Comprehensive approach to analyzing rare genetic variants

Rare variant association on unrelated individuals in case-control studies using aggregation tests: existing methods and current limitations

Over the past years, progress made in next-generation sequencing technologies and bioinformatics have sparked a surge in association studies. Especially, genome-wide association studies (GWASs) have demonstrated their effectiveness in identifying disease associations with common genetic variants. Yet, rare variants can contribute to additional disease risk or trait heterogeneity. Because GWASs are underpowered for detecting association with such variants, numerous statistical methods have been recently proposed. Aggregation tests collapse multiple rare variants within a genetic region (e.g. gene, gene set, genomic loci) to test for association. An increasing number of studies using such methods successfully identified trait-associated rare variants and led to a better understanding of the underlying disease mechanism. In this review, we compare existing aggregation tests, their statistical features and scope of application, splitting them into the five classical classes: burden, adaptive burden, variance-component, omnibus and other. Finally, we describe some limitations of current aggregation tests, highlighting potential direction for further investigations.

Excalibur: A new ensemble method based on an optimal combination of aggregation tests for rare-variant association testing for sequencing data

The development of high-throughput next-generation sequencing technologies and large-scale genetic association studies produced numerous advances in the biostatistics field. Various aggregation tests, i.e. statistical methods that analyze associations of a trait with multiple markers within a genomic region, have produced a variety of novel discoveries. Notwithstanding their usefulness, there is no single test that fits all needs, each suffering from specific drawbacks. Selecting the right aggregation test, while considering an unknown underlying genetic model of the disease, remains an important challenge. Here we propose a new ensemble method, called Excalibur, based on an optimal combination of 36 aggregation tests created after an in-depth study of the limitations of each test and their impact on the quality of result. Our findings demonstrate the ability of our method to control type I error and illustrate that it offers the best average power across all scenarios. The proposed method allows for novel advances in Whole Exome/Genome sequencing association studies, able to handle a wide range of association models, providing researchers with an optimal aggregation analysis for the genetic regions of interest.

Genetics in parkinson's disease: From better disease understanding to machine learning based precision medicine

Parkinson's Disease (PD) is a neurodegenerative disorder with highly heterogeneous phenotypes. Accordingly, it has been challenging to robustly identify genetic factors associated with disease risk, prognosis and therapy response via genome-wide association studies (GWAS). In this review we first provide an overview of existing statistical methods to detect associations between genetic variants and the disease phenotypes in existing PD GWAS. Secondly, we discuss the potential of machine learning approaches to better quantify disease phenotypes and to move beyond disease understanding towards a better-personalized treatment of the disease.

Rare Variants in the DNA Repair Pathway and the Risk of Colorectal Cancer

BACKGROUND

Inherited susceptibility is an important contributor to colorectal cancer risk, and rare variants in key genes or pathways could account in part for the missing proportion of colorectal cancer heritability.

METHODS

We conducted an exome-wide association study including 2,327 cases and 2,966 controls of European ancestry from three large epidemiologic studies. Single variant associations were tested using logistic regression models, adjusting for appropriate study-specific covariates. In addition, we examined the aggregate effects of rare coding variation at the gene and pathway levels using Bayesian model uncertainty techniques.

RESULTS

In an exome-wide gene-level analysis, we identified ST6GALNAC2 as the top associated gene based on the Bayesian risk index (BRI) method [summary Bayes factor (BF)BRI = 2604.23]. A rare coding variant in this gene, rs139401613, was the top associated variant (P = 1.01 × 10-6) in an exome-wide single variant analysis. Pathway-level association analyses based on the integrative BRI (iBRI) method found extreme evidence of association with the DNA repair pathway (BFiBRI = 17852.4), specifically with the nonhomologous end joining (BFiBRI = 437.95) and nucleotide excision repair (BFiBRI = 36.96) subpathways. The iBRI method also identified RPA2, PRKDC, ERCC5, and ERCC8 as the top associated DNA repair genes (summary BFiBRI ≥ 10), with rs28988897, rs8178232, rs141369732, and rs201642761 being the most likely associated variants in these genes, respectively.

CONCLUSIONS

We identified novel variants and genes associated with colorectal cancer risk and provided additional evidence for a role of DNA repair in colorectal cancer tumorigenesis.

IMPACT

This study provides new insights into the genetic predisposition to colorectal cancer, which has potential for translation into improved risk prediction.

A Bayesian hierarchically structured prior for rare-variant association testing

Although genome-wide association studies have been widely used to identify associations between complex diseases and genetic variants, standard single-variant analyses often have limited power when applied to rare variants. To overcome this problem, set-based methods have been developed with the aim of boosting power by borrowing strength from multiple rare variants. We propose the adaptive hierarchically structured variable selection (HSVS-A) before test for association of rare variants in a set with continuous or dichotomous phenotypes and to estimate the effect of individual rare variants simultaneously. HSVS-A has the flexibility to integrate a pairwise weighting scheme, which adaptively induces desirable correlations among variants of similar significance such that we can borrow information from potentially causal and noncausal rare variants to boost power. Simulation studies show that for both continuous and dichotomous phenotypes, HSVS-A is powerful when there are multiple causal rare variants, either in the same or opposite direction of effect, with the presence of a large number of noncausal variants. We also apply HSVS-A to the Wellcome Trust Case Control Consortium Crohn's disease data for testing the association of Crohn's disease with rare variants in pathways. HSVS-A identifies two pathways harboring novel protective rare variants for Crohn's disease.

[An improved association analysis pipeline for tumor susceptibility variant in haplotype amplification area]

OBJECTIVE

Haplotype amplification on germline variants is suggested to imply potential selective advantages and clonal expansion susceptibility and has become an important signature for seeking cancer susceptibility gene.Here we propose an improved association method that fully considers the haplotype amplification status.

METHODS

The haplotype amplification status was estimated by the variant allelic frequencies.We adopted a permutation test on variant allelic frequencies to divide the candidate variants into multiple groups.A likelihood clustering method was then applied to establish the neighborhood system of the hidden Markov random field framework.A filtering pipeline was introduced into the proposed method to further refine the candidate variants, including a Wilson's interval filter and a false discovery rate controller.The final candidate set along with the haplotype amplification status was collapsed into the weighted virtual sites for association tests.

RESULTS

Through simulated tests on a series of datasets, we compared the type Ⅰ error rates of different minor allele frequencies, which stably fell within 2%, suggesting good robustness of the algorithm.In addition, we compared another 5 published association approaches for Type-Ⅰ and Type-Ⅱ error rates with the proposed method, which resulted in the error rates all within 2%, demonstrating significant advantages and a good statistical ability of the proposed method.

