Increasing the resolution and precision of psychiatric genome‐wide association studies by re‐imputing summary statistics using a large, diverse reference panel

Abstract

Genotype imputation across populations of mixed ancestry is critical for optimal discovery in large‐scale genome‐wide association studies (GWAS). Methods for direct imputation of GWAS summary‐statistics were previously shown to be practically as accurate as summary statistics produced after raw genotype imputation, while incurring orders of magnitude lower computational burden. Given that direct imputation needs a precise estimation of linkage‐disequilibrium (LD) and that most of the methods using a small reference panel for example, ~2,500‐subject coming from the 1000 Genome‐Project, there is a great need for much larger and more diverse reference panels. To accurately estimate the LD needed for an exhaustive analysis of any cosmopolitan cohort, we developed DISTMIX2. DISTMIX2: (a) uses a much larger and more diverse reference panel compared to traditional reference panels, and (b) can estimate weights of ethnic‐mixture based solely on Z‐scores, when allele frequencies are not available. We applied DISTMIX2 to GWAS summary‐statistics from the psychiatric genetic consortium (PGC). DISTMIX2 uncovered signals in numerous new regions, with most of these findings coming from the rarer variants. Rarer variants provide much sharper location for the signals compared with common variants, as the LD for rare variants extends over a lower distance than for common ones. For example, while the original PGC post‐traumatic stress disorder GWAS found only 3 marginal signals for common variants, we now uncover a very strong signal for a rare variant in PKN2, a gene associated with neuronal and hippocampal development. Thus, DISTMIX2 provides a robust and fast (re)imputation approach for most psychiatric GWAS‐studies.

1. INTRODUCTION

Genotype imputation (B. L. Browning & Browning, 2009; Howie, Donnelly, & Marchini, 2009; Nicolae, 2006; Servin & Stephens, 2007) methods are commonly used to increase the genomic resolution for large‐scale multi‐ethnic genome‐wide association studies (GWAS) meta‐analyses (Consortium, 2015; Ripke et al., 2013; Ripke et al., 2011; Sklar et al., 2011; Sladek et al., 2007) by predicting genotypes at unmeasured single nucleotide polymorphisms (SNPs) markers based on cosmopolitan reference panels, for example, 1000 Genomes (1 KG) Project (Genomes Project et al., 2012). However, genotypic imputation is computationally burdensome and requires access to subject‐level genetic data, which is harder and slower to obtain than summary statistics.

To overcome these limitations, researchers proposed summary statistics‐based imputation methods, for example, DIST (Lee, Bigdeli, Riley, Fanous, & Bacanu, 2013) and ImpG (Pasaniuc et al., 2013). These methods can directly impute summary statistics (two‐tailed Z‐scores) for unmeasured SNPs from summary statistics of GWAS or called variants from sequencing studies. The methods were shown to i) substantially reduce the computational burden and ii) be practically as accurate as commonly used genotype imputation methods. These methods were successfully applied in gene‐level joint testing of functional variants and functional enrichment analyses. However, these first wave of direct imputation methods were only amenable for imputation in ethnically homogeneous cohorts.

To accommodate cosmopolitan cohorts, DIST method was extended (Lee et al., 2015) to directly imputing summary statistics for unmeasured SNPs from Mixed ethnicity cohorts (DISTMIX). It: (a) predicted a study's proportions (weights) of ethnicities from a multi‐ethnic reference panel based only on cohort allele frequencies (AFs) for (common) SNPs from the studied cohort or taking prespecified ethnic weights, (b) computed an ethnicity‐weighted correlation matrix based on the estimated/prespecified weights and genotypes of ethnicities from the reference panel and then, (c) used the weighted correlation matrix for accurate imputation. Currently, due to privacy concerns (Homer et al., 2008), cohort AFs are lately only rarely provided. To circumvent the lack of AFs, the ARDISS method (Togninalli, Roqueiro, Investigators, & Borgwardt, 2018) extended the inference to cosmopolitan cohorts using a gaussian field approach based only on Z‐scores. However, ARDISS software provides only a 1 KG‐derived reference panel. Unlike DISTMIX that is implemented as a standalone C++ software, ARDISS is implemented in Python that is more temperamental in diverse installing/working environments with various versions of libraries.

The direct imputation was already used in practice to impute GWAS data with success (Endo et al., 2018; Khor et al., 2018; Revez et al., 2020). Moreover, direct imputation is also performed in the background of other applications. For instance, unlike many alternatives, our transcriptome wide association study (TWAS) tools (Chatzinakos et al., 2020; Chatzinakos et al., 2018; Lee et al., 2015; Lee et al., 2016), internally impute statistics for expression Quantitative Trait Loci (eQTL) SNPs that are not reported in GWASAn additional need for direct imputation methods is to be able analyze studies (a) not reporting AFs and (b) also, containing a non‐trivial fractions of non‐European subjects (Cai et al., 2017; Ripke et al., 2013). To increase the resolution and relevance to such cosmopolitan cohorts, DIST/DISTMIX enlarged the reference panel by including genotypes from large sequencing studies, such as Haplotype Reference Consortium (HRC) (McCarthy et al., 2016) and CONVERGE (Consortium, 2015). The inclusion of >11 K Han Chinese cohort from the CONVERGE consortium complement nicely the (largely European) HRC panel and provides accurate linkage‐disequilibrium (LD) information for the second most studied continental population after Europeans.

