Relationship between genomic distance-based regression and kernel machine regression for multi-marker association testing

Similarity-based multimodal regression

To better understand complex human phenotypes, large-scale studies have increasingly collected multiple data modalities across domains such as imaging, mobile health, and physical activity. The properties of each data type often differ substantially and require either separate analyses or extensive processing to obtain comparable features for a combined analysis. Multimodal data fusion enables certain analyses on matrix-valued and vector-valued data, but it generally cannot integrate modalities of different dimensions and data structures. For a single data modality, multivariate distance matrix regression provides a distance-based framework for regression accommodating a wide range of data types. However, no distance-based method exists to handle multiple complementary types of data. We propose a novel distance-based regression model, which we refer to as Similarity-based Multimodal Regression (SiMMR), that enables simultaneous regression of multiple modalities through their distance profiles. We demonstrate through simulation, imaging studies, and longitudinal mobile health analyses that our proposed method can detect associations between clinical variables and multimodal data of differing properties and dimensionalities, even with modest sample sizes. We perform experiments to evaluate several different test statistics and provide recommendations for applying our method across a broad range of scenarios.

Phylogenetic association analysis with conditional rank correlation

Phylogenetic association analysis plays a crucial role in investigating the correlation between microbial compositions and specific outcomes of interest in microbiome studies. However, existing methods for testing such associations have limitations related to the assumption of a linear association in high-dimensional settings and the handling of confounding effects. Hence, there is a need for methods capable of characterizing complex associations, including nonmonotonic relationships. This article introduces a novel phylogenetic association analysis framework and associated tests to address these challenges by employing conditional rank correlation as a measure of association. The proposed tests account for confounders in a fully nonparametric manner, ensuring robustness against outliers and the ability to detect diverse dependencies. The proposed framework aggregates conditional rank correlations for subtrees using weighted sum and maximum approaches to capture both dense and sparse signals. The significance level of the test statistics is determined by calibration through a nearest-neighbour bootstrapping method, which is straightforward to implement and can accommodate additional datasets when these are available. The practical advantages of the proposed framework are demonstrated through numerical experiments using both simulated and real microbiome datasets.

Associating somatic mutation with clinical outcomes through kernel regression and optimal transport

Somatic mutations in cancer patients are inherently sparse and potentially high dimensional. Cancer patients may share the same set of deregulated biological processes perturbed by different sets of somatically mutated genes. Therefore, when assessing the associations between somatic mutations and clinical outcomes, gene-by-gene analysis is often under-powered because it does not capture the complex disease mechanisms shared across cancer patients. Rather than testing genes one by one, an intuitive approach is to aggregate somatic mutation data of multiple genes to assess their joint association with clinical outcomes. The challenge is how to aggregate such information. Building on the optimal transport method, we propose a principled approach to estimate the similarity of somatic mutation profiles of multiple genes between tumor samples, while accounting for gene-gene similarities defined by gene annotations or empirical mutational patterns. Using such similarities, we can assess the associations between somatic mutations and clinical outcomes by kernel regression. We have applied our method to analyze somatic mutation data of 17 cancer types and identified at least five cancer types, where somatic mutations are associated with overall survival, progression-free interval, or cytolytic activity.

A robust association test with multiple genetic variants and covariates

Due to the advancement of genome sequencing techniques, a great stride has been made in exome sequencing such that the association study between disease and genetic variants has become feasible. Some powerful and well-known association tests have been proposed to test the association between a group of genes and the disease of interest. However, some challenges still remain, in particular, many factors can affect the performance of testing power, e.g., the sample size, the number of causal and non-causal variants, and direction of the effect of causal variants. Recently, a powerful test, called T REM , is derived based on a random effects model. T REM has the advantages of being less sensitive to the inclusion of non-causal rare variants or low effect common variants or the presence of missing genotypes. However, the testing power of T REM can be low when a portion of causal variants has effects in opposite directions. To improve the drawback of T REM , we propose a novel test, called T ROB , which keeps the advantages of T REM and is more robust than T REM in terms of having adequate power in the case of variants with opposite directions of effect. Simulation results show that T ROB has a stable type I error rate and outperforms T REM when the proportion of risk variants decreases to a certain level and its advantage over T REM increases as the proportion decreases. Furthermore, T ROB outperforms several other competing tests in most scenarios. The proposed methodology is illustrated using the Shanghai Breast Cancer Study.

