Genetic association analyses of rare variants in next-generation sequencing (NGS) studies are fundamentally challenging due to the presence of a very large number of candidate variants at extremely low minor allele frequencies. Recent developments often focus on pooling multiple variants to provide association analysis at the gene instead of the locus level. Nonetheless, pinpointing individual variants is a critical goal for genomic researches as such information can facilitate the precise delineation of molecular mechanisms and functions of genetic factors on diseases. Due to the extreme rarity of mutations and high-dimensionality, significances of causal variants cannot easily stand out from those of noncausal ones. Consequently, standard false-positive control procedures, such as the Bonferroni and false discovery rate (FDR), are often impractical to apply, as a majority of the causal variants can only be identified along with a few but unknown number of noncausal variants. To provide informative analysis of individual variants in large-scale sequencing studies, we propose the Adaptive False-Negative Control (AFNC) procedure that can include a large proportion of causal variants with high confidence by introducing a novel statistical inquiry to determine those variants that can be confidently dispatched as noncausal. The AFNC provides a general framework that can accommodate for a variety of models and significance tests. The procedure is computationally efficient and can adapt to the underlying proportion of causal variants and quality of significance rankings. Extensive simulation studies across a plethora of scenarios demonstrate that the AFNC is advantageous for identifying individual rare variants, whereas the Bonferroni and FDR are exceedingly over-conservative for rare variants association studies. In the analyses of the CoLaus dataset, AFNC has identified individual variants most responsible for gene-level significances. Moreover, single-variant results using the AFNC have been successfully applied to infer related genes with annotation information.
Recent advances in next-generation sequencing (NGS) technologies have extended the focus of genetic studies of complex traits from that of common to rare variants. Having low minor allele frequencies (MAFs), usually defined to be less than 1% to 5%, rare variants are often evolved from recent mutations that have not yet been subjected to the pruning mechanism of natural selection and can potentially retain a larger proportion of inheritable variability than common variants. [1–5] Recent studies have already implicated the relevance of rare variants on several complex traits. [6–13] Despite its potential to uncover genetic factors contributing to missing disease heritability, the analysis of rare variants association studies bears fundamental challenges. As only a small proportion of samples may carry variant alleles at each locus, associations of individual rare variants are often underpowered. [1,14,15] Moreover, the number of candidate variants can be extremely large in high-throughput sequencing studies, in which available multiple testing strategies may impose excessively severe corrections, preventing the selection of potentially causal variants. [16] Recent proposals for rare variants association analysis often resort to collapsing or pooling multiple variants in a gene or pathway. Examples include the combined multivariate collapsing (CMC) [17], cohort allelic sum (CAST) [18], C-alpha [19], sum of squared scores [20–23], sequence kernel association (SKAT) [24], quality-weighted multivariate score association (qMSAT) [25], and similarity-based regression (simReg) [26] tests. The strategy increases power by aggregating effects of low-frequency variants and decreasing data dimension in multiple testing. It has been successfully applied in several applications that identified functional regions that may contain potentially relevant rare variants. [17–20,23–26] Nonetheless, variants-pooling tests that aggregate over a gene or pathway do not provide information at the individual locus and are ill-equipped to tap the full potential of NGS data in identifying causative mutations at the single-nucleotide resolution. Pinpointing potentially causal variants is a critical goal of genomic studies because such information would faciliate precise delineations of molecular mechanisms and functions of genetic factors on diseases. [27] Moreover, studies have shown that pooling over multiple variants may result in reduced power, as the inclusion of many noncausal variants may dilute the effects of relevant variants on a trait. [28–30] Thus, pooling over multiple variants can sometimes be inadequate for the identification of functional genomic regions. On the other hand, analysis of individual rare variants can provide practical advantages. Information of single-variant association can be used to pinpoint a small number of potentially causal variants for follow-up studies to facilitate the precise characterization of functions via molecular modeling and genetic experimentation, which are often too expensive and time consuming to conduct for all variants in a gene. [27] Further, single-variant results can be utilized a posteriori to objectively infer disease-related genes or pathways by comparing with annotation and functional databases. [31–34] This is useful as gene-level results can oftentimes be uninformative when the significance of a few causal variants are diluted by a large number of noncausal ones in the same gene. In the Results