In this paper we propose DISTMIX2 method/software, which addresses the above shortcomings by including two critical components. First, we provide a novel method to accurately estimate ethnic weights of the cohort which uses only summary statistics, for example, Z‐scores. Second, we build a larger, more diverse reference panel with 33 K subjects, which combines the subjects from the publicly available part of HRC and CONVERGE. While implementing the above 2 features, DISTMIX2: (a) adequately controls the false positive rate, and (b) provides much improved resolution when compared to methods based on older reference panels. Based on simulated data sets we provide guidance on the significance thresholds for rare and/or low information variants. Furthermore, in a practical application to reported summary statistics from studies of psychiatric disorders, we uncover numerous regions harboring signals. Most of these novel signals are associated with rarer variants that could not be robustly interrogating using the smaller panels from previous methods. Some of the new findings provide strong signals in new regions for traits that reported only marginal signals. In the quest to provide enhanced resolution for ethnically mixed GWAS studies, DISTMIX2 provides a robust and substantially faster alternative to the laborious genotype imputation.

2. METHOD

2.1. Larger and more diverse reference panel

To facilitate imputation of rarer variants, the current version uses the 33,000 subjects (33 K) as reference panel. It consists of 20,281 Europeans, 10,800 East Asians, 522 South Asians, 817 Africans and 533 Native Americans (Text S1, Table S1 in SI). The reference panel includes the publicly available 22,691 subjects from Haplotype Reference Consortium (HRC) and 10,262 CONVERGE. For CONVERGE subjects, we used province of origin to assign them to four populations (China North East ‐ CNE, China Central East ‐ CCE, China South East ‐ CSE and China Central South ‐ CCS). HRC subjects coming from the small Orkney (ORK) island provided the basis for an extra European population, that is, ORK. Subjects from 1 KG in HRC sample, CONVERGE and ORK along with their (a) population label, (b) first 20 ancestry principal components were used to train a quadratic discriminant model for predicting population label from principal components. Subsequently, to have more homogeneous populations in the panel, all available subjects were assigned(reassigned) population labels based on model prediction. Consequently, a subject might be re‐assigned to a different (but related) population.

To have reasonably accurate SNP LD estimators, we eliminate the rarest SNPs which did not have at least: (a) 20 alleles in European or East Asian superpopulations or (b) 5 in African, South Asian and America native superpopulations. Our final cosmopolitan reference panel contains 26 million SNPs.

2.2. Converge haplotypes

2.2.1. DNA sequencing

DNA was extracted from saliva samples using the Oragene protocol. A barcoded library was constructed for each sample. Sequencing reads obtained from Illumina Hiseq machines were aligned to Genome Reference Consortium Human Build 37 patch release 5 (GRCh37.p5) with Stampy (v1.0.17) (Lunter & Goodson, 2011) using default parameters, after filtering out reads containing adaptor sequencing or consisting of more than 50% poor quality (base quality <= 5) bases. Samtools (v0.1.18) (Li et al., 2009) was used to index the alignments in BAM format (Li et al., 2009) and Picardtools (v1.62) was used to mark PCR duplicates for downstream filtering. The Genome Analysis Toolkit's (GATK, version 2.6). Base quality score recalibration (BQSR) was then applied to the mapped sequencing reads using BaseRecalibrator in Genome Analysis Toolkit (GATK, basic version 2.6) (DePristo et al., 2011) with the known insertion and deletion (INDEL) variations in 1000 Genomes Projects Phase 1 (Genomes Project et al., 2010) and known single nucleotide polymorphisms (SNPs) from dbSNP (v137, excluding all sites added after v129) excluded from the empirical error rate calculation. GATKlite (v2.2.15) was then used to output sequencing reads with the recalibrated base quality scores while removing reads without the “proper pair” flag bit set by Stampy (1–5% of reads per sample) using the –read_filter ProperPair option (if the “proper pair” flag bit is set for a pair of reads, it means both reads in the mate‐pair are correctly oriented, and their separation is within 5 standard deviations from the mean insert size between mate‐pairs).

2.2.2. Variant calling, imputation, and phasing

Variant discovery and genotyping (for both SNPs and INDELs) at all polymorphic SNPs in 1000G Phase1 East Asian (ASN) reference panel(Genomes Project et al., 2012) was performed simultaneously using post‐BQSR sequencing reads from all samples using the GATK's UnifiedGenotyper (version 2.7‐2‐g6bda569). Variant quality score recalibration (VQSR) was then performed with GATK's VariantRecalibrator (v2.7‐4‐g6f46d11) in SNP variant calls using the SNPs in 1000 Genomes Phase 1 ASN Panel (Genomes Project et al., 2010) as the known, truth and training sets. A sensitivity threshold of 90% to SNPs in the 1000G Phase1 ASN panel was applied for SNP selection for imputation after optimizing for Transition to Transversion (TiTv) ratios in SNPs called. Genotype likelihoods (GLs) were calculated at selected sites using a sample‐specific binomial mixture model implemented in SNPtools (version 1.0), and imputation was performed at those sites without a reference panel using BEAGLE (version 3.3.2) (S. R. Browning & Browning, 2007). The second round of imputation was performed with BEAGLE on the same GLs, but only at biallelic SNPs polymorphic in the 1000G Phase 1 ASN panel using the 1000G Phase 1 ASN haplotypes as a reference panel. The genotypes derived from Beagle imputation were phased using Shapeit (version 2, revision 790) (Delaneau, Howie, Cox, Zagury, & Marchini, 2013). Genetic maps were obtained from the Impute2 (Howie et al., 2009) website. Chromosomes 13–22 and X were phased using 12 threads and default parameters. Chromosomes 1–12 were phased using 12 threads in four chunks that overlap by 1 MB. The phased chunks were ligated together using ligateHAPLOTYPES, available from the Shapeit website. A final set of allele dosages and genotype probabilities was generated from these two datasets by replacing the results in the former with those in the latter at all sites imputed in the latter. We then applied a conservative set of inclusion threshold for SNPs for genome‐wide association study (GWAS): a) p‐value for violation HWE > 10⁻⁶, b) Info score > 0.9, c) Minor‐AF (MAF) in CONVERGE >0.5% to arrive at the final set of 6,242,619 SNPs. Details can be found in (Cai et al., 2017).