Compositional Data Analysis using Kernels in mass cytometry data

MOTIVATION

Cell-type abundance data arising from mass cytometry experiments are compositional in nature. Classical association tests do not apply to the compositional data due to their non-Euclidean nature. Existing methods for analysis of cell type abundance data suffer from several limitations for high-dimensional mass cytometry data, especially when the sample size is small.

RESULTS

We proposed a new multivariate statistical learning methodology, Compositional Data Analysis using Kernels (CODAK), based on the kernel distance covariance (KDC) framework to test the association of the cell type compositions with important predictors (categorical or continuous) such as disease status. CODAK scales well for high-dimensional data and provides satisfactory performance for small sample sizes (n < 25). We conducted simulation studies to compare the performance of the method with existing methods of analyzing cell type abundance data from mass cytometry studies. The method is also applied to a high-dimensional dataset containing different subgroups of populations including Systemic Lupus Erythematosus (SLE) patients and healthy control subjects.

AVAILABILITY AND IMPLEMENTATION

CODAK is implemented using R. The codes and the data used in this manuscript are available on the web at http://github.com/GhoshLab/CODAK/.

CONTACT

prudra@okstate.edu.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics Advances online.

A Statistical Method for Association Analysis of Cell Type Compositions

Gene expression data are often collected from tissue samples that are composed of multiple cell types. Studies of cell type composition based on gene expression data from tissue samples have recently attracted increasing research interest and led to new method development for cell type composition estimation. This new information on cell type composition can be associated with individual characteristics (e.g., genetic variants) or clinical outcomes (e.g., survival time). Such association analysis can be conducted for each cell type separately followed by multiple testing correction. An alternative approach is to evaluate this association using the composition of all the cell types, thus aggregating association signals across cell types. A key challenge of this approach is to account for the dependence across cell types. We propose a new method to quantify the distances between cell types while accounting for their dependencies, and use this information for association analysis. We demonstrate our method in two applied examples: to assess the association between immune cell type composition in tumor samples of colorectal cancer patients versus survival time and SNP genotypes. We found immune cell composition has prognostic value, and our distance metric leads to more accurate survival time prediction than other distance metrics that ignore cell type dependencies. In addition, survival time-associated SNPs are enriched among the SNPs associated with immune cell composition.

A Multi-Marker Test for Analyzing Paired Genetic Data in Transplantation

Emerging evidence suggests that donor/recipient matching in non-HLA (human leukocyte antigen) regions of the genome may impact transplant outcomes and recognizing these matching effects may increase the power of transplant genetics studies. Most available matching scores account for either single-nucleotide polymorphism (SNP) matching only or sum these SNP matching scores across multiple gene-coding regions, which makes it challenging to interpret the association findings. We propose a multi-marker Joint Score Test (JST) to jointly test for association between recipient genotype SNP effects and a gene-based matching score with transplant outcomes. This method utilizes Eigen decomposition as a dimension reduction technique to potentially increase statistical power by decreasing the degrees of freedom for the test. In addition, JST allows for the matching effect and the recipient genotype effect to follow different biological mechanisms, which is not the case for other multi-marker methods. Extensive simulation studies show that JST is competitive when compared with existing methods, such as the sequence kernel association test (SKAT), especially under scenarios where associated SNPs are in low linkage disequilibrium with non-associated SNPs or in gene regions containing a large number of SNPs. Applying the method to paired donor/recipient genetic data from kidney transplant studies yields various gene regions that are potentially associated with incidence of acute rejection after transplant.

aPCoA: covariate adjusted principal coordinates analysis

SUMMARY

In fields, such as ecology, microbiology and genomics, non-Euclidean distances are widely applied to describe pairwise dissimilarity between samples. Given these pairwise distances, principal coordinates analysis is commonly used to construct a visualization of the data. However, confounding covariates can make patterns related to the scientific question of interest difficult to observe. We provide adjusted principal coordinates analysis as an easy-to-use tool, available as both an R package and a Shiny app, to improve data visualization in this context, enabling enhanced presentation of the effects of interest.