CONCLUSIONS

The proposed method can accurately identify tumor susceptibility variants in haplotype amplification area with good robustness and stability.

Adaptive Fisher method detects dense and sparse signals in association analysis of SNV sets

BACKGROUND

With the development of next generation sequencing (NGS) technology and genotype imputation methods, statistical methods have been proposed to test a set of genomic variants together to detect if any of them is associated with the phenotype or disease. In practice, within the set, there is an unknown proportion of variants truly causal or associated with the disease. There is a demand for statistical methods with high power in both dense and sparse scenarios, where the proportion of causal or associated variants is large or small respectively.

RESULTS

We propose a new association test - weighted Adaptive Fisher (wAF) that can adapt to both dense and sparse scenarios by adding weights to the Adaptive Fisher (AF) method we developed before. Using simulation, we show that wAF enjoys comparable or better power to popular methods such as sequence kernel association tests (SKAT and SKAT-O) and adaptive SPU (aSPU) test. We apply wAF to a publicly available schizophrenia dataset, and successfully detect thirteen genes. Among them, three genes are supported by existing literature; six are plausible as they either relate to other neurological diseases or have relevant biological functions.

CONCLUSIONS

The proposed wAF method is a powerful disease-variants association test in both dense and sparse scenarios. Both simulation studies and real data analysis indicate the potential of wAF for new biological findings.

Genomic Diversity Evaluation of Populus trichocarpa Germplasm for Rare Variant Genetic Association Studies

Genome-wide association studies are powerful tools to elucidate the genome-to-phenome relationship. In order to explain most of the observed heritability of a phenotypic trait, a sufficient number of individuals and a large set of genetic variants must be examined. The development of high-throughput technologies and cost-efficient resequencing of complete genomes have enabled the genome-wide identification of genetic variation at large scale. As such, almost all existing genetic variation becomes available, and it is now possible to identify rare genetic variants in a population sample. Rare genetic variants that were usually filtered out in most genetic association studies are the most numerous genetic variations across genomes and hold great potential to explain a significant part of the missing heritability observed in association studies. Rare genetic variants must be identified with high confidence, as they can easily be confounded with sequencing errors. In this study, we used a pre-filtered data set of 1,014 pure Populus trichocarpa entire genomes to identify rare and common small genetic variants across individual genomes. We compared variant calls between Platypus and HaplotypeCaller pipelines, and we further applied strict quality filters for improved genetic variant identification. Finally, we only retained genetic variants that were identified by both variant callers increasing calling confidence. Based on these shared variants and after stringent quality filtering, we found high genomic diversity in P. trichocarpa germplasm, with 7.4 million small genetic variants. Importantly, 377k non-synonymous variants (5% of the total) were uncovered. We highlight the importance of genomic diversity and the potential of rare defective genetic variants in explaining a significant portion of P. trichocarpa's phenotypic variability in association genetics. The ultimate goal is to associate both rare and common alleles with poplar's wood quality traits to support selective breeding for an improved bioenergy feedstock.

Rare-variant collapsing analyses for complex traits: guidelines and applications

The first phase of genome-wide association studies (GWAS) assessed the role of common variation in human disease. Advances optimizing and economizing high-throughput sequencing have enabled a second phase of association studies that assess the contribution of rare variation to complex disease in all protein-coding genes. Unlike the early microarray-based studies, sequencing-based studies catalogue the full range of genetic variation, including the evolutionarily youngest forms. Although the experience with common variants helped establish relevant standards for genome-wide studies, the analysis of rare variation introduces several challenges that require novel analysis approaches.

Powerful statistical method to detect disease-associated genes using publicly available genome-wide association studies summary data

Genome-wide association studies (GWAS) have thus far achieved substantial success. In the last decade, a large number of common variants underlying complex diseases have been identified through GWAS. In most existing GWAS, the identified common variants are obtained by single marker-based tests, that is, testing one single-nucleotide polymorphism (SNP) at a time. Generally, the basic functional unit of inheritance is a gene, rather than a SNP. Thus, results from gene-level association test can be more readily integrated with downstream functional and pathogenic investigation. In this paper, we propose a general gene-based p-value adaptive combination approach (GPA) which can integrate association evidence of multiple genetic variants using only GWAS summary statistics (either p-value or other test statistics). The proposed method could be used to test genetic association for both continuous and binary traits through not only one study but also multiple studies, which would be helpful to overcome the limitation of existing methods that can only be applied to a specific type of data. We conducted thorough simulation studies to verify that the proposed method controls type I errors well, and performs favorably compared to single-marker analysis and other existing methods. We demonstrated the utility of our proposed method through analysis of GWAS meta-analysis results for fasting glucose and lipids from the international MAGIC consortium and Global Lipids Consortium, respectively. The proposed method identified some novel trait associated genes which can improve our understanding of the mechanisms involved in β -cell function, glucose homeostasis, and lipids traits.

Identifying individual risk rare variants using protein structure guided local tests (POINT)

Rare variants are of increasing interest to genetic association studies because of their etiological contributions to human complex diseases. Due to the rarity of the mutant events, rare variants are routinely analyzed on an aggregate level. While aggregation analyses improve the detection of global-level signal, they are not able to pinpoint causal variants within a variant set. To perform inference on a localized level, additional information, e.g., biological annotation, is often needed to boost the information content of a rare variant. Following the observation that important variants are likely to cluster together on functional domains, we propose a protein structure guided local test (POINT) to provide variant-specific association information using structure-guided aggregation of signal. Constructed under a kernel machine framework, POINT performs local association testing by borrowing information from neighboring variants in the 3-dimensional protein space in a data-adaptive fashion. Besides merely providing a list of promising variants, POINT assigns each variant a p-value to permit variant ranking and prioritization. We assess the selection performance of POINT using simulations and illustrate how it can be used to prioritize individual rare variants in PCSK9, ANGPTL4 and CETP in the Action to Control Cardiovascular Risk in Diabetes (ACCORD) clinical trial data.

Real world scenarios in rare variant association analysis: the impact of imbalance and sample size on the power in silico

Background

The development of sequencing techniques and statistical methods provides great opportunities for identifying the impact of rare genetic variation on complex traits. However, there is a lack of knowledge on the impact of sample size, case numbers, the balance of cases vs controls for both burden and dispersion based rare variant association methods. For example, Phenome-Wide Association Studies may have a wide range of case and control sample sizes across hundreds of diagnoses and traits, and with the application of statistical methods to rare variants, it is important to understand the strengths and limitations of the analyses.