2.3. Automatic detection of cohort composition

Our group has previously described, in DISTMIX paper (Lee et al., 2015), a method to estimate the ethnic composition when the cohort AF are available. However, lately some consortia do not provide such measure; they often provide only the AF for Caucasian / European cohorts. Consequently, there is a great need to estimate the ethnic composition of the cohort even when no AFs are provided.

Below is the theoretical outline of such method. Suppose that the cohort genotype is a mixture of genotypes belonging k ethnic groups from the reference panel. The G_ij denotes the genotype for the i‐th subject at the j‐th SNP which belongs to the l‐th group, let $p_j^{\left(l\right)}$ be the frequency of the reference allele frequency for this SNP in the l‐th group. Let $G{\prime }_{\mathit{ij}}=\frac{G_{\mathit{ij}}-{2p}_j^{\left(l\right)}}{\sqrt{2p_j^{\left(l\right)}\left(1-p_j^{\left(l\right)}\right)}}$ be the normalized genotype, that is, the transformation to a variable with zero mean and unit variance. Near H₀, SNP Z‐score statics Z_j ′ s have the approximately the same correlation matrix as the genotypes used to construct it, G_*j's (Lee et al., 2014); given that G′_*j′s are linear combination (with positive slope) of G_*j's, it follows that Z‐scores have the same correlation structure G′_*j′s. However, given that both G′_*j ′ s and Z_j ′ s have unit variance, it follows that the two have the same covariance (i.e. not only the same correlation) structure. Therefore, for any s ≥ 1.

E(Z_jZ_j + s) = E(G′_*jG′_*j + s), which, due independence of genotypes in different ethnic groups becomes:

$$E\left(Z_j{Z}_{j+s}\right)=\sum _{l=1}^k{w}^{\left(l\right)}E\left[{G_{*j}^{\prime }}^{\left(l\right)}{G_{*\left(j+s\right)}^{\prime }}^{\left(l\right)}\right]=\sum _{l=1}^k{w}^{\left(l\right)}\mathit{Cor}\left({G_{*j}^{\prime }}^{\left(l\right)},{G_{*\left(j+s\right)}^{\prime }}^{\left(l\right)}\right),$$ (1)

where w^(l) is the expected fraction of subjects from the entire cohort that belong to the l‐th group.

While $\mathit{Cor}\left({G_{*j}^{\prime }}^{\left(l\right)},{G_{*\left(j+s\right)}^{\prime }}^{\left(l\right)}\right)$ is unknown, it can be easily approximated using their reference panel counterparts. Thus, the weights, w^(l), can be estimated by simply regressing the product of reasonably close SNP Z‐scores, Z′_jZ′_j + s, on correlations between normalized genotypes at the same SNP pairs for all subpopulations in the reference panel. To increase bias power, we chose the parameter s, such as to maximize the variance of the within‐panel ethnic group correlations while keeping j + s‐th SNP no more than 50Kb away from j−th SNP. Because some GWAS might have numerous large signals, for example, latest height meta‐analysis (Ripke et al., 2013; Wood et al., 2014), a more accurate estimation of the weights is very likely to be obtained by substituting expected gaussian quantiles for $Z_j^{\prime }$ (see Nonparametric robust estimation of weights subsection).

Due to the strong LD among SNPs, the estimation of the correlation using all SNPs in a genome might lead to a poor regression estimate in (1). To avoid this, we sequentially split GWAS SNPs into 1000 non‐overlapping SNP sets, for example, first set consists of the 1st, 1001st, 2001st, etc. map ordered SNPs in the study. The large distances between SNPs in the same set make them quasi‐independent which, thus, improves the accuracy of the estimated correlation. W = (w^(l) ) is subsequently estimated as the average of the weights obtained from the 1000 SNP sets. Finally, we set to zero the negatives weights and normalize the remaining weights to sum to 1 (Chatzinakos et al., 2018). This method should be even more useful when we already know the approximate continental (EUR, ASN, SAS, AFR and AMR) weights (as estimated from study information) but it is not always clear how these proportions should be allocated among continental subpopulations. This further apportioning of continental weights is likely to be extremely important when the GWAS cohorts contain many admixed populations, for example, African Americans and American native populations. Consequently, when continental proportions are provided by the users, we use our automatic detection to distribute these weights to the most likely subpopulations in the reference panel. To eliminate unforeseen artifacts, we strongly recommend to the users to provide continental proportions when AFs are not available.