section, we will illustrate both strategies for applying single-variant results using the CoLaus data set. Genome-wide association (GWA) studies, as the pre-eminent means for genetic discovery over the last decade, have largely relied on statistical genomic tools that can identify common variants at the individual single-nucleotide polymorphism (SNP) level. [35] Standard procedures for GWA studies evaluate each variant individually. [36,37] Potentially causal variants are identified by multiple-testing control on significances at each locus. The simplest strategy for multiple testing utilizes the Bonferroni correction that controls family-wise error rate, or the probability of having one or more false positives. [38] However, the Bonferroni correction can often be too conservative for GWA studies under the presence of thousands of SNPs. [39] To address this issue, the false discovery rate (FDR) is often utilized that provides a more liberal criterion by controlling the expected proportion instead of the presence of false positives. [40–42] Despite being extremely successful for common variants in GWA studies [43–46], procedures based on false-positive control are often underpowered in NGS studies involving rare variants (as illustrated in Fig 1). New approaches are needed to provide a meaningful way for powerful variants selection in large-scale sequencing studies. Fig 1 compares the statistical landscape of rare variants analysis in NGS studies with that of common variants in GWA studies. In GWA studies, we observe three regions of statistical inference: the Signals (“S”) region where strongly associated variants can be readily identified by controlling false positives, the Noise (“N”) region where noncausal variants can be identified by controlling false negatives, and the indistinguishable (“I”) region where causal and noncausal variants are inextricably mixed. [47,48] We have recently developed theoretical characterizations for the three regions in high-dimensional data analysis. [49] In NGS studies with rare variants, the Signals region tends to be very narrow and can often degenerate due to extremely low MAF and high dimensionality. Consequently, few causal variants can be identified by evaluating false positives, and results can be very unstable due to random perturbations of noncausal variants. To address the challenge of rare variants association analysis at the single-locus level, we propose the Adaptive False-Negative Control (AFNC) procedure in order to allow a large proportion of causal variants to be retained with high probability. Specifically, the AFNC applies a novel metric called the signal missing rate (Eq 2), defined as the probability of having a nontrivial proportion of false negatives among all causal variants (i. e. , FN/s in Table 1), to achieve informative variant selection by controlling the signal missing rate to be small (see Methods section). That is, AFNC seeks to determine those variants that can be confidently dispatched as noncausal and identifies variants from both the Signals and Indistinguishable regions. The results can provide informative inference in NGS studies where the Signals region is very small or degenerate (Fig 1). We note that this is quite different from classical methods that control false positives. For example, the Bonferroni controls for the presence of any false positives (i. e. , FP ≥ 1), whereas the FDR controls for the expectation of the proportion FP/R when R > 0 (see Table 1). Neither of these involve the number of causal variants s; thus, they cannot be used for controlling the proportion of causal variants selected. On the other hand, the AFNC, based on the proportion FN/s or 1 − TP/s, allows powerful variants selection by controlling the type II error or 1 − statistical power. Although there may exist a corresponding control level for the FDR (albeit very large) that can include the variants selected by the AFNC at a given false-negative control level (see Results section), this corresponding FDR control level is not known a priori and is expected to vary haphazardly across different studies. An arbitrarily assigned FDR control level would be inefficient for controlling false negatives in NGS studies, that can over- or under-select uncontrollably depending on the size of the Noise region. A corresponding control level usually does not exist for the stringent Bonferroni selection in large-scale sequencing studies (see Results section). The AFNC provides a general framework that can accommodate for a wide spectrum of models and test statistics, that may include biological prior knowledge and global genotype information (see Methods section). Moreover, it readily adapts to the quality of statistical tests employed. With improved quality of statistical tests, the Indistinguishable region (see Fig 1) narrows, and the AFNC can, in turn, select a smaller set of potentially causal variants. Extensive studies (see Results section) demonstrate that the AFNC can identify a modest number of potentially causal variants while avoiding a deluge of noncausal ones for follow-up analyses that focus on targeted variants. Our proposal employs recent developments in ultra high-dimensional statistical inference to derive a data-driven procedure that can readily adapt to the underlying sparsity and effect sizes of the data. [50–53] It readily controls type I error rates (see Results section). In addition, it is computationally very efficient and can be applicable for whole-genome sequencing (WGS) and whole-exome sequencing (WES) studies.