Results

We conducted a large-scale simulation of randomly selected low-frequency protein-coding regions using twelve different balanced samples with an equal number of cases and controls as well as twenty-one unbalanced sample scenarios. We further explored statistical performance of different minor allele frequency thresholds and a range of genetic effect sizes. Our simulation results demonstrate that using an unbalanced study design has an overall higher type I error rate for both burden and dispersion tests compared with a balanced study design. Regression has an overall higher type I error with balanced cases and controls, while SKAT has higher type I error for unbalanced case-control scenarios. We also found that both type I error and power were driven by the number of cases in addition to the case to control ratio under large control group scenarios. Based on our power simulations, we observed that a SKAT analysis with case numbers larger than 200 for unbalanced case-control models yielded over 90% power with relatively well controlled type I error. To achieve similar power in regression, over 500 cases are needed. Moreover, SKAT showed higher power to detect associations in unbalanced case-control scenarios than regression.

Conclusions

Our results provide important insights into rare variant association study designs by providing a landscape of type I error and statistical power for a wide range of sample sizes. These results can serve as a benchmark for making decisions about study design for rare variant analyses.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2591-6) contains supplementary material, which is available to authorized users.

Novel Methods for Family-Based Genetic Studies

The recent development of microarray and sequencing technology allows identification of disease susceptibility genes. Although the genome-wide association studies (GWAS) have successfully identified many genetic markers related to human diseases, the traditional statistical methods are not powerful to detect rare genetic markers. The rare genetic markers are usually grouped together and tested at the set level. One of such methods is the sequence kernel association test (SKAT), which has been commonly used in the rare genetic marker analysis. In recent publications, SKAT has been extended to be applicable for family-based rare variant analysis. Here, I present three published statistical approaches for family-based rare variant analysis for: 1. continuous traits, 2. binary traits, and 3. multiple correlated traits.

Assessing Rare Variation in Complex Traits

While genome-wide association studies have been very successful in identifying associations of common genetic variants with many different traits, the rarer frequency spectrum of the genome has not yet been comprehensively explored. Technological developments increasingly lift restrictions to access rare genetic variation. Dense reference panels enable improved genotype imputation for rarer variants in studies using DNA microarrays. Moreover, the decreasing cost of next generation sequencing makes whole exome and genome sequencing increasingly affordable for large samples. Large-scale efforts based on sequencing, such as ExAC, 100,000 Genomes, and TopMed, are likely to significantly advance this field.The main challenge in evaluating complex trait associations of rare variants is statistical power. The choice of population should be considered carefully because allele frequencies and linkage disequilibrium structure differ between populations. Genetically isolated populations can have favorable genomic characteristics for the study of rare variants.One strategy to increase power is to assess the combined effect of multiple rare variants within a region, known as aggregate testing. A  range of methods have been developed for this. Model performance depends on the genetic architecture of the region of interest.

The impact of rare and low-frequency genetic variants in common disease

Despite thousands of genetic loci identified to date, a large proportion of genetic variation predisposing to complex disease and traits remains unaccounted for. Advances in sequencing technology enable focused explorations on the contribution of low-frequency and rare variants to human traits. Here we review experimental approaches and current knowledge on the contribution of these genetic variants in complex disease and discuss challenges and opportunities for personalised medicine.

RAPIDSNPs: A new computational pipeline for rapidly identifying key genetic variants reveals previously unidentified SNPs that are significantly associated with individual platelet responses

Advances in omics technologies have led to the discovery of genetic markers, or single nucleotide polymorphisms (SNPs), that are associated with particular diseases or complex traits. Although there have been significant improvements in the approaches used to analyse associations of SNPs with disease, further optimised and rapid techniques are needed to keep up with the rate of SNP discovery, which has exacerbated the 'missing heritability' problem. Here, we have devised a novel, integrated, heuristic-based, hybrid analytical computational pipeline, for rapidly detecting novel or key genetic variants that are associated with diseases or complex traits. Our pipeline is particularly useful in genetic association studies where the genotyped SNP data are highly dimensional, and the complex trait phenotype involved is continuous. In particular, the pipeline is more efficient for investigating small sets of genotyped SNPs defined in high dimensional spaces that may be associated with continuous phenotypes, rather than for the investigation of whole genome variants. The pipeline, which employs a consensus approach based on the random forest, was able to rapidly identify previously unseen key SNPs, that are significantly associated with the platelet response phenotype, which was used as our complex trait case study. Several of these SNPs, such as rs6141803 of COMMD7 and rs41316468 in PKT2B, have independently confirmed associations with cardiovascular diseases (CVDs) according to other unrelated studies, suggesting that our pipeline is robust in identifying key genetic variants. Our new pipeline provides an important step towards addressing the problem of 'missing heritability' through enhanced detection of key genetic variants (SNPs) that are associated with continuous complex traits/disease phenotypes.

Detecting association of rare and common variants based on cross-validation prediction error

Despite the extensive discovery of disease-associated common variants, much of the genetic contribution to complex traits remains unexplained. Rare variants may explain additional disease risk or trait variability. Although sequencing technology provides a supreme opportunity to investigate the roles of rare variants in complex diseases, detection of these variants in sequencing-based association studies presents substantial challenges. In this article, we propose novel statistical tests to test the association between rare and common variants in a genomic region and a complex trait of interest based on cross-validation prediction error (PE). We first propose a PE method based on Ridge regression. Based on PE, we also propose another two tests PE-WS and PE-TOW by testing a weighted combination of variants with two different weighting schemes. PE-WS is the PE version of the test based on the weighted sum statistic (WS) and PE-TOW is the PE version of the test based on the optimally weighted combination of variants (TOW). Using extensive simulation studies, we are able to show that (1) PE-TOW and PE-WS are consistently more powerful than TOW and WS, respectively, and (2) PE is the most powerful test when causal variants contain both common and rare variants.

