Quantifying concordant genetic effects of de novo mutations on multiple disorders
Abstract
Exome sequencing on tens of thousands of parentproband trios has identified numerous deleterious de novo mutations (DNMs) and implicated risk genes for many disorders. Recent studies have suggested shared genes and pathways are enriched for DNMs across multiple disorders. However, existing analytic strategies only focus on genes that reach statistical significance for multiple disorders and require large trio samples in each study. As a result, these methods are not able to characterize the full landscape of genetic sharing due to polygenicity and incomplete penetrance. In this work, we introduce EncoreDNM, a novel statistical framework to quantify shared genetic effects between two disorders characterized by concordant enrichment of DNMs in the exome. EncoreDNM makes use of exomewide, summarylevel DNM data, including genes that do not reach statistical significance in singledisorder analysis, to evaluate the overall and annotationpartitioned genetic sharing between two disorders. Applying EncoreDNM to DNM data of nine disorders, we identified abundant pairwise enrichment correlations, especially in genes intolerant to pathogenic mutations and genes highly expressed in fetal tissues. These results suggest that EncoreDNM improves current analytic approaches and may have broad applications in DNM studies.
Editor's evaluation
Lu et al. provide a powerful statistical method that measures excess sharing of de novo mutations between pairs of disorders. This method extends the concept of 'genetic correlation' to disorders caused by denovo mutations, measuring the correlation in excess denovo mutations in genomewide genes for different classes of mutations. The authors apply the method to nine disorders including a developmental disorder, autism spectrum disorder, congenital heart disease, schizophrenia, and intellectual disability, finding a statistically significant overlap between 12 pairs of disorders in de novo mutations that cause a loss of gene function. This method will be of interest to researchers working on disorders caused by denovo mutations.
https://doi.org/10.7554/eLife.75551.sa0Introduction
De novo mutations (DNMs) can be highly deleterious and provide important insights into the genetic cause for disease (Veltman and Brunner, 2012). As the cost of sequencing continues to drop, wholeexome sequencing (WES) studies conducted on tens of thousands of family trios have pinpointed numerous risk genes for a variety of disorders (Lelieveld et al., 2016; Kaplanis et al., 2020; Satterstrom et al., 2020). In addition, accumulating evidence suggests that risk genes enriched for pathogenic DNMs may be shared by multiple disorders (Hoischen et al., 2014; Fromer et al., 2014; Homsy et al., 2015; Li et al., 2016; Nguyen et al., 2020). These shared genes could reveal biological pathways that play prominent roles in disease etiology and shed light on clinically heterogeneous yet genetically related diseases (Homsy et al., 2015; Li et al., 2016; Nguyen et al., 2020).
Most efforts to identify shared risk genes directly compare genes that are significantly associated with each disorder (Nguyen et al., 2017; Willsey et al., 2018). There have been some successes with this approach in identifying shared genes and pathways (e.g. chromatin modifiers) underlying developmental disorder (DD), autism spectrum disorder (ASD), and congenital heart disease (CHD), thanks to the large trio samples in these studies (Kaplanis et al., 2020; Satterstrom et al., 2020; Jin et al., 2017), whereas findings in smaller studies remain suggestive (Allen et al., 2013; Jin et al., 2020b). Even in the largest studies to date, statistical power remains moderate for risk genes with weaker effects (Kaplanis et al., 2020; Howrigan et al., 2020). It is estimated that more than 1000 haploinsufficient genes contributing to developmental disorder risk have not yet achieved statistical significance in large WES studies (Kaplanis et al., 2020). Therefore, analytic approaches that only account for top significant genes cannot capture the full landscape of genetic sharing in multiple disorders. Recently, a Bayesian framework named mTADA was proposed to jointly analyze DNM data of two diseases and improve risk gene mapping (Nguyen et al., 2020). Although mTADA produces estimates for the proportion of shared risk genes, the statistical property of these parameter estimates has not been studied. There is a pressing need for powerful, robust, and interpretable methods that quantify concordant DNM association patterns for multiple disorders using exomewide DNM counts.
Recent advances in estimating genetic correlations using summary data from genomewide association studies (GWAS) may provide a blueprint for approaching this problem in DNM research (Zhang et al., 2021a). Modeling ‘omnigenic’ associations as independent random effects, linear mixedeffects models leverage genomewide association profiles to quantify the correlation between additive genetic components of multiple complex traits (Lee et al., 2012; BulikSullivan et al., 2015; Lu et al., 2017; Ning et al., 2020). These methods have identified ubiquitous genetic correlations across many human traits and revealed significant and robust genetic correlations that could not be inferred from significant GWAS associations alone (Shi et al., 2017; Brainstorm, 2018; Guo et al., 2021; Zhang et al., 2021b).
Here, we introduce EncoreDNM (Enrichment correlation estimator for De Novo Mutations), a novel statistical framework that leverages exomewide DNM counts, including genes that do not reach exomewide statistical significance in singledisorder analysis, to estimate concordant DNM associations between disorders. EncoreDNM uses a generalized linear mixedeffects model to quantify the occurrence of DNMs while accounting for de novo mutability of each gene and technical inconsistencies between studies. We demonstrate the performance of EncoreDNM through extensive simulations and analyses of DNM data of nine disorders.
Results
Method overview
DNM counts in the exome deviate from the null (i.e. expected counts based on de novo mutability) when mutations play a role in disease etiology. Disease risk genes will show enrichment for deleterious DNMs in probands and nonrisk genes may be slightly depleted for DNM counts. Our goal is to estimate the correlation of such deviation between two disorders, which we refer to as the DNM enrichment correlation. More specifically, we use a pair of mixedeffects Poisson regression models (Munkin and Trivedi, 1999) to quantify the occurrence of DNMs in two studies.