2.4. Nonparametric robust estimation of weights

To estimate robust weights and to avoid false positives, we apply a two‐step, robust algorithm to the Z‐scores of the SNPs. First, let $Z_{\sigma }=\left(z_{{\sigma }_1},z_{{\sigma }_2},\dots ,z_{{\sigma }_m}\right)$, where σ indicates the permutation of indices for sorting in increasing order Z‐scores, Z, for the m SNPs. Second, $z_i^{\prime }={\Phi }^{-1}\left(\frac{{\sigma }_{\iota }}{m+1}\right)$, where Φ⁻¹ is the inverse normal cumulative distribution function. Subsequently, these transformed risk scores are used for estimating ethnic weights.

2.5. Simulation

To estimate the accuracy and false positive rates of DISTMIX2, for five different cosmopolitan studies scenarios, we simulated (under H₀: no association between trait and variants) 100 cosmopolitan cohorts of 10,000 subjects for autosomal SNPs in Ilumina 1 M panel (Lee et al., 2015) using 1 KG haplotype patterns (Text S1, Table S2 in SI). The subject phenotypes were simulated independent of genotypes as a random Gaussian sample. SNP phenotype–genotype association summary statistics were computed from a correlation test.

The accuracy of the procedure was assessed by masking 5% of the SNPs (Experiment 1, Table 1 – three type of parameter settings). Subsequently, the true values and the imputed values at these masked SNPs were used to compute: (a) their correlation and (b) the mean squared error of the imputation. We assess these measures at four different levels of MAF. To compare the Type I error rate of our proposed method, DISTMIX2, we estimated the relative Type I error (the empirical divided by the nominal Type I error rate) as a function of the nominal Type I error rate, for the same four MAF levels for all the cohorts. Finally, for all the combinations between MAFs and Info we performed DISTMIX2 analyses with three different parameters for the length of the predicted window (the length of the predicted window also depends on the minimum number of measured SNPs it encompasses).

TABLE 1.

Experiment 1 parameter settings

MAF levels	Panel	Window length
MAF<5%	1 K	250Kb
5 % <MAF<10%	33 K	500Kb
10%<MAF<20%		1000Kb
20%<MAF<50%

Abbreviation: MAF, minor‐AF.

To assess the reliability of DISTMIX2 results for rare and very rare variants, for the above cohorts, we also estimate DISTMIX2 size of the test for very low MAFs (rare variants), (Experiment 2, Table 2 – two type of parameter settings). The size of the test is assessing for 5 imputation Info intervals and 6 MAF intervals.

TABLE 2.

Experiment 2 variable parameter settings. Fixed parameters for this experiment: 33 K panel and 500Kb length of predicting window

MAF levels	Info levels
0.05 % <MAF<0.5%	Info<20%
0.5 % <MAF<1%	20%<Info<40%
1 % <MAF<2%	40%<Info<60%
2 % <MAF<5%	60%<Info<80%
5 % <MAF<10%	Info>80%
10 % <MAF<50%

Abbreviation: MAF, minor‐AF.

However, given that: 1) the simulated cohorts might not reflect real data and 2) these data sets do not have the sample sizes needed to detect very rare SNPs (e.g. MAFs <0.05%), which is important for DISTMIX2 inference in practical applications, we used real data sets to create so‐called nullified data sets (Experiment 3, Table 3 – two types of parameter settings). These nullified data are based on 20‐real and mostly Caucasian GWAS schizophrenia (SCZ), attention deficit hyperactive disorder (ADHD), autism (AUT), major depressive disorder (MDD) and 16 GWAS meta‐analyses that are not yet publicly available. This approximation for null data is obtained by substituting the expected quantile of the Gaussian distribution for the (ordered) Z‐score. We note that, while the quantile estimation adjusts the non‐centrality parameter (enrichment) of the statistics to zero, it does not change the order of the statistics. One effect of this fact is that imputing statistics within/near the peak signals in original GWASs might result in increased false positive rates and, thus, the genome‐wide false positive rates might appear to be moderately inflated.

TABLE 3.

Experiment 3 variable parameter settings. Fixed parameters for this experiment: 33 K panel and 500Kb window length

MAF levels	Info levels
MAF<0.05%	Info<20%
0.05 % <MAF<0.5%	20 % <Info<40%
0.5 % <MAF<1%	40 % <Info<60%
1 % <MAF<2%	60 % <Info<80%
2 % <MAF<5%	Info>80%
5 % <MAF<10%
10 % <MAF<50%

Abbreviation: MAF, minor‐AF.

2.6. Applications in psychiatric GWAS

We applied DISTMIX2 to a subset of the psychiatric summary datasets available for download from Psychiatric Genetics Consortium (PGC‐ http://www.med.unc.edu/pgc/), that is, SCZ, ADHD, AUT, eating disorder (ED), bipolar (BIP) disorder, MDD and post‐traumatic stress disorder (PTSD) (see Table 4 for references). For PTSD, we also analyzed an admixed African (PTSD‐AA) GWAS by combing 20 PTSD African cohorts, which were part of the recent PTSD study (Nievergelt et al., 2019), by using METAL (Willer, Li, & Abecasis, 2010). Based on the results from simulations under the null hypothesis (Experiment 1), for all these applications we used: a) the larger 33 K size panel and b) a length of the predicted window (500Kb). To improve the imputation of the unmeasured SNPs for SCZ, we denote as “measured SNPs” only those with very high information (Info>0.997). For the ADHD, AUT, BIP, MDD, PTSD and PTSD‐AA data sets, because the imputation information is not available, we accept as measured SNPs the set consisting of the intersection between SNPs in each GWAS and the above SCZ's “measured” SNPs. Where available (e.g. MDD), we also filtered out SNPs with effective sample sizes below the maximum.