We considered the Cohorte Latusannoise (CoLaus) sequence study [58–61], where almost 6000 unrelated Caucasian residents of Lausanne, Switzerland were assessed for risk factors of cardiovascular diseases (CVD). Targeted sequencing genotypes on 202 drug-targeted genes (human genome build 36) were obtained for n = 1769 of these subjects. Cholesterol levels were collected for each subject to evaluate risk of CVD, along with 12 clinical factors—age, gender, and 10 ethnicity covariates using the first 10 principal components [62]. We considered d = 9665 autosomal rare variants from the sequencing study with 0 < M A F < 1 / 2 n = 0. 0072. For each variant, t-statistic was obtained by linear association with log cholesterol levels as the response while adjusting for the 12 clinical covariates. The AFNC, FDR, and Bonferroni were, then, applied on significances of t-statistics to identify potentially causal variants. At threshold levels of 0. 05, Bonferroni and FDR only identified 4 variants. At α = 0. 05 and β = 0. 1, AFNC identified 56 candidate rare variants. The AFNC algorithm obtained cd = 0. 0494 based on M = 10,000 randomly generated samples under the global null of no causal variants and π ^ = 0. 001784 (Eqs 4 and 5). As CVD tends to be influenced by multiple factors [63,64] and the study focused on genes having clinical relevance, one expects a larger number of causal variants than those identified by the FDR and Bonferroni. Our estimated number of signals, s ^ = π ^ × 9665 = 17. 244, suggests that at least 18 variants need to be selected, and potentially much more due to signals dispersed in the Indistinguishable region, to encompass a high proportion of causal variants. That is, false-positive control procedures can be much too conservative in NGS studies, where the Signals region tends to be degenerate (see Fig 1). In the following, we illustrate potential applications of the AFNC for pinpointing individual variants in candidate genes and inferring disease-related genes with annotation information.
We have proposed a novel bioinformatic approach that allows the identification of individual rare variants in large-scale sequencing association studies. Extensive studies based on simulated data generated with COSI at realistic population parameters have been used to compare our method with the Bonferroni and FDR across various scenarios. [54] Results have suggested that the AFNC can provide informative variant selection by including a large proportion of causal variants while avoiding a deluge of noncausal ones. On the other hand, the Bonferroni and FDR are shown to be excessively over-conservative under extremely low MAFs and high dimensionality. Analyses of the CoLaus dataset for cardiovascular diseases using the AFNC have pinpointed individual variants most responsible for explaining significances of genes identified in gene-level aggregation tests. Moreover, single-variant results have been successfully applied to objectively infer potentially relevant genes when cross-referenced with annotation information. The R package ‘AFNC’ for performing the AFNC is publicly and freely available at https: //github. com/zjdaye/AFNC or http: //sites. google. com/site/zhongyindaye/software. The AFNC provides a unified framework to accommodate for a wide spectrum of models, test statistics, and data scenarios. To achieve a succinct presentation, we focused on quantitative traits using p-values obtained from linear association tests in this paper. The AFNC can be easily adopted for case-control studies [23–25,105], family-structured data [106,107], and many other scenarios. Moreover, empirical p-values, as from permutation or bootstrap, can be employed for improved significance ranking. [108] Clearly, performance results of the AFNC using p-values based on associations with quantitative traits, shown in this paper, can be extended to those obtained under a spectrum of models and data scenarios. Moreover, the analysis of large-scale genomic data is a dynamic and fast-evolving field. The AFNC, that readily adapts to the quality of statistical tests employed, will be able to provide increasingly efficient inclusion of causal variants as ever more accurate and computationally efficient means for assessing significances are developed. A few very recent works have sought to identify individual rare variants by incorporating prior-knowledge information in statistical inference. [109,110] These methods typically upweight individual variants predicted to be most likely to be causal based on prior GWA