A novel statistical method for rare-variant association studies in general pedigrees

Both population-based and family-based designs are commonly used in genetic association studies to identify rare variants that underlie complex diseases. For any type of study design, the statistical power will be improved if rare variants can be enriched in the samples. Family-based designs, with ascertainment based on phenotype, may enrich the sample for causal rare variants and thus can be more powerful than population-based designs. Therefore, it is important to develop family-based statistical methods that can account for ascertainment. In this paper, we develop a novel statistical method for rare-variant association studies in general pedigrees for quantitative traits. This method uses a retrospective view that treats the traits as fixed and the genotypes as random, which allows us to account for complex and undefined ascertainment of families. We then apply the newly developed method to the Genetic Analysis Workshop 19 data set and compare the power of the new method with two other methods for general pedigrees. The results show that the newly proposed method increases power in most of the cases we consider, more than the other two methods.

A Nonparametric Regression Approach to Control for Population Stratification in Rare Variant Association Studies

Recently, there is increasing interest to detect associations between rare variants and complex traits. Rare variant association studies usually need large sample sizes due to the rarity of the variants, and large sample sizes typically require combining information from different geographic locations within and across countries. Although several statistical methods have been developed to control for population stratification in common variant association studies, these methods are not necessarily controlling for population stratification in rare variant association studies. Thus, new statistical methods that can control for population stratification in rare variant association studies are needed. In this article, we propose a principal component based nonparametric regression (PC-nonp) approach to control for population stratification in rare variant association studies. Our simulations show that the proposed PC-nonp can control for population stratification well in all scenarios, while existing methods cannot control for population stratification at least in some scenarios. Simulations also show that PC-nonp's robustness to population stratification will not reduce power. Furthermore, we illustrate our proposed method by using whole genome sequencing data from genetic analysis workshop 18 (GAW18).

Identifying rare and common variants with Bayesian variable selection

Background

Recent advances in next-generation sequencing technologies have made it possible to generate large amounts of sequence data with rare variants in a cost-effective way. Yet, the statistical aspect of testing disease association of rare variants is quite challenging as the typical assumptions fail to hold owing to low minor allele frequency (<0.5 or 1 %).

Methods

I present a Bayesian variable selection approach to detect associations with both rare and common genetic variants for quantitative traits simultaneously. In my model, I frame the problem of identifying disease-associated variants as a problem of variable selection in a sparse space, that is, how best to model the relationship between phenotypes and a set of genetic variants. By constructing a risk index score for a group of rare variants, my method can effectively consider all variants in a multivariate model. I also use a within-chain permutation to generate the empirical thresholds to detect true-positive variants.

Results

I apply our method to study the association between increases in baseline systolic and diastolic blood pressure (SBP and DBP, respectively) and genetic variants in the data from Genetic Analysis Workshop 19 unrelated samples. I identify several rare and common variants in the gene MAP4 that are potentially associated with SBP and DBP.

Conclusions

The application shows that my method is powerful in identifying disease-associated variants even with the extreme rarity.

Selection and explosive growth alter genetic architecture and hamper the detection of causal rare variants

The role of rare alleles in complex phenotypes has been hotly debated, but most rare variant association tests (RVATs) do not account for the evolutionary forces that affect genetic architecture. Here, we use simulation and numerical algorithms to show that explosive population growth, as experienced by human populations, can dramatically increase the impact of very rare alleles on trait variance. We then assess the ability of RVATs to detect causal loci using simulations and human RNA-seq data. Surprisingly, we find that statistical performance is worst for phenotypes in which genetic variance is due mainly to rare alleles, and explosive population growth decreases power. Although many studies have attempted to identify causal rare variants, few have reported novel associations. This has sometimes been interpreted to mean that rare variants make negligible contributions to complex trait heritability. Our work shows that RVATs are not robust to realistic human evolutionary forces, so general conclusions about the impact of rare variants on complex traits may be premature.

Association Tests for Rare Variants

Over the past few years, interest in the identification of rare variants that influence human phenotype has led to the development of many statistical methods for testing for association between sets of rare variants and binary or quantitative traits. Here, I review some of the most important ideas that underlie these methods and the most relevant issues when choosing a method for analysis. In addition to the tests for association, I review crucial issues in performing a rare variant study, from experimental design to interpretation and validation. I also discuss the many challenges of these studies, some of their limitations, and future research directions.

Strategies for Imputing and Analyzing Rare Variants in Association Studies

Rare genetic variants may be responsible for a significant amount of the uncharacterized genetic risk underlying many diseases. An efficient approach to characterizing the disease burden of rare variants may be to impute them into existing large datasets. It is well known that the ability to impute a rare variant is dependent both on the array choice and number of individuals in the reference panel carrying that variant, although it is still unclear exactly how well imputation will work for rare variants. Here, we review the additional challenges that arise when imputing rare variants, looking at studies that have been able to impute rare variants, methods behind merging reference panels, approaches for imputing rare variants, and methods for analyzing rare variants.

Rare variants analysis using penalization methods for whole genome sequence data

BACKGROUND

Availability of affordable and accessible whole genome sequencing for biomedical applications poses a number of statistical challenges and opportunities, particularly related to the analysis of rare variants and sparseness of the data. Although efforts have been devoted to address these challenges, the performance of statistical methods for rare variants analysis still needs further consideration.

RESULT

We introduce a new approach that applies restricted principal component analysis with convex penalization and then selects the best predictors of a phenotype by a concave penalized regression model, while estimating the impact of each genomic region on the phenotype. Using simulated data, we show that the proposed method maintains good power for association testing while keeping the false discovery rate low under a verity of genetic architectures. Illustrative data analyses reveal encouraging result of this method in comparison with other commonly applied methods for rare variants analysis.

CONCLUSION

By taking into account linkage disequilibrium and sparseness of the data, the proposed method improves power and controls the false discovery rate compared to other commonly applied methods for rare variant analyses.

Weighted Score Tests Implementing Model-Averaging Schemes in Detection of Rare Variants in Case-Control Studies

Multi-locus effect modeling is a powerful approach for detection of genes influencing a complex disease. Especially for rare variants, we need to analyze multiple variants together to achieve adequate power for detection. In this paper, we propose several parsimonious branching model techniques to assess the joint effect of a group of rare variants in a case-control study. These models implement a data reduction strategy within a likelihood framework and use a weighted score test to assess the statistical significance of the effect of the group of variants on the disease. The primary advantage of the proposed approach is that it performs model-averaging over a substantially smaller set of models supported by the data and thus gains power to detect multi-locus effects. We illustrate these proposed approaches on simulated and real data and study their performance compared to several existing rare variant detection approaches. The primary goal of this paper is to assess if there is any gain in power to detect association by averaging over a number of models instead of selecting the best model. Extensive simulations and real data application demonstrate the advantage the proposed approach in presence of causal variants with opposite directional effects along with a moderate number of null variants in linkage disequilibrium.