TABLE 4.

Description of data sets used for practical application

Trait	Trait abbreviation	Dataset description
Schizophrenia	SCZ	PGC SCZ1
Attention deficit hyperactivity disorder	ADHD	PGC ADHD2
Autism	AUT	PGC AUT3
Bipolar	BIP	PGC BIP4
Eating disorders	ED	PGC ED5
Major depression disorder	MDD	PGC MDD6
Post‐traumatic stress disorder	PTSD	PGC PTSD7

Note: ¹Schizophrenia Working Group of the Psychiatric Genomics, C., 2014. ²Demontis, D. et al., 2019. ³Anney, R. J. L. et al., 2017. ⁴Stahl, E. A. et al., 2019. ⁵ Duncan, L. et al., 2017. ⁶Wray, N. R. et al., 2018. ⁷Nievergelt, C. M. et al., 2019.

2.7. Increasing power of TWAS tools

TWAS methods (Barbeira et al., 2018; Chatzinakos et al., 2020; Chatzinakos et al., 2018; Mancuso et al., 2018), are based on genetically regulated gene expression (GReX) models (Gamazon et al., 2015) in order to estimate gene‐associations with the trait. These GReX models are practically a tissue‐specific linear combination of eQTL SNPs for each gene. Often the GWAS (i.e. TWAS input) does not include all those eQTL SNPs from GReX models. To assess the decrease in power of TWAS tools not imputing SNP internally, we applied TWAS JEPEGMIX2 (Chatzinakos et al., 2018) using GTEx version 6 release GReX models (Barbeira et al., 2018; Gamazon et al., 2015) to PGC data sets above and to Re‐Experiencing Symptoms GWAS (PTSD‐REX) (Gelernter et al., 2019) [having summary statistics for only 4,374,623 SNPs] with and without re‐imputing GWAS first.

3. RESULTS

For Illumina 1 M SNPs (Marenne et al., 2011) that were masked, and then imputed, DISTMIX2 with our novel automatic ethnic weight detection, controls the false positive rates at or below nominal threshold, even at very low type I error, for example, 10⁻⁶ (Text S2, Figure S1 in SI). R² between true values and estimated ones is above 0.92 for our five simulated mixed‐cohort scenarios (Text S2, Figures S2‐S6 in SI). Also, DISTMIX2 imputed statistics had very good mean squared error (RMS) (Text S2, Figures S7‐S11 in SI). For the above three measurements (size of the test, R² and RMS) the setting of 250Kb for the length of the predicted window was the least precise, while 500Kb and 1000Kb had practically identical precision.

For rare and very rare variants, the size of the test was up to 300–1,000X higher than the nominal one and even up to 5,000–10,000X for cohorts that have large fractions of subpopulations that are underrepresented in the reference panel (e.g. Americans, Africans etc.), especially for the setting Minor Allele Frequency (MAF), 0.05%<MAF<0.5% and Information (Info), Info<0.2 (Text S2, Figures S12‐S47 in SI).

For the “nullified” data sets, for example, those obtained from real data sets by substituting the study Z‐scores by their expected quantile under the null hypothesis (H₀) (Method evaluation section and Text S2, Figures S42‐S48 in SI), DISTMIX2 controlled reasonably well the size of the test ‐ up to 20X higher than the nominal rate (even for SNPs with low MAFs and low Info).The minimum GWAS p‐values for the nullified data sets that were imputed ranged between 8.13 * 10⁻⁷ and 1.11 * 10⁻¹¹. By fitting a normal distribution to −log₁₀(minimum p‐values), we estimated the mean to be 8.655 and the standard deviation to be 1.172. Using as criterion the conservative three standard deviations above the mean, we obtain from these realistic data a 12.17 as the upper bound for the −log₁₀ (p‐value). That is in DISTMIX2 applications in PGC GWAS, a conservative threshold for significance is 10⁻¹², regardless of imputation Info and SNP MAF. Consequently, in all applied analyses in this paper we added this very stringent threshold for DISTMIX2 imputed summary statistics. Using as criterion the even more conservative five standard deviations above the mean (the very conservative Chebyshev inequality for the upper bound of the p‐value of exceeding this threshold $=\frac{1}{5^2}=0.04)$, we obtained a 14.515 upper bound for the −log₁₀ (p‐values), that is a super‐conservative significance threshold of 3 * 10⁻¹⁵.

For the applications to PGC GWAS (Table 4), we constructed Manhattan plots for all autosome chromosomes (1–22) and, individually, for chromosomes harboring novel signals (defined as imputed SNPs with statistically significant p‐values that are at least 250Kb away from the reported GWAS signal) (Figure 1 and Figure 2, Text S3, Figure S49‐S61 in SI). Furthermore, in order to investigate the potential risk of genomic inflation, we constructed Q‐Q plots for the following three scenarios (i) all the SNPs, (ii) rare SNPs and (iii) common SNPS, for all the traits (Figure 3, Text S3, Figures S62‐S84 in SI). Finally, we compared DISTMIX2 with ARDISS (Text S3, Figures S85‐S91 in SI). Since ARDISS software did not provide minor allele frequency and Info estimation, we subset the imputed signals according to DISTMIX2 for MAF > 0.05. For all Manhattan plots we drew two dash lines denoting threshold for statistically significant signals. The red line is the default genome‐wide threshold of p = 5 * 10⁻⁸, which is applicable to signals from measured SNPs and common imputed SNPs with high Info values. The purple line at p = 10⁻¹² is the threshold to be used for rare/very rare variants and/or variants with low information; it corresponds to the above mentioned upper bound for nullified data. As an illustration, we present PTSD Manhattan plot for all chromosomes, only for chromosome 1 and Q‐Q plots for all signals (Figure 1, Figure 2 and Figure 3 respectively).