Here, ${Y}_{i1},{Y}_{i2}$ are the DNM counts for the ith gene and ${N}_{1},{N}_{2}$ are the number of parentproband trios in two studies, respectively. The log Poisson rates of DNM occurrence are decomposed into three components: the elevation component, the background component, and the deviation component. The elevation component ${\beta}_{k}$ ($k=\mathrm{1,2}$) is a fixed effect term adjusting for systematic, exomewide bias in DNM counts. One example of such bias is the batch effect caused by different sequencing and variant calling pipelines in two studies. The elevation parameter ${\beta}_{k}$ tends to be positive when DNMs are overcalled with higher sensitivity and negative when DNMs are undercalled with higher specificity (Wei et al., 2015). The background component $\mathrm{l}\mathrm{o}\mathrm{g}\left(2{N}_{k}{m}_{i}\right)$ is a genespecific fixed effect that reflects the expected mutation counts determined by the genomic sequence context under the null (Samocha et al., 2014). ${m}_{i}$ is the de novo mutability for the ith gene, and $2{N}_{1}{m}_{i}$ and $2{N}_{2}{m}_{i}$ are the expected DNM counts in the ith gene under the null in two studies. The deviation component ${\varphi}_{ik}$ is a genespecific random effect that quantifies the deviation of DNM profile from what is expected under the null (i.e. no risk genes for the disorder). ${\varphi}_{i1}$ and ${\varphi}_{i2}$ follow a multivariate normal distribution with dispersion parameters ${\sigma}_{1}$ and ${\sigma}_{2}$ and a correlation $\rho $. A larger value of the dispersion parameter ${\sigma}_{k}$ indicates a more substantial deviation from the null. That is, DNM counts show strong enrichment in some genes and depletion in other genes compared to the expectation based on de novo mutability. A smaller value of ${\sigma}_{k}$ suggests that the DNM count data is well in line with what is expected based on the null model. DNM enrichment correlation is denoted by $\rho $ and is our main parameter of interest. It quantifies the concordance of DNM burden in two disorders.
Parameters in this model can be estimated using a Monte Carlo maximum likelihood estimation (MLE) procedure. Standard errors of the estimates are obtained through inversion of the observed Fisher information matrix. In practice, we use annotated DNM data as input and fit mixedeffects Poisson models for each variant class separately: loss of function (LoF), deleterious missense (Dmis, defined as MetaSVMdeleterious), tolerable missense (Tmis, defined as MetaSVMtolerable), and synonymous (Figure 1). More details about model setup and parameter estimation are discussed in Materials and methods.
Simulation results
We conducted simulations to assess the parameter estimation performance of EncoreDNM in various settings. We focused on two variant classes, that is, Tmis and LoF variants, since they have the highest and lowest median mutabilities in the exome. We used EncoreDNM to estimate the elevation parameter $\beta $, dispersion parameter $\sigma $, and enrichment correlation $\rho $ (Materials and methods). Under various parameter settings, EncoreDNM always provided unbiased estimation of the parameters (Figure 2 and Figure 2—figure supplements 1–2). Furthermore, the 95% Wald confidence intervals achieved coverage rates close to 95% under all simulation settings, demonstrating the effectiveness of EncoreDNM to provide accurate statistical inference.
Next, we compared the performance of EncoreDNM with mTADA (Nguyen et al., 2020), a Bayesian framework that estimates the proportion of shared risk genes for two disorders. First, we simulated DNM data under the mixedeffects Poisson model. We evaluated two methods across a range of combinations of elevation parameter, dispersion parameter, and sample size for two disorders. The false positive rates for our method were wellcalibrated in all parameter settings, but mTADA produced false positive findings when the observed DNM counts were relatively small (e.g. due to reduced elevation or dispersion parameters or a lower sample size; Figure 3a). We also assessed the statistical power of two approaches under a baseline setting where false positives for both methods were controlled. As enrichment correlation increased, EncoreDNM achieved universally greater statistical power compared to mTADA (Figure 3b).
To ensure a fair comparison, we also considered a misspecified model setting where we randomly distributed the total DNM counts for each disorder into all genes with an enrichment in causal genes (Materials and methods). EncoreDNM showed wellcontrolled false positive rate across all simulation settings, whereas severe inflation of false positives arose for mTADA when the total mutation count, the proportion of probands that can be explained by DNMs, or the sample size were small (Figure 3c). Furthermore, we compared the statistical power of two methods under this model in a baseline setting where false positive rate was controlled. EncoreDNM showed higher statistical power compared to mTADA as the fraction of shared causal genes increased (Figure 3d).
Pervasive enrichment correlation of damaging DNMs among developmental disorders
We applied EncoreDNM to DNM data of nine disorders (Supplementary file 1STable 1; Materials and methods): developmental disorder (n=31,058; number of trios; Kaplanis et al., 2020), autism spectrum disorder (n=6430; Satterstrom et al., 2020), schizophrenia (SCZ; n=2772; Howrigan et al., 2020), congenital heart disease (n=2645; Jin et al., 2017), intellectual disability (ID; n=820; Lelieveld et al., 2016), Tourette disorder (TD; n=484) Willsey et al., 2017, epileptic encephalopathies (EP; n=264; Allen et al., 2013), cerebral palsy (CP; n=250; Jin et al., 2020b), and congenital hydrocephalus (CH; n=232; Jin et al., 2020a). In addition, we also included 1789 trios comprising healthy parents and unaffected siblings of autism probands as controls (Krumm et al., 2015).