Group association test using a hidden Markov model

In the genomic era, group association tests are of great interest. Due to the overwhelming number of individual genomic features, the power of testing for association of a single genomic feature at a time is often very small, as are the effect sizes for most features. Many methods have been proposed to test association of a trait with a group of features within a functional unit as a whole, e.g. all SNPs in a gene, yet few of these methods account for the fact that generally a substantial proportion of the features are not associated with the trait. In this paper, we propose to model the association for each feature in the group as a mixture of features with no association and features with non-zero associations to explicitly account for the possibility that a fraction of features may not be associated with the trait while other features in the group are. The feature-level associations are first estimated by generalized linear models; the sequence of these estimated associations is then modeled by a hidden Markov chain. To test for global association, we develop a modified likelihood ratio test based on a log-likelihood function that ignores higher order dependency plus a penalty term. We derive the asymptotic distribution of the likelihood ratio test under the null hypothesis. Furthermore, we obtain the posterior probability of association for each feature, which provides evidence of feature-level association and is useful for potential follow-up studies. In simulations and data application, we show that our proposed method performs well when compared with existing group association tests especially when there are only few features associated with the outcome.

Insights into blood lipids from rare variant discovery

Large-scale genome wide screens have discovered over 160 common variants associated with plasma lipids, which are risk factors often linked to heart disease. A large fraction of lipid heritability remains unexplained, and it is hypothesized that rare variants of functional consequence may account for some of the missing heritability. Finding lipid-associated variants that occur less frequently in the human population poses a challenge, primarily due to lack of power and difficulties to identify and test them. Interrogation of the protein-coding regions of the genome using array and sequencing techniques has led to important discoveries of rare variants that affect lipid levels and related disease risk. Here, we summarize the latest methods and findings that contribute to our current understanding of rare variant lipid genetics.

A Sequence Kernel Association Test for Dichotomous Traits in Family Samples under a Generalized Linear Mixed Model

OBJECTIVE

The existing methods for identifying multiple rare variants underlying complex diseases in family samples are underpowered. Therefore, we aim to develop a new set-based method for an association study of dichotomous traits in family samples.

METHODS

We introduce a framework for testing the association of genetic variants with diseases in family samples based on a generalized linear mixed model. Our proposed method is based on a kernel machine regression and can be viewed as an extension of the sequence kernel association test (SKAT and famSKAT) for application to family data with dichotomous traits (F-SKAT).

RESULTS

Our simulation studies show that the original SKAT has inflated type I error rates when applied directly to family data. By contrast, our proposed F-SKAT has the correct type I error rate. Furthermore, in all of the considered scenarios, F-SKAT, which uses all family data, has higher power than both SKAT, which uses only unrelated individuals from the family data, and another method, which uses all family data.

CONCLUSION

We propose a set-based association test that can be used to analyze family data with dichotomous phenotypes while handling genetic variants with the same or opposite directions of effects as well as any types of family relationships.

A powerful approach to test an optimally weighted combination of rare variants in admixed populations

Population stratification has long been recognized as an issue in genetic association studies because unrecognized population stratification can lead to both false-positive and false-negative findings and can obscure true association signals if not appropriately corrected. This issue can be even worse in rare variant association analyses because rare variants often demonstrate stronger and potentially different patterns of stratification than common variants. To correct for population stratification in genetic association studies, we proposed a novel method to Test the effect of an Optimally Weighted combination of variants in Admixed populations (TOWA) in which the analytically derived optimal weights can be calculated from existing phenotype and genotype data. TOWA up weights rare variants and those variants that have strong associations with the phenotype. Additionally, it can adjust for the direction of the association, and allows for local ancestry difference among study subjects. Extensive simulations show that the type I error rate of TOWA is under control in the presence of population stratification and it is more powerful than existing methods. We have also applied TOWA to a real sequencing data. Our simulation studies as well as real data analysis results indicate that TOWA is a useful tool for rare variant association analyses in admixed populations.

Rare variant testing across methods and thresholds using the multi-kernel sequence kernel association test (MK-SKAT)

Analysis of rare genetic variants has focused on region-based analysis wherein a subset of the variants within a genomic region is tested for association with a complex trait. Two important practical challenges have emerged. First, it is difficult to choose which test to use. Second, it is unclear which group of variants within a region should be tested. Both depend on the unknown true state of nature. Therefore, we develop the Multi-Kernel SKAT (MK-SKAT) which tests across a range of rare variant tests and groupings. Specifically, we demonstrate that several popular rare variant tests are special cases of the sequence kernel association test which compares pair-wise similarity in trait value to similarity in the rare variant genotypes between subjects as measured through a kernel function. Choosing a particular test is equivalent to choosing a kernel. Similarly, choosing which group of variants to test also reduces to choosing a kernel. Thus, MK-SKAT uses perturbation to test across a range of kernels. Simulations and real data analyses show that our framework controls type I error while maintaining high power across settings: MK-SKAT loses power when compared to the kernel for a particular scenario but has much greater power than poor choices.

Genomic architecture of pharmacological efficacy and adverse events

The pharmacokinetic and pharmacodynamic disciplines address pharmacological traits, including efficacy and adverse events. Pharmacogenomics studies have identified pervasive genetic effects on treatment outcomes, resulting in the development of genetic biomarkers for optimization of drug therapy. Pharmacogenomics-based tests are already being applied in clinical decision making. However, despite substantial progress in identifying the genetic etiology of pharmacological response, current biomarker panels still largely rely on single gene tests with a large portion of the genetic effects remaining to be discovered. Future research must account for the combined effects of multiple genetic variants, incorporate pathway-based approaches, explore gene-gene interactions and nonprotein coding functional genetic variants, extend studies across ancestral populations, and prioritize laboratory characterization of molecular mechanisms. Because genetic factors can play a key role in drug response, accurate biomarker tests capturing the main genetic factors determining treatment outcomes have substantial potential for improving individual clinical care.