AVAILABILITY AND IMPLEMENTATION

The R package 'aPCoA' and Shiny app can be accessed at https://cran.r-project.org/web/packages/aPCoA/index.html and https://biostatistics.mdanderson.org/shinyapps/aPCoA/.

TS: a powerful truncated test to detect novel disease associated genes using publicly available gWAS summary data

BACKGROUND

In the last decade, a large number of common variants underlying complex diseases have been identified through genome-wide association studies (GWASs). Summary data of the GWASs are freely and publicly available. The summary data is usually obtained through single marker analysis. Gene-based analysis offers a useful alternative and complement to single marker analysis. Results from gene level association tests can be more readily integrated with downstream functional and pathogenic investigations. Most existing gene-based methods fall into two categories: burden tests and quadratic tests. Burden tests are usually powerful when the directions of effects of causal variants are the same. However, they may suffer loss of statistical power when different directions of effects exist at the causal variants. The power of quadratic tests is not affected by the directions of effects but could be less powerful due to issues such as the large number of degree of freedoms. These drawbacks of existing gene based methods motivated us to develop a new powerful method to identify disease associated genes using existing GWAS summary data.

METHODS AND RESULTS

In this paper, we propose a new truncated statistic method (TS) by utilizing a truncated method to find the genes that have a true contribution to the genetic association. Extensive simulation studies demonstrate that our proposed test outperforms other comparable tests. We applied TS and other comparable methods to the schizophrenia GWAS data and type 2 diabetes (T2D) GWAS meta-analysis summary data. TS identified more disease associated genes than comparable methods. Many of the significant genes identified by TS may have important mechanisms relevant to the associated traits. TS is implemented in C program TS, which is freely and publicly available online.

CONCLUSIONS

The proposed truncated statistic outperforms existing methods. It can be employed to detect novel traits associated genes using GWAS summary data.

A review of kernel methods for genetic association studies

Evaluating the association of multiple genetic variants with a trait of interest by use of kernel-based methods has made a significant impact on how genetic association analyses are conducted. An advantage of kernel methods is that they tend to be robust when the genetic variants have effects that are a mixture of positive and negative effects, as well as when there is a small fraction of causal variants. Another advantage is that kernel methods fit within the framework of mixed models, providing flexible ways to adjust for additional covariates that influence traits. Herein, we review the basic ideas behind the use of kernel methods for genetic association analysis as well as recent methodological advancements for different types of traits, multivariate traits, pedigree data, and longitudinal data. Finally, we discuss opportunities for future research.

An adaptive gene-level association test for pedigree data

Background

We propose a gene-level association test that accounts for individual relatedness and population structures in pedigree data in the framework of linear mixed models (LMMs). Our method data-adaptively combines the results across a class of score-based tests, only requiring fitting a single null model (under the null hypothesis) for the whole genome, thereby being computationally efficient.

Results

We applied our approach to test for association with the high-density lipoprotein (HDL) ratio of post- and pretreatments in GAW20 data. Using the LMM similar to that used by Aslibekyan et al. (PLos One, 7:48663, 2012), our method identified 2 nearly significant genes (APOA5 and ZNF259) near rs964184, whereas neither the other gene-level tests nor the standard test on each individual single-nucleotide polymorphism (SNP) detected any significant gene in a genome-wide scan.

Conclusions

Gene-level association testing can be a complementary approach to the SNP-level association testing and our method is adaptive and efficient compared to several other existing gene-level association tests.