We first performed singletrait analysis under the mixedeffects Poisson model for each disorder. The estimated elevation parameters (i.e. $\beta $) were negative for almost all disorders and variant classes (Figure 4a), with LoF variants showing particularly lower parameter estimates. This may be explained by more stringent quality control in LoF variant calling (Jin et al., 2017) and potential survival bias (Lek et al., 2016). It is also consistent with a depletion of LoF DNMs in healthy control trios (Homsy et al., 2015). The dispersion parameter estimates (i.e. $\sigma $) were higher for LoF variants than other variant classes (Figure 4b), which is consistent with our expectation that LoF variants have stronger effects on disease risk and should show a larger deviation from the null mutation rate in disease probands. We also compared the goodness of fit of our proposed mixedeffects Poisson model to a simpler fixedeffects model without the deviation component (Materials and methods). The expected distribution of recurrent DNM counts showed substantial and statistically significant improvement under the mixedeffects Poisson model (Figure 4c–f, Figure 4—figure supplement 1, and Supplementary file 1STable 2).
Next, we estimated pairwise DNM enrichment correlations for 9 disorders. In total, we identified 25 pairs of disorders with significant correlations at a false discovery rate (FDR) cutoff of 0.05 (Figure 5 and Figure 5—figure supplement 1), including 12 significant correlations for LoF variants, 7 for Dmis variants, 5 for Tmis variants, and only 1 significant correlation for synonymous variants. Notably, all significant correlations are positive (Supplementary file 1STable 3). No significant correlation was identified between any disorder and healthy controls (Figure 5—figure supplement 2). This is consistent with our expectation, since DNMs in the control groups will distribute proportionally according to the de novo mutability without showing enrichment in certain genes. The number of identified significant correlations for each disorder was proportional to the sample size in each study (Spearman correlation = 0.70) with controls being a notable outlier (Figure 5—figure supplement 3).
We identified highly concordant and significant LoF DNM enrichment among developmental disorder, autism, intellectual disability, and congenital heart disease, which is consistent with previous reports (Li et al., 2016; Nguyen et al., 2020; Nguyen et al., 2017; Hormozdiari et al., 2015). Schizophrenia shows highly significant LoF correlations with developmental disorder (p=2.0e3) and intellectual disability (3.7e5). The positive enrichment correlation between autism and cerebral palsy in LoF variants ($\rho $=0.81, p=3.3e3) is consistent with their cooccurrence (Christensen et al., 2014). The high enrichment correlation between intellectual disability and cerebral palsy in LoF variants ($\rho $=0.68, p=1.0e4) is consistent with the associations between intellectual disability and motor or nonmotor abnormalities caused by cerebral palsy (Reid et al., 2018). A previous study also suggested significant genetic sharing of intellectual disability and cerebral palsy by overlapping genes harboring rare damaging variants (Jin et al., 2020b). Here, we obtained consistent results after accounting for de novo mutabilities and potential confounding bias.
Some significant correlations identified in our analysis are consistent with phenotypic associations in epidemiological studies, but have not been reported using genetic data to the extent of our knowledge. For example, the LoF enrichment correlation between congenital heart disease and cerebral palsy ($\rho $=0.88, p=1.7e3) is consistent with findings that reduced supply of oxygenated blood in fetal brain due to cardiac malformations may be a risk factor for cerebral palsy (Garne et al., 2008). The enrichment correlation between intellectual disability and congenital hydrocephalus in LoF variants ($\rho $=0.63, p=2.4e3) is consistent with lower intellectual performance in a proportion of children with congenital hydrocephalus (Lumenta and Skotarczak, 1995).
Genes showing pathogenic DNMs in multiple disorders may shed light on the mechanisms underlying enrichment correlations (Supplementary file 1STable 4). We identified five genes (CTNNB1, NBEA, POGZ, SPRED2, and KMT2C) with LoF DNMs in five different disorders and 21 genes had LoF DNMs in four disorders (Supplementary file 1STable 5). These 26 genes with LoF variants in at least four disorders were significantly enriched for 63 gene ontology (GO) terms with FDR <0.05 (Supplementary file 1STable 6). Chromatin organization (p=7.8e11), nucleoplasm (p=2.8e10), chromosome organization (p=6.8e10), histone methyltransferase complex (p=1.4e9), and positive regulation of gene expression (p=2.2e9) were the most significantly enriched GO terms. One notable example consistently included in these gene sets is CTNNB1 (Figure 5—figure supplement 4). It encodes $\beta $catenin, is one of the only two genes reaching genomewide significance in a recent WES study for cerebral palsy (Jin et al., 2020b), and also harbors multiple LoF variants in developmental disorder, intellectual disability, autism, and congenital heart disease. It is a fundamental component of the canonical Wnt signaling pathway which is known to confer genetic risk for autism (O’Roak et al., 2012). Genes with recurrent damaging DNMs in multiple disorders also revealed shared biological function across these disorders (Rees et al., 2021). We identified 30 recurrent crossdisorder LoF mutations that were not recurrent in developmental disorder alone (Supplementary file 1). FBXO11, encoding the Fbox only protein 31, shows two recurrent p.Ser831fs LoF variants in autism and congenital hydrocephalus (Figure 5—figure supplement 5; p=1.9e3; Materials and methods). The Fbox protein constitutes a substraterecognition component of the SCF (SKP1cullinFbox) complex, an E3ubiquitin ligase complex responsible for ubiquitination and proteasomal degradation (Cardozo and Pagano, 2004). DNMs in FBXO11 have been previously implicated in severe intellectual disability individuals with autistic behavior problem (Jansen et al., 2019) and neurodevelopmental disorder (Gregor et al., 2018).