FIGURE 1.

Manhattan plot for chromosomes 1–22 for PTSD. ● denotes reported signals from the original GWAS and the remain symbols and colors denote DISTMIX2 imputed signals. Among imputed signals blue denotes info<0.2, red denotes 0.2 < info<0.4, cyan denotes 0.4 < info<0.6, brown denotes 0.6 < info<0.8, orange denotes info>0.8, □ denotes MAF <0.05%, △ denotes 0.05% < MAF < 0.5%, ▽denotes 0.5% < MAF < 1%, + denotes 1% < MAF < 2%, ◊ denotes 2% < MAF < 5%, x denotes 5% < MAF < 10% and * denotes 10% < MAF < 50%. The red line is the default genome‐wide threshold of p = 5*10e‐8, which is applicable common SNPs with moderate to large Info values. The purple line at p = 10e‐12 is the threshold to be used for rare and/or low Info variants. GWAS, genome‐wide association studies; MAF, minor‐AF; PTSD, post‐traumatic stress disorder; SNPs, single nucleotide polymorphisms [Color figure can be viewed at wileyonlinelibrary.com]

FIGURE 2.

Manhattan plot for chromosome 1 for PTSD (see Figure 1 for background). PTSD, post‐traumatic stress disorder [Color figure can be viewed at wileyonlinelibrary.com]

FIGURE 3.

Q‐Q plot for all SNPs of imputed PTSD GWAS. GWAS, genome‐wide association studies; PTSD, post‐traumatic stress disorder; SNPs, single nucleotide polymorphisms [Color figure can be viewed at wileyonlinelibrary.com]

These applications of DISTMIX2 to PGC data sets suggested the existence of numerous new signals, most associated with rare SNPs (see Table 5). For instance, in chromosome 12 for schizophrenia (rs143374), with MAF=0.0007, Info=0.245 and p‐value=9.26 * 10⁻⁴⁶ the magnitude of the p‐value along with the lambda of the correspond Q‐Q plot of the SCZ trait suggested that this signal is likely not to be an artifact (above the most stringent threshold), in chromosome 11 for ADHD (rs5681132) where the MAF=0.0004, the Info= 0.018 and p‐value=7.40 * 10⁻¹⁶, in chromosome 22 for AUT (rs1380986), with MAF=0.0006, Info=0.498 and p‐value=8.01 * 10⁻¹⁵, in chromosome 7 for BIP (rs76350051), with MAF=0.0004, Info=0.04 and p‐value=2.47 * 10⁻³⁷, in chromosome 12 for MDD (rs567868887), with MAF=0.0009, Info=0.28 and p‐value=1.57 * 10⁻⁵⁵, in chromosome 1 for PTSD (rs150642422), with MAF = 0.0002, Info = 0.5512 and p‐value=1.3 * 10⁻⁴³, and in chromosome 1 for PTSD‐AA (rs111819353), with MAF = 0.001, Info = 0.3121 and p‐value=1.16 * 10⁻¹⁷.

TABLE 5.

Best three signals for each PGC dataset

Trait	rs_id	chr	bp	P pval	Info	MAF	Genes/Distance (Kbp)
ADHD	rs568113293	11	54,899,533	7.40 * 10−16	0.0189	0.00049	TRIM48,130.125 RP11‐72 M10.2,135.351
	rs544637819	3	15,310,737	1.78 * 10−14	0.1543	0.00171	SH3BP5, 0 SH3BP5‐AS1, 4.737
	chr6:30450452	6	30,450,452	6.44 * 10−13	0.0698	0.00151	RANP1, 3.265 HLA‐E, 6.792
AUT	rs138098629	22	36,584,165	8.01 * 10−15	0.4980	0.00063	APOL4, 1.007 MTND1P10, 8.732
BIP	rs76350051	7	64,164,245	2.42 * 10−37	0.0417	0.00046	ZNF107, 0 RP11‐561 N12.7, 16.474
	rs138549126	3	52,592,843	6.65 * 10−16	0.073	0.00052	SMIM4, 0 PBRM1, 0
	rs149257260	15	71,600,045	1.40 * 10−15	0.4246	0.00017	THSD4, 0 RP11‐592 N21.1, 33.421
ED	rs78958069	8	43,539,021	4.17 * 10−10	0.005	0.0002	RP11‐643 N23.2, 10.803 AC134698.1, 123.105
	rs144485994	20	4,963,320	5.18 * 10−9	0.15	0.0001	SLC23A2, 0 RP5‐1116H23.1, 30.846
MDD	rs567868887	12	31,931,432	1.57 * 10−55	0.2800	0.00098	H3F3C, 12.691 RP11‐467 L13.5, 23.377
	rs112241719	11	111,514,969	8.14 * 10−45	0.4900	0.00025	SIK2, 0 AP000925.2, 26.711
	rs182264017	1	188,992,506	5.05 * 10−44	0.2775	0.00035	LINC01035, 0 CLPTM1LP1, 12.586
PTSD	rs150642422	1	89,223,553	1.3 * 10−43	0.5512	0.0002	PKN2, 0 RNU6‐125P, 58.909
	rs7521099	1	88,875,371	1.4 * 10−15	0.4521	0.0002	GBP3, 248.796
	rs111229512	2	31,800,662	6.7 * 10−14	0.6325	0.0002	BP7, 373.881 GBP4, 423.278
PTSD‐AA	rs111819353	7	127,907,569	1.1 * 10−17	0.312	0.001	LEP, 9.8 RBM28,
	rs370549636	20	58,131,312	7.2 * 10−15	0.37	0.001	PHACTR3, 21.252 PIEZO1P1,95.42
	rs554371692	13	20,632,168	3.2 * 10−12	0.21	0.001	ZMYM2, 0 KRR1P1, 21.222
SCZ	rs559199817	3	17,267,731	1.30 * 10−87	0.0213	0.00073	TBC1D5, 0 AC090644.1, 90.517
	rs143337489	12	11,2089,686	9.26 * 10−46	0.2464	0.00019	BRAP, 0 PCNPP1, 17.97
	rs193224736	16	8,593,132	3.79 * 10−21	0.28476	0.00018	RP11‐483 K5.3, 11.117 TMEM114, 26.37