Population genetic simulations of complex phenotypes with implications for rare variant association tests

Demographic events and natural selection alter patterns of genetic variation within populations and may play a substantial role in shaping the genetic architecture of complex phenotypes and disease. However, the joint impact of these basic evolutionary forces is often ignored in the assessment of statistical tests of association. Here, we provide a simulation-based framework for generating DNA sequences that incorporates selection and demography with flexible models for simulating phenotypic variation (sfs_coder). This tool also allows the user to perform locus-specific simulations by automatically querying annotated genomic functional elements and genetic maps. We demonstrate the effects of evolutionary forces on patterns of genetic variation by simulating recently inferred models of human selection and demography. We use these simulations to show that the demographic model and locus-specific features, such as the proportion of sites under selection, may have practical implications for estimating the statistical power of sequencing-based rare variant association tests. In particular, for some phenotype models, there may be higher power to detect rare variant associations in African populations compared to non-Africans, but power is considerably reduced in regions of the genome with rampant negative selection. Furthermore, we show that existing methods for simulating large samples based on resampling from a small set of observed haplotypes fail to recapitulate the distribution of rare variants in the presence of rapid population growth (as has been observed in several human populations).

Testing genetic association with rare and common variants in family data

With the advance of next-generation sequencing technologies in recent years, rare genetic variant data have now become available for genetic epidemiology studies. For family samples, however, only a few statistical methods for association analysis of rare genetic variants have been developed. Rare variant approaches are of great interest, particularly for family data, because samples enriched for trait-relevant variants can be ascertained and rare variants are putatively enriched through segregation. To facilitate the evaluation of existing and new rare variant testing approaches for analyzing family data, Genetic Analysis Workshop 18 (GAW18) provided genotype and next-generation sequencing data and longitudinal blood pressure traits from extended pedigrees of Mexican American families from the San Antonio Family Study. Our GAW18 group members analyzed real and simulated phenotype data from GAW18 by using generalized linear mixed-effects models or principal components to adjust for familial correlation or by testing binary traits using a correction factor for familial effects. With one exception, approaches dealt with the extended pedigrees in their original state using information based on the kinship matrix or alternative genetic similarity measures. For simulated data our group demonstrated that the family-based kernel machine score test is superior in power to family-based single-marker or burden tests, except in a few specific scenarios. For real data three contributions identified significant associations. They substantially reduced the number of tests before performing the association analysis. We conclude from our real data analyses that further development of strategies for targeted testing or more focused screening of genetic variants is strongly desirable.

Cohen's h for detection of disease association with rare genetic variants

Background

The power of the genome wide association studies starts to go down when the minor allele frequency (MAF) is below 0.05. Here, we proposed the use of Cohen’s h in detecting disease associated rare variants. The variance stabilizing effect based on the arcsine square root transformation of MAFs to generate Cohen’s h contributed to the statistical power for rare variants analysis. We re-analyzed published datasets, one microarray and one sequencing based, and used simulation to compare the performance of Cohen’s h with the risk difference (RD) and odds ratio (OR).

Results

The analysis showed that the type 1 error rate of Cohen’s h was as expected and Cohen’s h and RD were both less biased and had higher power than OR. The advantage of Cohen’s h was more obvious when MAF was less than 0.01.

Conclusions

Cohen’s h can increase the power to find genetic association of rare variants and diseases, especially when MAF is less than 0.01.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-875) contains supplementary material, which is available to authorized users.

Performance of statistical methods on CHARGE targeted sequencing data

Background

The CHARGE (Cohorts for Heart and Aging Research in Genomic Epidemiology) Sequencing Project is a national, collaborative effort from 3 studies: Framingham Heart Study (FHS), Cardiovascular Health Study (CHS), and Atherosclerosis Risk in Communities (ARIC). It uses a case-cohort design, whereby a random sample of study participants is enriched with participants in extremes of traits. Although statistical methods are available to investigate the role of rare variants, few have evaluated their performance in a case-cohort design.

Results

We evaluate several methods, including the sequence kernel association test (SKAT), Score-Seq, and weighted (Madsen and Browning) and unweighted burden tests. Using genotypes from the CHARGE targeted-sequencing project for FHS (n = 1096), we simulate phenotypes in a large population for 11 correlated traits and then sample individuals to mimic the CHARGE Sequencing study design. We evaluate type I error and power for 77 targeted regions.

Conclusions

We provide some guidelines on the performance of these aggregate-based tests to detect associations with rare variants when applied to case-cohort study designs, using CHARGE targeted sequencing data. Type I error is conservative when we consider variants with minor allele frequency (MAF) < 1%. Power is generally low, although it is relatively larger for Score-Seq. Greater numbers of causal variants and a greater proportion of variance improve the power, but it tends to be lower in the presence of bi-directionality of effects of causal genotypes, especially for Score-Seq.

Electronic supplementary material

The online version of this article (doi:10.1186/s12863-014-0104-9) contains supplementary material, which is available to authorized users.

TARV: tree-based analysis of rare variants identifying risk modifying variants in CTNNA2 and CNTNAP2 for alcohol addiction

Since the development of next generation sequencing (NGS) technology, researchers have been extending their efforts on genome-wide association studies (GWAS) from common variants to rare variants to find the missing inheritance. Although various statistical methods have been proposed to analyze rare variants data, they generally face difficulties for complex disease models involving multiple genes. In this paper, we propose a tree-based analysis of rare variants (TARV) that adopts a nonparametric disease model and is capable of exploring gene-gene interactions. We found that TARV outperforms the sequence kernel association test (SKAT) in most of our simulation scenarios, and by notable margins in some cases. By applying TARV to the study of addiction: genetics and environment (SAGE) data, we successfully detected gene CTNNA2 and its 43 specific variants that increase the risk of alcoholism in women, with an odds ratio (OR) of 1.94. This gene has not been detected in the SAGE data. Post hoc literature search also supports the role of CTNNA2 as a likely risk gene for alcohol addiction. In addition, we also detected a plausible protective gene CNTNAP2, whose 97 rare variants can reduce the risk of alcoholism in women, with an OR of 0.55. These findings suggest that TARV can be effective in dissecting genetic variants for complex diseases using rare variants data.

Identifying rare and common disease associated variants in genomic data using Parkinson's disease as a model

BACKGROUND

Genome-wide association studies have been successful in identifying common genetic variants for human diseases. However, much of the heritable variation associated with diseases such as Parkinson's disease remains unknown suggesting that many more risk loci are yet to be identified. Rare variants have become important in disease association studies for explaining missing heritability. Methods for detecting this type of association require prior knowledge on candidate genes and combining variants within the region. These methods may suffer from power loss in situations with many neutral variants or causal variants with opposite effects.