For comparison, we also applied mTADA to the same nine disorders and control trios. In total, mTADA identified 117 disorder pairs with significant genetic sharings at an FDR cutoff of 0.05 (Supplementary file 1STable 8 and Figure 5—figure supplement 6). Notably, we identified significant synonymous DNM correlations for all 36 disorder pairs and between all disorders and healthy controls (Figure 5—figure supplement 7). These results are consistent with the simulation results and suggest a substantially inflated false positive rate in mTADA.
Partitioning DNM enrichment correlation by gene set
To gain biological insights into the shared genetic architecture of nine disorders, we repeated EncoreDNM correlation analysis in several gene sets. First, we defined genes with high/low probability of intolerance to LoF variants using pLI scores (Karczewski et al., 2020), and identified genes with high/low brain expression (HBE/LBE) (Werling et al., 2020; Materials and methods; Supplementary file 1STable 9). We identified 11 and 12 disorder pairs showing significant enrichment correlations for LoF DNMs in highpLI genes and HBE genes, respectively (Figure 6a–b). We observed fewer significant correlations for Dmis and Tmis variants in these gene sets (Figure 6—figure supplements 1–2). All identified significant correlations were positive (Supplementary file 1STables 10 11). No significant correlations were identified for synonymous variants (Figure 6—figure supplements 1–2) or between disorders and controls (Figure 6—figure supplements 3–4).
We observed a clear enrichment of significant correlations in diseaserelevant gene sets. Overall, highpLI genes showed substantially stronger correlations across disorders than genes with low pLI (onesided KolmogorovSmirnov test; p=2.3e6). Similarly, enrichment correlations were stronger in HBE genes than in LBE genes (p=8.8e7). Among the 11 disorder pairs showing significant enrichment correlations in highpLI genes, two pairs, that is, autismschizophrenia ($\rho $=0.68, p=2.4e3) and developmental disordercongenital hydrocephalus ($\rho $=0.43, p=1.5e3), were not identified in the exomewide analysis. We also identified four novel disorder pairs with significant correlations in HBE genes, including developmental disordercerebral palsy ($\rho $=0.80, p=9.5e5), developmental disordercongenital hydrocephalus ($\rho $=0.67, p=1.4e3), autismcongenital hydrocephalus ($\rho $=0.82, p=4.7e4), and schizophreniaepileptic encephalopathies ($\rho $=0.66, p=2.0e3). These novel enrichment correlations are consistent with known comorbidities between these disorders (Kielinen et al., 2004; Kilincaslan and Mukaddes, 2009) and findings based on significant risk genes (Li et al., 2016; Jin et al., 2020a; Kume et al., 1998; Cao and Wu, 2015).
Furthermore, we estimated DNM enrichment correlations in genes with high/low expression in mouse developing heart (HHE/LHE) (Homsy et al., 2015; Materials and methods; Supplementary file 1STable 9). We identified 9 significant enrichment correlations for LoF variants in HHE genes (Figure 6c). Strength of enrichment correlations did not show a significant difference between HHE and LHE genes (p=0.846), possibly due to a lack of cardiac disorders in our analysis. Finally, we estimated enrichment correlations between congenital heart disease and other disorders in known pathways for congenital heart disease (Zaidi and Brueckner, 2017; Materials and methods; Supplementary file 1STable 9). We identified five significant correlations for LoF variants (Figure 6d), including a novel correlation between congenital heart disease and Tourette disorder ($\rho $=0.93, p=3.3e9). Of note, arrhythmia caused by congenital heart disease is a known risk factor for Tourette disorder (Gulisano et al., 2011). In these analyses, all significant enrichment correlations were positive (Supplementary file 1) and other variant classes showed generally weaker correlations than LoF variants (Figure 6—figure supplements 5–6). We did not observe significant correlations in these gene sets between disorders and controls (Figure 6—figure supplements 7–8).
Discussion
In this paper, we introduced EncoreDNM, a novel statistical framework to quantify correlated DNM enrichment between two disorders. Through extensive simulations and analyses of DNM data for nine disorders, we demonstrated that our proposed mixedeffects Poisson regression model provides unbiased parameter estimates, shows wellcontrolled false positive rate, and is robust to exomewide technical biases. Leveraging exomewide DNM counts and genomic contextbased mutability data, EncoreDNM achieves superior fit for real DNM datasets compared to simpler models and provides statistically powerful and computationally efficient estimation of DNM enrichment correlation. Further, EncoreDNM can quantify concordant genetic effects for userdefined variant classes within prespecified gene sets, thus is suitable for exploring diverse types of hypotheses and can provide crucial biological insights into the shared genetic etiology in multiple disorders. In comparison, the Bayesian approach implemented in mTADA can produce false positives findings, especially when the DNM count is low, possibility due to the overestimated proportion of risk genes. We still observed inflation in false positive rates under a more stringent significance cutoff or using posterior probability threshold strategy (Supplementary file 1STables 1417).