Abbreviations: ADHD, attention deficit hyperactive disorder; AUT, autism; BIP, bipolar; ED, eating disorder; MAF, minor‐AF; MDD, major depressive disorder; PTSD, post‐traumatic stress disorder; PTSD‐AA, Africanpost‐traumatic stress disorder; SCZ, schizophrenia.

Note: Bolded and underlined entries correspond to the most stringent threshold of p < 3 * 10⁻¹⁵, not bolded but underlined to the second most conservative threshold 3 * 10⁻¹⁵ < p < 10⁻¹² and not bolded not underlined 10⁻¹² < p < 5 * 10⁻⁸.

When imputing in parallel SNPs regions of 40 Mbp, the analysis of each data set had a running time of less than 5 days on a cluster node with 4x Intel Xeon 6 core 2.67 GHz.

By imputing GWAS before a generic TWAS analysis (Table 6), we could impute TWAS signals for a larger number of genes, especially for the traits with the smallest number of variants (i.e. PTSD‐REX). Additionally, the Q‐Q plots (Text S3, Figures S92‐S96 in SI) showed that all the analysis gained statistical power when we applied the imputation step.

TABLE 6.

Number genes with successful TWAS prediction under no imputation and imputation scenarios

Trait	Number of original variants	Number of Imputed variants	Number of gene‐tissue pairs with TWAS statistics under no imputation scenario	Number of gene‐tissue pairs with TWAS statistics under imputation scenario
BIP	13,413,244	13,800	26,772	26,894
MDD	13,554,550	14,805	26,734	26,889
PTSD	9,766,174	27,439	26,513	26,892
PTSD‐REX	4,374,623	189,823	21,634	26,894
SCZ	14,225,895	6,444	26,846	26,894

Abbreviation: TWAS, transcriptome wide association study.

4. DISCUSSION

DISTMIX2, is a software/method for “off‐the‐shelf” direct imputation of the unmeasured SNP statistics in cosmopolitan cohorts. The main features of the updated version are: (a) a much larger (33 K subjects) and more diverse (includes ~11 K Han Chinese) reference panel and (b) a procedure for estimating the ethnic composition of the cohort without the need for AF information. Using simulated and the very novel nullified (real) data sets we propose conservative and very conservative significance thresholds for low info and low MAF signal. Application of DISTMIX2 to PGC data sets provides numerous new signal regions, most harboring rarer variants.

It is noteworthy that we uncovered a potentially very strong signal in PGC PTSD (p < 10⁻⁴²) in a rare variant of PKN2 gene, when the initial publication reported only 3 marginal signals on common variants. While PKN2 has not been extensively characterized, it would be a potentially interesting target in PTSD given that it has been associated with Rho/Rock and mTOR cell pathways previously associated with fear learning and processing (Lachmann et al., 2011; Schmidt, Durgan, Magalhaes, & Hall, 2007; Wallace, Magalhaes, & Hall, 2011). It has also been associated with hippocampal functioning and development (Buchser, Slepak, Gutierrez‐Arenas, Bixby, & Lemmon, 2010; Schmidt et al., 2007). All these cellular and neurobiological processes have been established as important in PTSD development and recovery (Maddox, Hartmann, Ross, & Ressler, 2019; Parsons & Ressler, 2013).

Due to our reassignment of subjects to subpopulations when constructing the 33 K reference panel, the naive assignment of the pre‐estimated weights to only specific subpopulations from the reference panel that are considered the closest ones to the perceived cohort composition, can greatly increase the type I error (false positives). For that reason, when AF is not available, we recommend that users provide continental cohort weights (i.e. European [EUR], East Asian [ASN], South Asian [SAS], African [AFR] and America native [AMR]) and our software automatically will allocate these meta‐weights to the most likely within‐continent subpopulations. However, when AF is available there is no need to provide this additional information.