RESULTS

We propose a method capable of scanning genetic variants to identify the region most likely harbouring disease gene with rare and/or common causal variants. Our method assigns a score at each individual variant based on our scoring system. It uses aggregate scores to identify the region with disease association. We evaluate performance by simulation based on 1000 Genomes sequencing data and compare with three commonly used methods. We use a Parkinson's disease case-control dataset as a model to demonstrate the application of our method. Our method has better power than CMC and WSS and similar power to SKAT-O with well-controlled type I error under simulation based on 1000 Genomes sequencing data. In real data analysis, we confirm the association of α-synuclein gene (SNCA) with Parkinson's disease (p = 0.005). We further identify association with hyaluronan synthase 2 (HAS2, p = 0.028) and kringle containing transmembrane protein 1 (KREMEN1, p = 0.006). KREMEN1 is associated with Wnt signalling pathway which has been shown to play an important role for neurodegeneration in Parkinson's disease.

CONCLUSIONS

Our method is time efficient and less sensitive to inclusion of neutral variants and direction effect of causal variants. It can narrow down a genomic region or a chromosome to a disease associated region. Using Parkinson's disease as a model, our method not only confirms association for a known gene but also identifies two genes previously found by other studies. In spite of many existing methods, we conclude that our method serves as an efficient alternative for exploring genomic data containing both rare and common variants.

The power comparison of the haplotype-based collapsing tests and the variant-based collapsing tests for detecting rare variants in pedigrees

Background

Both common and rare genetic variants have been shown to contribute to the etiology of complex diseases. Recent genome-wide association studies (GWAS) have successfully investigated how common variants contribute to the genetic factors associated with common human diseases. However, understanding the impact of rare variants, which are abundant in the human population (one in every 17 bases), remains challenging. A number of statistical tests have been developed to analyze collapsed rare variants identified by association tests. Here, we propose a haplotype-based approach. This work inspired by an existing statistical framework of the pedigree disequilibrium test (PDT), which uses genetic data to assess the effects of variants in general pedigrees. We aim to compare the performance between the haplotype-based approach and the rare variant-based approach for detecting rare causal variants in pedigrees.

Results

Extensive simulations in the sequencing setting were carried out to evaluate and compare the haplotype-based approach with the rare variant methods that drew on a more conventional collapsing strategy. As assessed through a variety of scenarios, the haplotype-based pedigree tests had enhanced statistical power compared with the rare variants based pedigree tests when the disease of interest was mainly caused by rare haplotypes (with multiple rare alleles), and vice versa when disease was caused by rare variants acting independently. For most of other situations when disease was caused both by haplotypes with multiple rare alleles and by rare variants with similar effects, these two approaches provided similar power in testing for association.

Conclusions

The haplotype-based approach was designed to assess the role of rare and potentially causal haplotypes. The proposed rare variants-based pedigree tests were designed to assess the role of rare and potentially causal variants. This study clearly documented the situations under which either method performs better than the other. All tests have been implemented in a software, which was submitted to the Comprehensive R Archive Network (CRAN) for general use as a computer program named rvHPDT.

A rare variant association test based on combinations of single-variant tests

Next generation sequencing technologies make direct testing rare variant associations possible. However, the development of powerful statistical methods for rare variant association studies is still underway. Most of existing methods are burden and quadratic tests. Recent studies show that the performance of each of burden and quadratic tests depends strongly upon the underlying assumption and no test demonstrates consistently acceptable power. Thus, combined tests by combining information from the burden and quadratic tests have been proposed recently. However, results from recent studies (including this study) show that there exist tests that can outperform both burden and quadratic tests. In this article, we propose three classes of tests that include tests outperforming both burden and quadratic tests. Then, we propose the optimal combination of single-variant tests (OCST) by combining information from tests of the three classes. We use extensive simulation studies to compare the performance of OCST with that of burden, quadratic and optimal single-variant tests. Our results show that OCST either is the most powerful test or has similar power with the most powerful test. We also compare the performance of OCST with that of the two existing combined tests. Our results show that OCST has better power than the two combined tests.

Incorporating gene-environment interaction in testing for association with rare genetic variants

OBJECTIVES

The incorporation of gene-environment interactions could improve the ability to detect genetic associations with complex traits. For common genetic variants, single-marker interaction tests and joint tests of genetic main effects and gene-environment interaction have been well-established and used to identify novel association loci for complex diseases and continuous traits. For rare genetic variants, however, single-marker tests are severely underpowered due to the low minor allele frequency, and only a few gene-environment interaction tests have been developed. We aimed at developing powerful and computationally efficient tests for gene-environment interaction with rare variants.

METHODS

In this paper, we propose interaction and joint tests for testing gene-environment interaction of rare genetic variants. Our approach is a generalization of existing gene-environment interaction tests for multiple genetic variants under certain conditions.

RESULTS

We show in our simulation studies that our interaction and joint tests have correct type I errors, and that the joint test is a powerful approach for testing genetic association, allowing for gene-environment interaction. We also illustrate our approach in a real data example from the Framingham Heart Study.

CONCLUSION

Our approach can be applied to both binary and continuous traits, it is powerful and computationally efficient.

Rare-variant association analysis: study designs and statistical tests

Despite the extensive discovery of trait- and disease-associated common variants, much of the genetic contribution to complex traits remains unexplained. Rare variants can explain additional disease risk or trait variability. An increasing number of studies are underway to identify trait- and disease-associated rare variants. In this review, we provide an overview of statistical issues in rare-variant association studies with a focus on study designs and statistical tests. We present the design and analysis pipeline of rare-variant studies and review cost-effective sequencing designs and genotyping platforms. We compare various gene- or region-based association tests, including burden tests, variance-component tests, and combined omnibus tests, in terms of their assumptions and performance. Also discussed are the related topics of meta-analysis, population-stratification adjustment, genotype imputation, follow-up studies, and heritability due to rare variants. We provide guidelines for analysis and discuss some of the challenges inherent in these studies and future research directions.

Evaluation of logistic Bayesian LASSO for identifying association with rare haplotypes

It has been hypothesized that rare variants may hold the key to unraveling the genetic transmission mechanism of many common complex traits. Currently, there is a dearth of statistical methods that are powerful enough to detect association with rare haplotypes. One of the recently proposed methods is logistic Bayesian LASSO for case-control data. By penalizing the regression coefficients through appropriate priors, logistic Bayesian LASSO weeds out the unassociated haplotypes, making it possible for the associated rare haplotypes to be detected with higher powers. We used the Genetic Analysis Workshop 18 simulated data to evaluate the behavior of logistic Bayesian LASSO in terms of its power and type I error under a complex disease model. We obtained knowledge of the simulation model, including the locations of the functional variants, and we chose to focus on two genomic regions in the MAP4 gene on chromosome 3. The sample size was 142 individuals and there were 200 replicates.