Multitrait analyses of GWAS data have revealed shared genetic architecture among many neuropsychiatric traits (Brainstorm, 2018; Lee et al., 2013; Gratten et al., 2014; Abdellaoui and Verweij, 2021). These findings have led to the identification of pleiotropic variants, genes, and hub genomic regions underlying many traits and have revealed multiple psychopathological factors jointly affecting human neurological phenotypes (Lee, 2019; Wang et al., 2015). Although emerging evidence suggests that causal DNMs underlying several disorders with wellpowered studies (e.g. congenital heart disease and neurodevelopmental disorders; Homsy et al., 2015) may be shared, our understanding of the extent and the mechanism underlying such sharing remains incomplete. Applied to DNM data for nine disorders, EncoreDNM identified pervasive enrichment correlations of DNMs. We observed particularly strong correlations in pathogenic variant classes (e.g. LoF and Dmis variants) and diseaserelevant genes (e.g. genes with high pLI and genes highly expressed in relevant tissues). Genes underlying these correlations were significantly enriched in pathways involved in chromatin organization and modification and gene expression regulation. The DNM correlations were substantially attenuated in genes with lower expression and genes with frequent occurrences of LoF variants in the population. A similar attenuation was observed in less pathogenic variant classes (e.g., synonymous variants). Further, no significant correlations were identified between any disorder and healthy controls. We also compared DNM enrichment correlations of five disorders with genetic correlations estimated from GWAS summary statistics (Supplementary file 1STable 18). We had consistent findings from GWAS and DNM data (Spearman correlation = 0.70; Figure 5—figure supplement 8 and Supplementary file 1STable 19). These results lay the groundwork for future investigations of pleiotropic mechanisms of DNMs.
Our study has some limitations. First, EncoreDNM assumes probands from different input studies to be independent. In rare cases when two studies have overlapping proband samples, enrichment correlation estimates may be inflated and must be interpreted with caution. Second, genetic correlation methods based on GWAS summary data provided key motivations for the mixedeffects Poisson regression model in our study. Built upon genetic correlations, a plethora of methods have been developed in the GWAS literature to jointly model more than two GWAS (Turley et al., 2018), identify and quantify common factors underlying multiple traits (Grotzinger et al., 2019; Grotzinger et al., 2020), estimate causal effects among different traits (Pickrell et al., 2016), and identify pleiotropic genomic regions through hypothesisfree scans (Guo et al., 2021). Future directions of EncoreDNM include using enrichment correlation to improve gene discovery, learning the directional effects and the causal structure underlying multiple disorders, and dynamically searching for gene sets and annotation classes with shared genetic effects without prespecifying the hypothesis.
Taken together, we provide a new analytic approach to an important problem in DNM studies. We believe EncoreDNM improves the statistical rigor in multidisorder DNM modeling and opens up many interesting future directions in both method development and followup analyses in WES studies. As trio sample size in WES studies continues to grow, EncoreDNM will have broad applications and can greatly benefit DNM research.
Materials and methods
Statistical model
Request a detailed protocolFor a single study, we assume that DNM counts in a given variant class (for example, synonymous variants) follow a mixedeffects Poisson model:
where ${Y}_{i}$ is the DNM count in the ith gene, $N$ is the number of trios, ${m}_{i}$ is the de novo mutability for the ith gene (for example, mutation rate per chromosome per generation) which is known a priori (Samocha et al., 2014), and $G$ is the total number of genes in the study. The elevation parameter $\beta $ quantifies the global elevation of mutation rate compared to mutability estimates based on genomic sequence alone. Genespecific deviation from expected DNM rate is quantified by random effect ${\varphi}_{i}$ with a dispersion parameter $\sigma $. Here, the ${\varphi}_{i}$ are assumed to be independent across different genes, in which case the observed DNM counts of different genes are independent. There is no constraint on the value of $\beta $, and the dispersion parameter $\sigma $ can be any positive value.
Next, we describe how we expand this model to quantify the shared genetics of two disorders. We adopt a flexible Poissonlognormal mixture framework that can accommodate both overdispersion and correlation (Munkin and Trivedi, 1999). We assume DNM counts in a given variant class for two diseases follow:
where ${Y}_{i1},{Y}_{i2}$ are the DNM counts for the ith gene and ${N}_{1},{N}_{2}$ are the trio sizes in two studies, respectively. Similar to the singletrait model, ${m}_{i}$ is the mutability for the ith gene. ${\beta}_{1},{\beta}_{2}$ are the elevation parameters, and ${\varphi}_{i1},{\varphi}_{i2}$ are the genespecific random effects with dispersion parameters ${\sigma}_{1},{\sigma}_{2}$ , for two disorders respectively. $\rho $ is the enrichment correlation which quantifies the concordance of the genespecific DNM burden between two disorders. Here, ${\beta}_{1},{\beta}_{2},{\sigma}_{1},{\sigma}_{2},\rho $ are unknown parameters. The gene specific effects for two disorders are assumed to be independent for different genes. We also assume that there is no shared sample for two disorders, in which case ${Y}_{i1}$ is independent with ${Y}_{i2}$ given $\left[\begin{array}{c}{\lambda}_{i1}\\ {\lambda}_{i2}\end{array}\right]$ .
Parameter estimation
Request a detailed protocolWe implement an MLE procedure to estimate unknown parameters. For singletrait analysis, the loglikelihood function can be expressed as follows:
where $\mathit{Y}={\left[{Y}_{1},\dots ,{Y}_{G}\right]}^{T}$ , ${\lambda}_{i}=2N{m}_{i}\mathrm{exp}(\beta +{\varphi}_{i})$ , $C=\sum _{i=1}^{G}\mathrm{log}\left({Y}_{i}!\right)$ , and $f\left({\varphi}_{i}\right)=\frac{1}{\sqrt{2\pi}\sigma}\mathrm{exp}\left(\frac{{\varphi}_{i}^{2}}{2{\sigma}^{2}}\right)$ . Note that there is no closed form for the integral in the loglikelihood function. Therefore, we use Monte Carlo integration to evaluate the loglikelihood function. Let ${\varphi}_{ij}=\sigma {\xi}_{ij}$ , where the ${\xi}_{ij}$ are independently and identically distributed random variables following a standard normal distribution. We have
where ${\lambda}_{ij}=2N{m}_{i}\mathrm{exp}(\beta +\sigma {\xi}_{ij})$ , and $M$ is the Monte Carlo sample size which is set to be 1,000. Then, we could obtain the MLE of $\beta ,\sigma $ through maximization of ${l}^{\prime}(\beta ,\sigma \mathit{Y})$. We obtain the standard error of the MLE through inversion of the observed Fisher information matrix. However, when the DNM count is small, the Fisher information may be noninvertible and the parameter vector is not numerically identifiable. In this case, we employ groupwise jackknife using 100 randomly partitioned gene groups to obtain standard errors for parameter estimates. This approach produces consistent standard errors compared to the Fisher information approach (Figure 5—figure supplement 9).