DISTMIX2 maintains the type I error reasonably accurately, even for low MAFs and low Info variants, especially for mostly European and East Asian cohorts that are overrepresented in our reference panel. When MAF > 5% (common variants), DISTMIX2 appears to maintain the false positive rates up to an order of magnitude higher than the nominal ones for all levels of information. Simulation results suggest that, when a larger part of study cohort consist of subpopulations underrepresented in our reference panel, it is reasonable to lower (by a factor of ~10,000) the genome‐wide Bonferroni threshold of significance for p‐values of imputed rarer variants. For imputed variants (especially rarer or with lower Info) in study of Europeans, we also use novel nullified data sets to propose a conservative threshold for significance of p = 10⁻¹² and a very conservative threshold of p = 3 * 10⁻¹⁵. The yield of just one strong signal close to the LEP gene for PTSD‐AA sample also suggests that the guidance also holds for the continental cohorts less represented in the reference panel. These rules‐of‐thumb are likely to be useful for similar methods when users enlarge their reference panels.

The length of the prediction window (250Kb, 500Kb, 1000Kb) is an important design parameter due to its implications for speed and precision of analyses. Simulations results suggest that, while the accuracies for 500Kb and 1000Kb estimates are very close, the computational burden increases ~2.5 times for the 1000 kb window. For that reason, we recommend that researchers use a 500Kb prediction window.

While mentioned only briefly in this manuscript, for application we used as “measured” SNP in the input summary statistic file only the GWAS SNPs reported to have close to perfect information and/or effective sample size. Our approach is rooted in preserving the cardinal assumption, of our and all but one other imputation methods (Rueger, McDaid, & Kutalik, 2018), that the LD between SNP Z‐scores is very well approximated by the LD of the same SNPs in the reference panels. It is well known that when there are non‐negligible missing rates for the variant pair this assumption is not met (Rueger et al., 2018). While the LD of Z‐scores can be estimated by making reasonably realistic assumptions about co‐missingness patterns of such SNP pairs, to avoid even the rarer circumstances in which these assumptions might not be met, we decided to avoid such an approach. Consequently, we employed (and recommend) the conservative approach of deeming as measured only SNPs with close to perfect imputation information and/or effective sample sizes in the original GWAS.

In the applications to PGC GWAS, the very low MAF and Info for some SNPs were associated with up to four orders of magnitude inflation in false positive rates, especially when the cohorts contain many subjects belonging to populations that are underrepresented in the reference panel. While signals for rarer SNPs from PGC data sets reported in this paper can be viewed as “softer” signals than the ones associated with common and high Info variants, the very low p‐values for some of them (e.g. p < 10⁻⁴² in PKN2 gene for PTSD) suggest that most of these signals are likely to be real. This suggestion is enhanced by the fact that, to avoid the pitfalls of estimating covariances from just very few minor alleles, we did not include in the imputation panel SNPs that do not have at least: (a) 20 minor alleles in the Europeans or East Asians or (b) 5 minor alleles in all other continental groups. Nonetheless, we recognize that signals for these SNPs should be treated with more skepticism than the more common/higher Info variants and subjected to more stringent wet‐lab validations.

Finally, we recommend users to re‐impute summary statistics using the latest reference panels before employing most omics‐based prediction tools, for example, TWAS (Chatzinakos, Georgiadis, & Daskalakis, 2021). The re‐imputation of GWAS summary statistics is likely to increase the number of gene signals, especially for studies that employed older and smaller imputation panels. For instance, besides increasing the number of genes with TWAS predictions, the PTSD‐REX imputation increased the significance of the MAPT (TWAS p = 1.4 * 10⁻⁵ to p = 1.12 * 10⁻⁹) and PLEKHM1 (TWAS p = 1.82 * 10⁻⁸ to p = 2.72 * 10⁻⁹) genes for the Cortex tissue analyses. There is no such need when using TWAS methods from our group (Chatzinakos et al., 2020; Chatzinakos et al., 2018; Lee et al., 2015; Lee et al., 2016) because they impute all missing eQTL SNPs by default].

CONFLICT OF INTEREST

Nikolaos P. Daskalakis has held a part‐time paid position at Cohen Veteran Biosciences, has served as a paid consultant for Sunovion Pharmaceuticals and is on the scientific advisory board for Sentio Solutions, Inc. for unrelated work. The remaining authors have nothing to disclose.

AUTHORS' CONTRIBUTIONS

Chris Chatzinakos and Silviu‐Alin Bacanu conceived and designed the method, simulations and applications. Chris Chatzinakos designed the code and performed all computations, conducted all simulations and produced the application results, created all visualizations and packaged/validated/maintained the software. Silviu‐Alin Bacanu supervised the work. Vladimir I. Vladimirov, Bradley T. Webb, Brien P. Riley and Nikolaos P. Daskalakis contributed to the interpretation of the simulation experiments and application results. Donghyung Lee and Na Cai contributed to the data preparation. Jonathan Flint, Kenneth S. Kendler and Kerry J. Ressler gave inputs regarding the overall interpretation of the method and results. Nikolaos P. Daskalakis gave input in the presentation of results and writing of the manuscript. Chris Chatzinakos and Silviu‐Alin Bacanu wrote the first draft and revisions of the manuscript. All authors commented and edited all the version of the manuscript.

Supporting information

Appendix S1: Supporting information

Chatzinakos C, Lee D, Cai N, et al. Increasing the resolution and precision of psychiatric genome‐wide association studies by re‐imputing summary statistics using a large, diverse reference panel. Am J Med Genet Part B. 2021;186B:16–27. 10.1002/ajmg.b.32834

DATA AVAILABILITY STATEMENT

The data (GWAS) that support the findings of this paper, except PTSD‐AA and PTSD‐REX, are openly available in https://www.med.unc.edu/pgc/