studies, functional annotation, sequence conservation, and other computational means. The AFNC can be readily utilized with models and test statistics that incorporate biological prior knowledge. In the Results section, we illustrated an alternative way to incorporate this bioinformatic knowledge. Specifically, we started with an agnostic interrogation of each variant and obtained a set of statistically promising variants using AFNC. We then compared the selected variants with prior-knowledge information to allow investigators to form educated hypothesis in designing follow-up studies. Statistically promising variants, that are selected objectively by AFNC, can also be explored in follow-up studies without comparing with annotation information, such as when prior knowledge is not available for novel variants or believed to be inaccurate. Due to extremely low MAFs, rare variants do not usually exhibit strong linkage disequilibrium. [1,111] Thus, we designed the AFNC for rare variants association studies, in which dependence among test statistics is assumed to be weak. The AFNC procedure is also applicable in the situation when causal variants are dependent, but noncausal variants are independent. [112] In other applications where noncausal genetic factors are expected to be strongly dependent, the AFNC procedure can be adapted to account for arbitrary dependence using several recent techniques for multiple testing. [113,114] One potential limitation of AFNC is that it may underperform when the signal intensity of the causal variants is too low. The signal intensity of a causal variant depends on the effect sizes and sample size. As shown in Figs 2 and 3, the sensitivity of AFNC deteriorates as effect size or sample size becomes smaller. Indeed, low effect sizes and small sample size are fatal limitations to all methods. In single-variant analysis of rare variants, such challenges may arise from identifying the extremely rare causal variants (e. g. , singletons in the data). Although effect size is believed to be high for rare causal variants, the overall signal intensity may still be low given the extremely low sample size. Under this scenario, gene-based tests coupled with functional annotation would have better potential to identify these causal variants. Therefore, gene-based tests, functional annotation and AFNC should be used in an integrated fashion in the detection of rare causal variants: as we have illustrated in our analysis of the CoLaus data, AFNC coupled with gene-based tests can help to pinpoint potential causal variants that lead to gene-level significance; AFNC coupled with functional annotation can help to identify causal genes that are insignificant at gene level due to a few causal variants mixed with a large number of noncausal variants; finally, gene-based tests coupled with functional annotation can facilitate the identification of extremely rare causal variants. Recent developments in the multiple testing literature have introduced the false nondiscovery rate (Fndr). [115–117] We note that this is quite different from the AFNC control procedure. The Fndr controls for the expectation of the proportion FN/ (d − R), which do not involve the number of causal variants s (see Table 1). Moreover, this is not a sensitive measure and will be very close to zero in large-scale NGS studies, as the number of variants that are not selected d − R will be very large. On the other hand, the AFNC, based on the proportion FN/s, allows robust variants selection in large-scale sequencing studies, as the number of causal variants s is expected to be small and the proportion FN/s is receptive to changes in the number of false negatives. In S7 Fig, we compared the AFNC with the Fndr at a threshold level of β = 0. 1. Results suggest that the AFNC dominates the Fndr in terms of overall performances of g-measure and the Fndr performs poorly in terms of specificity. Innovative technological advances have imposed new bioinformatic and statistical challenges by introducing genomic data at ever increasing resolution and dimensions. The proliferation of GWA studies in the last decade has largely led to the development and adaptation of the FDR as a conventional genomic tool. [42–46] In this paper, we introduced the AFNC to enable the identification of rare variants in large-scale sequencing studies. It is computationally efficient for applications in WGS and WES studies and can provide informative results for investigators charged with the task of analyzing large-scale sequencing studies.