The estimation procedure can be generalized to multitrait analysis. Loglikelihood function can be expressed as follows:
where ${\mathit{Y}}_{1}={\left[{Y}_{11},\dots ,{Y}_{G1}\right]}^{T}$ , ${\mathit{Y}}_{2}={\left[{Y}_{12},\dots ,{Y}_{G2}\right]}^{T}$ , ${\lambda}_{i1}=2{N}_{1}{m}_{i}\mathrm{exp}({\beta}_{1}+{\varphi}_{i1})$ , ${\lambda}_{i2}=2{N}_{2}{m}_{i}\mathrm{exp}({\beta}_{2}+{\varphi}_{i2})$ , $C=\sum _{i=1}^{G}\left[\mathrm{log}\left({Y}_{i1}!\right)+\mathrm{log}\left({Y}_{i2}!\right)\right]$ , and $f\left({\varphi}_{i1},{\varphi}_{i2}\right)=\frac{1}{2\pi {\sigma}_{1}{\sigma}_{2}\sqrt{1{\rho}^{2}}}\mathrm{exp}\left[\frac{1}{2\sqrt{1{\rho}^{2}}}\left(\frac{{\varphi}_{i1}^{2}}{{\sigma}_{1}^{2}}+\frac{{\varphi}_{i2}^{2}}{{\sigma}_{2}^{2}}\frac{2\rho {\varphi}_{i1}{\varphi}_{i2}}{{\sigma}_{1}{\sigma}_{2}}\right)\right]$ . We use Monte Carlo integration to evaluate the loglikelihood function. Let ${\varphi}_{i1j}={\sigma}_{1}{\xi}_{i1j}$ and ${\varphi}_{i2j}={\sigma}_{2}\left(\rho {\xi}_{i1j}+\sqrt{1{\rho}^{2}}{\xi}_{i2j}\right)$ , where the ${\xi}_{i1j}$ and ${\xi}_{i2j}$ are independently and identically distributed random variables following a standard normal distribution. We have
where ${\lambda}_{i1j}=2{N}_{1}{m}_{i}\mathrm{exp}({\beta}_{1}+{\sigma}_{1}{\xi}_{i1j})$ and ${\lambda}_{i2j}=2{N}_{2}{m}_{i}\mathrm{exp}\left[{\beta}_{2}+{\sigma}_{2}\left(\rho {\xi}_{i1j}+\sqrt{1{\rho}^{2}}{\xi}_{i2j}\right)\right]$ . Then, we obtain the MLE of ${\beta}_{1},{\beta}_{2},{\sigma}_{1},{\sigma}_{2},\rho $ through maximization of $l`\left({\beta}_{1},{\beta}_{2},{\sigma}_{1},{\sigma}_{2},\rho {\mathit{Y}}_{1},{\mathit{Y}}_{2}\right)$ . Standard error of MLE can be obtained either through inversion of the observed Fisher information matrix or groupwise jackknife if noninvertibility issue occurs.
Computation time
Request a detailed protocolAnalysis of a typical pair of disorders with 18,000 genes takes about 10 min on a 2.5 GHz cluster with 1 core.
DNM data and variant annotation
Request a detailed protocolWe obtained DNM data from published studies (Supplementary file 1STable 1). DNM data for epileptic encephalopathies from the original release (Allen et al., 2013) were not in an editable format and were instead collected from denovodb (Turner et al., 2017). We used ANNOVAR (Wang et al., 2010) to annotate all DNMs. Synonymous variants were determined based on the ‘synonymous SNV’ annotation in ANNOVAR; Variants with ‘startloss’, ‘stopgain’, ‘stoploss’, ‘splicing’, ‘frameshift insertion’, ‘frameshift deletion’, or ‘frameshift substitution’ annotations were classified as LoF; Dmis variants were defined as nonsynonymous SNVs predicted to be deleterious by MetaSVM Dong et al., 2015; nonsynonymous SNVs predicted to be tolerable by MetaSVM were classified as Tmis. Other DNMs which did not fall into these categories were removed from the analysis. For each variant class, we estimated the mutability of each gene using a sequencebased mutation model (Samocha et al., 2014) while adjusting for the sequencing coverage factor based on control trios as previously described (Jin et al., 2017; Supplementary file 1STable 20). We included 18,454 autosomal proteincoding genes in our analysis. TTN was removed due to its substantially larger size.
Description and implementation of mTADA
Request a detailed protocolThe method mTADA employs a Bayesian framework and estimates the proportion of shared risk genes. Specifically, mTADA assigns all genes into four groups: genes that are not relevant for either disorder, risk genes for the first disorder alone, risk genes for the second disorder alone, and risk genes shared by both disorders. The proportion of these groups are parametrized as ${\pi}_{0},{\pi}_{1},{\pi}_{2},{\pi}_{3}$ , respectively. In particular, parameter ${\pi}_{3}$ quantifies the extent of genetic sharing between two disorders, with a larger value indicating stronger genetic overlap (Nguyen et al., 2020). The 95% credible interval constructed through MCMC is used to measure the uncertainty in ${\pi}_{3}$ estimates.