Despite the small sample size, logistic Bayesian LASSO showed high power to detect two haplotypes containing functional variants in these regions while maintaining low type I errors. At the same time, a commonly used approach for haplotype association implemented in the software hapassoc failed to converge because of the presence of rare haplotypes. Thus, we conclude that logistic Bayesian LASSO can play an important role in the search for rare haplotypes.

Methodology for the analysis of rare genetic variation in genome-wide association and re-sequencing studies of complex human traits

Genome-wide association studies have been successful in identifying common variants that impact complex human traits and diseases. However, despite this success, the joint effects of these variants explain only a small proportion of the genetic variance in these phenotypes, leading to speculation that rare genetic variation might account for much of the ‘missing heritability’. Consequently, there has been an exciting period of research and development into the methodology for the analysis of rare genetic variants, typically by considering their joint effects on complex traits within the same functional unit or genomic region. In this review, we describe a general framework for modelling the joint effects of rare genetic variants on complex traits in association studies of unrelated individuals. We summarise a range of widely used association tests that have been developed from this model and provide an overview of the relative performance of these approaches from published simulation studies.

Kernel-machine testing coupled with a rank-truncation method for genetic pathway analysis

Traditional genome-wide association studies (GWASs) usually focus on single-marker analysis, which only accesses marginal effects. Pathway analysis, on the other hand, considers biological pathway gene marker hierarchical structure and therefore provides additional insights into the genetic architecture underlining complex diseases. Recently, a number of methods for pathway analysis have been proposed to assess the significance of a biological pathway from a collection of single-nucleotide polymorphisms. In this study, we propose a novel approach for pathway analysis that assesses the effects of genes using the sequence kernel association test and the effects of pathways using an extended adaptive rank truncated product statistic. It has been increasingly recognized that complex diseases are caused by both common and rare variants. We propose a new weighting scheme for genetic variants across the whole allelic frequency spectrum to be analyzed together without any form of frequency cutoff for defining rare variants. The proposed approach is flexible. It is applicable to both binary and continuous traits, and incorporating covariates is easy. Furthermore, it can be readily applied to GWAS data, exome-sequencing data, and deep resequencing data. We evaluate the new approach on data simulated under comprehensive scenarios and show that it has the highest power in most of the scenarios while maintaining the correct type I error rate. We also apply our proposed methodology to data from a study of the association between bipolar disorder and candidate pathways from Wellcome Trust Case Control Consortium (WTCCC) to show its utility.

A powerful and adaptive association test for rare variants

This article focuses on conducting global testing for association between a binary trait and a set of rare variants (RVs), although its application can be much broader to other types of traits, common variants (CVs), and gene set or pathway analysis. We show that many of the existing tests have deteriorating performance in the presence of many nonassociated RVs: their power can dramatically drop as the proportion of nonassociated RVs in the group to be tested increases. We propose a class of so-called sum of powered score (SPU) tests, each of which is based on the score vector from a general regression model and hence can deal with different types of traits and adjust for covariates, e.g., principal components accounting for population stratification. The SPU tests generalize the sum test, a representative burden test based on pooling or collapsing genotypes of RVs, and a sum of squared score (SSU) test that is closely related to several other powerful variance component tests; a previous study (Basu and Pan 2011) has demonstrated good performance of one, but not both, of the Sum and SSU tests in many situations. The SPU tests are versatile in the sense that one of them is often powerful, although its identity varies with the unknown true association parameters. We propose an adaptive SPU (aSPU) test to approximate the most powerful SPU test for a given scenario, consequently maintaining high power and being highly adaptive across various scenarios. We conducted extensive simulations to show superior performance of the aSPU test over several state-of-the-art association tests in the presence of many nonassociated RVs. Finally we applied the SPU and aSPU tests to the GAW17 mini-exome sequence data to compare its practical performance with some existing tests, demonstrating their potential usefulness.

A variational Bayes discrete mixture test for rare variant association

Recently, many statistical methods have been proposed to test for associations between rare genetic variants and complex traits. Most of these methods test for association by aggregating genetic variations within a predefined region, such as a gene. Although there is evidence that "aggregate" tests are more powerful than the single marker test, these tests generally ignore neutral variants and therefore are unable to identify specific variants driving the association with phenotype. We propose a novel aggregate rare-variant test that explicitly models a fraction of variants as neutral, tests associations at the gene-level, and infers the rare-variants driving the association. Simulations show that in the practical scenario where there are many variants within a given region of the genome with only a fraction causal our approach has greater power compared to other popular tests such as the Sequence Kernel Association Test (SKAT), the Weighted Sum Statistic (WSS), and the collapsing method of Morris and Zeggini (MZ). Our algorithm leverages a fast variational Bayes approximate inference methodology to scale to exome-wide analyses, a significant computational advantage over exact inference model selection methodologies. To demonstrate the efficacy of our methodology we test for associations between von Willebrand Factor (VWF) levels and VWF missense rare-variants imputed from the National Heart, Lung, and Blood Institute's Exome Sequencing project into 2,487 African Americans within the VWF gene. Our method suggests that a relatively small fraction (~10%) of the imputed rare missense variants within VWF are strongly associated with lower VWF levels in African Americans.

Valid Monte Carlo permutation tests for genetic case-control studies with missing genotypes

Monte Carlo permutation tests can be formally constructed by choosing a set of permutations of individual indices and a real-valued test statistic measuring the association between genotypes and affection status. In this paper, we develop a rigorous theoretical framework for verifying the validity of these tests when there are missing genotypes. We begin by specifying a nonparametric probability model for the observed genotype data in a genetic case-control study with unrelated subjects. Under this model and some minimal assumptions about the test statistic, we establish that the resulting Monte Carlo permutation test is exact level α if (1) the chosen set of permutations of individual indices is a group under composition and (2) the distribution of the observed genotype score matrix under the null hypothesis does not change if the assignment of individuals to rows is shuffled according to an arbitrary permutation in this set. We apply these conditions to show that frequently used Monte Carlo permutation tests based on the set of all permutations of individual indices are guaranteed to be exact level α only for missing data processes satisfying a rather restrictive additional assumption. However, if the missing data process depends on covariates that are all identified and recorded, we also show that Monte Carlo permutation tests based on the set of permutations within strata of individuals with identical covariate values are exact level α. Our theoretical results are verified and supplemented by simulations for a variety of missing data processes and test statistics.