁷Genetics and Computational Biology, QIMR Berghofer Medical Research Institute, Brisbane, QLD, AU. ⁷⁸Department of Psychological Medicine, University of Worcester, Worcester, GB. ⁷⁹School of Biomedical Sciences, Plymouth University Peninsula Schools of Medicine and Dentistry, University of Plymouth, Plymouth, GB. ⁸⁰School of Psychiatry, University of New South Wales, Sydney, NSW, AU. ⁸¹Bioinformatics Research Centre, Aarhus University, Aarhus, DK. ⁸²Biostatistics, University of Minnesota System, Minneapolis, MN, US. ⁸³Mental Health Department, University Regional Hospital, Biomedicine Institute (IBIMA), Málaga, ES. ⁸⁴Department of Psychology, Eberhard Karls Universität Tübingen, Tubingen, DE. ⁸⁵Department of Psychiatry and Behavioral Sciences, Howard University Hospital, Washington, DC, US. ⁸⁶Center for Multimodal Imaging and Genetics, University of California San Diego, La Jolla, CA, US. ⁸⁷Psychiatrie Translationnelle, Inserm U955, Créteil, FR. ⁸⁸Faculté de Médecine, Université Paris Est, Créteil, FR. ⁸⁹Campbell Family Mental Health Research Institute, Centre for Addiction and Mental Health, Toronto, ON, CA. ⁹⁰Neurogenetics Section, Centre for Addiction and Mental Health, Toronto, ON, CA. ⁹¹Department of Psychiatry, University of Toronto, Toronto, ON, CA. ⁹²Institute of Medical Sciences, University of Toronto, Toronto, ON, CA. ⁹³Department of Psychiatry, Psychosomatic Medicine and Psychotherapy, University Hospital Frankfurt, Frankfurt am Main, DE. ⁹⁴Cell Biology, SUNY Downstate Medical Center College of Medicine, Brooklyn, NY, US. ⁹⁵Institute for Genomic Health, SUNY Downstate Medical Center College of Medicine, Brooklyn, NY, US. ⁹⁶ISGlobal, Barcelona, ES. ⁹⁷Psychiatry, Altrecht, Utrecht, NL. ⁹⁸Psychiatry, GGZ inGeest, Amsterdam, NL. ⁹⁹Psychiatry, VU medisch centrum, Amsterdam, NL. ¹⁰⁰Psychiatry, North East London NHS Foundation Trust, Ilford, GB. ¹⁰¹Clinic for Psychiatry and Psychotherapy, University Hospital Cologne, Cologne, DE. ¹⁰²Psychiatric and Neurodevelopmental Genetics Unit, Massachusetts General Hospital, Boston, MA, US. ¹⁰³HudsonAlpha Institute for Biotechnology, Huntsville, AL, US. ¹⁰⁴Department of Human Genetics, University of Michigan, Ann Arbor, MI, US. ¹⁰⁵Psychiatry, University of Illinois at Chicago College of Medicine, Chicago, IL, US. ¹⁰⁶Max Planck Institute of Psychiatry, Munich, DE. ¹⁰⁷Mental Health, NHS 24, Glasgow, GB. ¹⁰⁸Division of Psychiatry, Centre for Clinical Brain Sciences, University of Edinburgh, Edinburgh, GB. ¹⁰⁹Psychiatry, Brigham and Women’s Hospital, Boston, MA, US. ¹¹⁰Department of Psychiatry and Psychotherapy, University of Bonn, Bonn, DE. ¹¹¹Department of Genetics, Harvard Medical School, Boston, MA, US. ¹¹²Department of Psychiatry, University of Michigan, Ann Arbor, MI, US. ¹¹³Genetic Cancer Susceptibility Group, International Agency for Research on Cancer, Lyon, FR. ¹¹⁴Estonian Genome Center, University of Tartu, Tartu, EE. ¹¹⁵Discipline of Biochemistry, Neuroimaging and Cognitive Genomics (NICOG) Centre, National University of Ireland, Galway, Galway, IE. ¹¹⁶Neuropsychiatric Genetics Research Group, Dept of Psychiatry and Trinity Translational Medicine Institute, Trinity College Dublin, Dublin, IE. ¹¹⁷Institute of Neuroscience and Medicine (INM-1), Research Centre Jülich, Jülich, DE. ¹¹⁸Research/Psychiatry, Veterans Affairs San Diego Healthcare System, San Diego, CA, US. ¹¹⁹Department of Clinical Sciences, Psychiatry, Umeå University Medical Faculty, Umeå, SE. ¹²⁰Department of Clinical Psychiatry, Psychiatry Clinic, Clinical Center University of Sarajevo, Sarajevo, BA. ¹²¹Department of Neurobiology, Care sciences, and Society, Karolinska Institutet