The software mTADA requires the following parameters as inputs: proportion of risk genes (${\pi}_{1}^{S},{\pi}_{2}^{S}$), mean relative risks (${\stackrel{}{\gamma}}_{1}^{S},{\stackrel{}{\gamma}}_{2}^{S}$), and dispersion parameters (${\stackrel{}{\beta}}_{1}^{S},{\stackrel{}{\beta}}_{2}^{S}$) for both disorders. We used extTADA (Nguyen et al., 2017 )to estimate these parameters as suggested by the mTADA paper (Nguyen et al., 2020). mTADA reported the estimated proportion of shared risk genes ${\pi}_{3}$ (posterior mode of ${\pi}_{3}$) and its corresponding 95% credible interval $[\mathrm{L}\mathrm{B},\mathrm{}\mathrm{U}\mathrm{B}]$. We considered ${\pi}_{1}^{S}*{\pi}_{2}^{S}$ as the expected proportion of shared risk genes, and there is significant genetic sharing between two disorders when $\mathrm{L}\mathrm{B}>{\pi}_{1}^{S}\ast {\pi}_{2}^{S}$ . We quantify statistical evidence for genetic sharing by comparing the posterior distribution of ${\pi}_{3}$ with ${\pi}_{1}^{S}*{\pi}_{2}^{S}$ ,
where ${\pi}_{3}^{i}$ is the ith MCMC iteration sample, ${N}_{MCMC}$ is the number of iterations, and $I\left(\right)$ is the indicator function. This is also equivalent to performing twosided inference using posterior probability P $\left({\pi}_{3}>{\pi}_{1}^{S}\ast {\pi}_{2}^{S}\right)$ . Number of MCMC chain was set as 2 and number of iterations was set as 10,000.
Simulation settings
Request a detailed protocolWe assessed the performance of EncoreDNM under the mixedeffects Poisson model. We performed simulations for two variant classes: Tmis and LoF variants, which have the largest and the smallest median mutability values across all genes. First, we performed singletrait simulations to assess estimation precision of elevation parameter $\beta $ and dispersion parameter $\sigma $. We set the true values of $\beta $ to be −0.5,–0.25, and 0, and the true values of $\sigma $ to be 0.5, 0.75, and 1. These values were chosen based on the estimated parameters in real DNM data analyses and ensured simulation settings to be realistic. Next, we performed simulations for crosstrait analysis to assess estimation precision of enrichment correlation $\rho $, whose true values were set to be 0, 0.2, 0.4, 0.6, and 0.8. Sample size for each disorder was set to be 5000. Coverage rate was calculated as the percentage of simulations that the 95% Wald confidence interval covered the true parameter value. Each parameter setting was repeated 100 times.
We also carried out simulations to compare the performance of EncoreDNM and mTADA. False positive rate and statistical power for EncoreDNM were calculated as the proportion of simulation repeats that pvalue for enrichment correlation $\rho $ was smaller than 0.05. and the proportion of simulation repeats that pvalue for estimated proportion of shared risk genes ${\pi}_{3}$ was smaller than 0.05 was used for mTADA. We aggregated all variant classes together, so mutability for each gene was determined as the sum of mutabilities across four variant classes (i.e. LoF, Dmis, Tmis, and synonymous).
First, we simulated DNM data under the mixedeffects Poisson model. To see whether two methods would produce false positive findings, we performed simulations under the null hypothesis that the enrichment correlation $\rho $ is zero. We compared two methods under a range of parameter combinations of ($\beta ,\sigma ,N$) for both disorders: (–0.25, 0.75, 5000) for the baseline setting, (–1, 0.75, 5000) for a setting with small $\beta $, (–0.25, 0.5, 5000) for a setting with small $\sigma $, and (–0.25, 0.75, 1000) for a setting with small sample size. We also assessed the statistical power of two methods under the alternative hypothesis. True value of enrichment correlation $\rho $ was set to be 0.05, 0.1, 0.15, and 0.2. In the power analysis, parameters ($\beta ,\sigma ,N$) were fixed at (–0.25, 0.75, 5000) as in the baseline setting when both methods had wellcontrolled false positive rate.
To ensure a fair comparison, we also compared EncoreDNM and mTADA under a multinomial model, which is different from the data generation processes for the two approaches. For each disorder ($k=\mathrm{1,2}$), we randomly selected causal genes of proportion ${\pi}_{k}^{S}$ . A proportion (i.e. ${\pi}_{3}$) of causal genes overlap between two disorders. We assumed that the total DNM count to follow a Poisson distribution: ${C}_{k}~\mathrm{P}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{o}\mathrm{n}\left({u}_{k}\mathrm{*}2{N}_{k}\sum _{i=1}^{G}{m}_{i}\right)$, where ${u}_{k}$ represents an elevation factor to represent systematic bias in the data. Let ${\mathbf{Y}}_{k}$ denote the vector of DNMs counts in the exome, $\mathit{m}$ denote the vector of mutability values for all genes, and ${\mathit{m}}_{causal,k}$ denote the vector of mutability with values set to be 0 for noncausal genes of disorder $k$. We assumed that a proportion ${p}_{k}$ of the probands could be attributed to DNMs burden in causal genes, and $1{p}_{k}$ of the probands obtained DNMs by chance:
To check whether false positive findings could arise, we performed simulations under the null hypothesis that ${\pi}_{3}={\pi}_{1}^{S}*{\pi}_{2}^{S}$ across a range of parameter combinations of ($u,p,N$) for both disorders: (0.95, 0.25, 5000) for the baseline setting, (0.75, 0.25, 5000) for a setting with small $u$ (i.e., reduced total mutation count), (0.95, 0.15, 5000) for a setting with small $p$ (fewer probands explained by DNMs), and (0.95, 0.25, 1000) for a setting with smaller sample size. ${\pi}_{1}^{S}$ and ${\pi}_{2}^{S}$ were set as 0.1. We also assessed the statistical power of two methods under the alternative hypothesis that $\pi}_{3}>{\pi}_{1}^{S}\ast {\pi}_{2}^{S$ . In power analysis, ($u,p,N$) were fixed at (0.95, 0.25, 5000) as in the baseline setting when false positive rate for both methods were wellcalibrated.