The proposed procedure is general and can accommodate a spectrum of models and significance tests. Suppose that we have test statistics for each variant T1 (G, Z), T2 (G, Z), …, Td (G, Z) based on i = 1,2, …, n subjects, such that G = {Gij} is a matrix of vectors of genotypes across all variants j = 1,2, …, d and Z = {Zik} is a matrix of vectors of additional covariates across various clinical factors and prior biological knowledge k = 1, …, K. Examples for Tj (G, Z) include the classical t-test statistic that depends only on genotypes of the jth variant and the local FDR statistic that utilizes genotypes across all variants in an empirical Bayes construction. [108] Further, prior knowledge from functional annotation can be incorporated, such as by using a generalized linear mixed-effects model. [110] We assume that the test statistic Tj (G, Z) for j = 1,2, …, d is drawn from the mixture distribution (1 - π) F 0 + π F 1, (1) where π = s/d is the signal proportion, s is the number of causal variants, F0 is the null distribution of Tj (G, Z) when the jth variant is noncausal, and F1 is the alternative distribution when the jth variant is causal. [52,53,118] Let T (1) (G, Z) ≥ T (2) (G, Z) ≥ … ≥ T (d) (G, Z) be the ordered test statistics at decreasing significances. To evaluate false negatives in NGS studies, we introduce the signal missing rate (SMR) for selecting the top j ranked variants as S M R ϵ (j) = P F N (j) / s > ϵ, (2) where FN (j) is the number of causal variants missed by selecting the top j ranked variants and ϵ > 0 is a small constant. The SMR can be interpreted as the probability of neglecting at least a small proportion of causal variants among the top j ranked variants. By controlling the SMR, potentially causal variants can be included from both the Signals and Indistinguishable regions while dispatching with a very large number of irrelevant variants in the Noise region (see Fig 1). Compared to another possible measure of false negatives, P (FN (j) >0), SMR provides a more liberal control as it allows some, instead of zero, false negatives. SMR is also substantially different from the control of false nondiscovery rate (Fndr), which is an analog of FDR in terms of false negatives. Fndr is defined as the expectation of the proportion of false negatives among the accepted null hypotheses. [115,119] In the analysis of data with extremely high dimensions and relatively small number of causal variants, Fndr is very close to zero and hence not an informative measure. To provide informative analysis of rare variants in NGS studies, we propose the false-negative control screening (AFNC) procedure as follows.
Next-generation sequencing technologies have allowed genetic association studies of complex traits at the single base-pair resolution, where most genetic variants have extremely low mutation frequencies. These rare variants have been the focus of modern statistical-computational genomics due to their potential to explain missing disease heritability. The identification of individual rare variants associated with diseases can provide new biological insights and enable the precise delineation of disease mechanisms. However, due to the extreme rarity of mutations and large numbers of variants, significances of causative variants tend to be mixed inseparably with a few noncausative ones, and standard multiple testing procedures controlling for false positives fail to provide a meaningful way to include a large proportion of the causative variants. To address the challenge of detecting weak biological signals, we propose a novel statistical procedure, based on false-negative control, to provide a practical approach for variant inclusion in large-scale sequencing studies. By determining those variants that can be confidently dispatched as noncausative, the proposed procedure offers an objective selection of a modest number of potentially causative variants at the single-locus level. Results can be further prioritized or used to infer disease-associated genes with annotation information.
sequencing techniques
genome-wide association studies
medicine and health sciences
neuroscience
cardiovascular medicine
next-generation sequencing
mathematics
statistics (mathematics)
test statistics
computational neuroscience
genome analysis
molecular biology techniques
coding mechanisms
research and analysis methods
mathematical and statistical techniques
statistical methods
molecular biology
genetic loci
genetics
transcriptome analysis
biology and life sciences
cardiovascular diseases
physical sciences
genomics
dna sequencing
genetics of disease
computational biology
human genetics
Rare Variants Association Analysis in Large-Scale Sequencing Studies at the Single Locus Level