and Center for Molecular Medicine, Karolinska University Hospital, Stockholm, SE. ¹²²Psychiatry, Harvard Medical School, Boston, MA, US. ¹²³Division of Clinical Research, Massachusetts General Hospital, Boston, MA, US. ¹²⁴Outpatient Clinic for Bipolar Disorder, Altrecht, Utrecht, NL. ¹²⁵Department of Psychiatry, Washington University in Saint Louis, Saint Louis, MO, US. ¹²⁶Department of Biochemistry and Molecular Biology II, Institute of Neurosciences, Center for Biomedical Research, University of Granada, Granada, ES. ¹²⁷Department of Neuroscience, Icahn School of Medicine at Mount Sinai, New York, NY, US. ¹²⁸Medicine, Psychiatry, Biomedical Informatics, Vanderbilt University Medical Center, Nashville, TN, US. ¹²⁹Department of Health Sciences Research, Mayo Clinic, Rochester, MN, US. ¹³⁰Psychiatry and Behavioral Sciences, Stanford University School of Medicine, Stanford, CA, US. ¹³¹Rush University Medical Center, Chicago, IL, US. ¹³²Scripps Translational Science Institute, La Jolla, CA, US. ¹³³Neuroscience Research Australia, Sydney, NSW, AU. ¹³⁴Faculty of Medicine, Department of Psychiatry, School of Health Sciences, University of Iceland, Reykjavik, IS. ¹³⁵Division of Mental Health and Addiction, Oslo University Hospital, Oslo, NO. ¹³⁶NORMENT, University of Oslo, Oslo, NO. ¹³⁷Psychiatry and the Behavioral Sciences, University of Southern California, Los Angeles, CA, US. ¹³⁸Mood Disorders, PsyQ, Rotterdam, NL. ¹³⁹Institute for Medical Sciences, University of Aberdeen, Aberdeen, UK. ¹⁴⁰Research Division, Federal Institute for Drugs and Medical Devices (BfArM), Bonn, DE. ¹⁴¹Centre for Addiction and Mental Health, Toronto, ON, CA. ¹⁴²Neurogenomics, TGen, Los Angeles, AZ, US. ¹⁴³Psychiatry, Psychiatrisches Zentrum Nordbaden, Wiesloch, DE. ¹⁴⁴Computational Sciences Center of Emphasis, Pfizer Global Research and Development, Cambridge, MA, US. ¹⁴⁵Department of Biostatistics, Princess Margaret Cancer Centre, Toronto, ON, CA. ¹⁴⁶Dalla Lana School of Public Health, University of Toronto, Toronto, ON, CA. ¹⁴⁷Psychological Medicine, Institute of Psychiatry, Psychology & Neuroscience, King’s College London, London, GB. ¹⁴⁸Department of Mental Health, Johns Hopkins University Bloomberg School of Public Health, Baltimore, MD, US. ¹⁴⁹Institute of Genetic Medicine, Johns Hopkins University School of Medicine, Baltimore, MD, US. ¹⁵⁰NORMENT, KG Jebsen Centre for Psychosis Research, Division of Mental Health and Addiction, Institute of Clinical Medicine and Diakonhjemmet Hospital, University of Oslo, Oslo, NO. ¹⁵¹National Institute of Mental Health, Klecany, CZ. ¹⁵²Department of Psychiatry, University of Melbourne, Melbourne, Victoria, AU. ¹⁵³Department of Psychiatry and Addiction Medicine, Assistance Publique—Hôpitaux de Paris, Paris, FR. ¹⁵⁴Paris Bipolar and TRD Expert Centres, FondaMental Foundation, Paris, FR. ¹⁵⁵UMR-S1144 Team 1: Biomarkers of relapse and therapeutic response in addiction and mood disorders, INSERM, Paris, FR. ¹⁵⁶Psychiatry, Université Paris Diderot, Paris, FR. ¹⁵⁷Psychiatry, University of Pennsylvania, Philadelphia, PA, US. ¹⁵⁸Department of Psychiatry, University of Münster, Münster, DE. ¹⁵⁹Division of Endocrinology, Children’s Hospital Boston, Boston, MA, US. ¹⁶⁰Centre for Affective Disorders, Institute of Psychiatry, Psychology and Neuroscience, London, GB. ¹⁶¹Department of Psychiatry & Psychology, Mayo Clinic, Rochester, MN, US. ¹⁶²School of Medical Sciences, University of New South Wales, Sydney, NSW, AU. ¹⁶³Department of Human Genetics, University of Chicago, Chicago, IL, US. ¹⁶⁴Biometric Psychiatric Genetics Research Unit, Alexandru Obregia Clinical Psychiatric