Comparison to the fixedeffects Poisson model
Request a detailed protocolFor singletrait analysis, the fixedeffects Poisson model assumes that
Note that the fixedeffects Poisson model is a special case of our proposed mixedeffects Poisson model when $\sigma =0$. We compared the two models using likelihood ratio test. Under the null hypothesis that $\sigma =0$, $2\left({l}_{alt}{l}_{null}\right)\sim \frac{1}{2}{\chi}_{1}^{2}$ asymptotically, where ${l}_{alt}$ and ${l}_{null}$ represent the log likelihood of the fitted mixedeffects and fixedeffects Poisson models respectively.
Recurrent genes and DNMs
Request a detailed protocolWe used FUMA (Watanabe et al., 2017) to perform GO enrichment analysis for genes harboring LoF DNMs in multiple disorders. Due to potential sample overlap between the studies of developmental disorder (Kaplanis et al., 2020) and intellectual disability (Lelieveld et al., 2016), we excluded intellectual disability from the analysis of recurrent DNMs. We calculated the probability of observing two identical DNMs in two disorders using a Monte Carlo simulation method. For each disorder, we simulated exomewide DNMs profile from a multinomial distribution, where the size was fixed at the observed DNM count and the perbase mutation probability was determined by the trinucleotide base context. We repeated the simulation procedure 100,000 times to evaluate the significance of recurrent DNMs. Lollipop plots for recurrent mutations were generated using MutationMapper on the cBio Cancer Genomics Portal (Cerami et al., 2012).
Implementation of crosstrait LD score regression
Request a detailed protocolWe used crosstrait LDSC (BulikSullivan et al., 2015) to estimate genetic correlations between disorders. LD scores were computed using European samples from the 1000 Genomes Project Phase 3 data (Auton et al., 2015). Only HapMap 3 SNPs were used as observations in the explanatory variable with the mergealleles flag. Intercepts were not constrained in the analyses.
Estimating enrichment correlation in gene sets
Request a detailed protocolGenes with a high/low probability of intolerance to LoF variants (highpLI/lowpLI) were defined as the 4,614 genes in the upper/lower quartiles of pLI scores (Karczewski et al., 2020). Genes with high/low brain expression (HBE/LBE) were defined as the 4,614 genes in the upper/lower quartiles of expression in the human fetal brain (Werling et al., 2020). Genes with high/low heart expression (HHE/LHE) were defined as the 4,614 genes in the upper/lower quartiles of expression in the developing heart of embryonic mouse (Zaidi et al., 2013). Five biological pathways have been reported to be involved in congenital heart disease: chromatin remodeling, Notch signaling, cilia function, sarcomere structure and function, and RAS signaling (Zaidi and Brueckner, 2017). We extracted 1730 unique genes that belong to these five pathways from the gene ontology database (Ashburner et al., 2000) and referred to the union set as CHDrelated genes. We repeated EncoreDNM enrichment correlation analysis in these gene sets. Onesided KolmogorovSmirnov test was used to assess the statistical difference between enrichment correlation signal strength in different gene sets.
URLs
GWAS summary statistics data of autism spectrum disorder, schizophrenia, and Tourette disorder were downloaded on the PGC website, https://www.med.unc.edu/pgc/downloadresults/; Summary statistics of cognitive performance were downloaded on the SSGAC website, https://thessgac.com/; Summary statistics of epilepsy were downloaded on the epiGAD website, https://www.epigad.org/; pLI scores were downloaded from gnomAD v3.1 repository https://gnomad.broadinstitute.org/downloads; mTADA, https://github.com/hoangtn/mTADA, Nguyen et al., 2021; denovodb, https://denovodb.gs.washington.edu/denovodb/; MutationMapper on cBioPortal, https://www.cbioportal.org/mutation_mapper; LDSC, https://github.com/bulik/ldsc; Schorsch, 2020.
Code availability
Request a detailed protocolEncoreDNM software is available at https://github.com/ghm17/EncoreDNM; Guo, 2022.
Data availability
The current manuscript is a computational study, so no data have been generated for this manuscript.
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Article and author information
Author details
Funding
National Science Foundation of China (No. 12071243)
 Lin Hou
Shanghai Municipal Science and Technology Major Project (No. 2017SHZDZX01)
 Lin Hou
Wisconsin Alumni Research Foundation
 Qiongshi Lu
Waisman Center pilot grant program at University of WisconsinMadison
 Qiongshi Lu
National Institutes of Health (No. R03HD100883 and R01GM134005)
 Hongyu Zhao
National Science Foundation (DMS 1902903)
 Hongyu Zhao
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
LH acknowledges research support from the National Science Foundation of China (Grant No. 12071243) and Shanghai Municipal Science and Technology Major Project (Grant No. 2017SHZDZX01). QL acknowledges research support from the University of WisconsinMadison Office of the Chancellor and the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation and the Waisman Center pilot grant program at University of WisconsinMadison. HZ acknowledges research support from the National Institutes of Health (Grant No. R03HD100883 and R01GM134005) and the National Science Foundation (DMS 1902903).
Copyright
© 2022, Guo et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
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