Hospital, Bucharest, RO. ¹⁶⁵Institute of Neuroscience and Physiology, University of Gothenburg, Gothenburg, SE. ¹⁶⁶INSERM, Paris, FR. ¹⁶⁷Department of Medical & Molecular Genetics, King’s College London, London, GB. ¹⁶⁸Neuroscience Therapeutic Area, Janssen Research and Development, LLC, Titusville, NJ, US. ¹⁶⁹Cancer Epidemiology and Prevention, M. Sklodowska-Curie Cancer Center and Institute of Oncology, Warsaw, PL. ¹⁷⁰School of Psychology, The University of Queensland, Brisbane, QLD, AU. ¹⁷¹Research Institute, Lindner Center of HOPE, Mason, OH, US. ¹⁷²Centre for Cognitive Ageing and Cognitive Epidemiology, University of Edinburgh, Edinburgh, GB. ¹⁷³Human Genetics Branch, Intramural Research Program, National Institute of Mental Health, Bethesda, MD, US. ¹⁷⁴Division of Mental Health and Addiction, Oslo University Hospital, Oslo, NO. ¹⁷⁵Division of Mental Health and Addiction, University of Oslo, Institute of Clinical Medicine, Oslo, NO. ¹⁷⁶Institute of Molecular and Cell Biology, University of Tartu, Tartu, EE. ¹⁷⁷Mental Health, Faculty of Medicine and Health Sciences, Norwegian University of Science and Technology—NTNU, Trondheim, NO. ¹⁷⁸Psychiatry, St Olavs University Hospital, Trondheim, NO. ¹⁷⁹Psychosis Research Unit, Aarhus University Hospital, Risskov, DK. ¹⁸⁰Munich Cluster for Systems Neurology (SyNergy), Munich, DE. ¹⁸¹University of Liverpool, Liverpool, GB. ¹⁸²Psychiatry and Human Genetics, University of Pittsburgh, Pittsburgh, PA, US. ¹⁸³Mental Health Services in the Capital Region of Denmark, Mental Health Center Copenhagen, University of Copenhagen, Copenhagen, DK. ¹⁸⁴Division of Psychiatry, Haukeland Universitetssjukehus, Bergen, NO. ¹⁸⁵Faculty of Medicine and Dentistry, University of Bergen, Bergen, NO. ¹⁸⁶Human Genetics and Computational Biomedicine, Pfizer Global Research and Development, Groton, CT, US. ¹⁸⁷College of Medicine Institute for Genomic Health, SUNY Downstate Medical Center College of Medicine, Brooklyn, NY, US. ¹⁸⁸Department of Clinical Genetics, Amsterdam Neuroscience, Vrije Universiteit Medical Center, Amsterdam, NL. ¹⁸⁹Department of Neurology and Neurosurgery, McGill University, Faculty of Medicine, Montreal, QC, CA. ¹⁹⁰Montreal Neurological Institute and Hospital, Montreal, QC, CA. ¹⁹¹Department of Biomedical and NeuroMotor Sciences, University of Bologna, Bologna, IT. ¹⁹²Department of Psychiatry, Massachusetts General Hospital, Boston, MA, US. ¹⁹³Psychiatric and Neurodevelopmental Genetics Unit (PNGU), Massachusetts General Hospital, Boston, MA, US. ¹⁹⁴Faculty of Medicine, University of Iceland, Reykjavik, IS. ¹⁹⁵Department of Psychiatry, Hospital Namsos, Namsos, NO. ¹⁹⁶Department of Neuroscience, Norges Teknisk Naturvitenskapelige Universitet Fakultet for naturvitenskap og teknologi, Trondheim, NO. ¹⁹⁷Department of Genetics, University of North Carolina at Chapel Hill, Chapel Hill, NC, US. ¹⁹⁸Department of Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, NC, US. ¹⁹⁹Department of Psychiatry, McGill University, Montreal, QC, CA. ²⁰⁰Dept of Psychiatry, Sankt Olavs Hospital Universitetssykehuset i Trondheim, Trondheim, NO. ²⁰¹Clinical Institute of Neuroscience, Hospital Clinic, University of Barcelona, IDIBAPS, CIBERSAM, Barcelona, ES. ²⁰²Institute of Biological Psychiatry, MHC Sct. Hans, Mental Health Services Copenhagen, Roskilde, DK. ²⁰³Department of Clinical Medicine, University of Copenhagen, Copenhagen, DK. ²⁰⁴Psychiatry, Indiana University School of Medicine, Indianapolis, IN, US. ²⁰⁵Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, IN, US. ²⁰⁶Department of Pathology and Laboratory Medicine, University of California Los Angeles, Los Angeles, CA, US. ^† deceased.