KERNEL-PENALIZED REGRESSION FOR ANALYSIS OF MICROBIOME DATA

The analysis of human microbiome data is often based on dimension-reduced graphical displays and clusterings derived from vectors of microbial abundances in each sample. Common to these ordination methods is the use of biologically motivated definitions of similarity. Principal coordinate analysis, in particular, is often performed using ecologically defined distances, allowing analyses to incorporate context-dependent, non-Euclidean structure. In this paper, we go beyond dimension-reduced ordination methods and describe a framework of high-dimensional regression models that extends these distance-based methods. In particular, we use kernel-based methods to show how to incorporate a variety of extrinsic information, such as phylogeny, into penalized regression models that estimate taxonspecific associations with a phenotype or clinical outcome. Further, we show how this regression framework can be used to address the compositional nature of multivariate predictors comprised of relative abundances; that is, vectors whose entries sum to a constant. We illustrate this approach with several simulations using data from two recent studies on gut and vaginal microbiomes. We conclude with an application to our own data, where we also incorporate a significance test for the estimated coefficients that represent associations between microbial abundance and a percent fat.

Adaptive SNP-Set Association Testing in Generalized Linear Mixed Models with Application to Family Studies

In genome-wide association studies (GWAS), it has been increasingly recognized that, as a complementary approach to standard single SNP analyses, it may be beneficial to analyze a group of functionally related SNPs together. Among the existent population-based SNP-set association tests, two adaptive tests, the aSPU test and the aSPUpath test, offer a powerful and general approach at the gene- and pathway-levels by data-adaptively combining the results across multiple SNPs (and genes) such that high statistical power can be maintained across a wide range of scenarios. We extend the aSPU and the aSPUpath test to familial data under the framework of the generalized linear mixed models (GLMMs), which can take account of both subject relatedness and possible population structure. As in population-based GWAS, the proposed aSPU and aSPUpath tests require only fitting a single and common GLMM (under the null hypothesis) for all the SNPs, thus are computationally efficient and feasible for large GWAS data. We illustrate our approaches in identifying genes and pathways associated with alcohol dependence in the Minnesota Twin Family Study. The aSPU test detected a gene associated with the trait, in contrast to none by the standard single SNP analysis. Our aSPU test also controlled Type I errors satisfactorily in a small simulation study. We provide R code to conduct the aSPU and aSPUpath tests for familial and other correlated data.

Imaging-wide association study: Integrating imaging endophenotypes in GWAS

A new and powerful approach, called imaging-wide association study (IWAS), is proposed to integrate imaging endophenotypes with GWAS to boost statistical power and enhance biological interpretation for GWAS discoveries. IWAS extends the promising transcriptome-wide association study (TWAS) from using gene expression endophenotypes to using imaging and other endophenotypes with a much wider range of possible applications. As illustration, we use gray-matter volumes of several brain regions of interest (ROIs) drawn from the ADNI-1 structural MRI data as imaging endophenotypes, which are then applied to the individual-level GWAS data of ADNI-GO/2 and a large meta-analyzed GWAS summary statistics dataset (based on about 74,000 individuals), uncovering some novel genes significantly associated with Alzheimer's disease (AD). We also compare the performance of IWAS with TWAS, showing much larger numbers of significant AD-associated genes discovered by IWAS, presumably due to the stronger link between brain atrophy and AD than that between gene expression of normal individuals and the risk for AD. The proposed IWAS is general and can be applied to other imaging endophenotypes, and GWAS individual-level or summary association data.

A Powerful Framework for Integrating eQTL and GWAS Summary Data

Two new gene-based association analysis methods, called PrediXcan and TWAS for GWAS individual-level and summary data, respectively, were recently proposed to integrate GWAS with eQTL data, alleviating two common problems in GWAS by boosting statistical power and facilitating biological interpretation of GWAS discoveries. Based on a novel reformulation of PrediXcan and TWAS, we propose a more powerful gene-based association test to integrate single set or multiple sets of eQTL data with GWAS individual-level data or summary statistics. The proposed test was applied to several GWAS datasets, including two lipid summary association datasets based on [Formula: see text] and [Formula: see text] samples, respectively, and uncovered more known or novel trait-associated genes, showcasing much improved performance of our proposed method. The software implementing the proposed method is freely available as an R package.

An adaptive two-sample test for high-dimensional means

Several two-sample tests for high-dimensional data have been proposed recently, but they are powerful only against certain alternative hypotheses. In practice, since the true alternative hypothesis is unknown, it is unclear how to choose a powerful test. We propose an adaptive test that maintains high power across a wide range of situations and study its asymptotic properties. Its finite-sample performance is compared with that of existing tests. We apply it and other tests to detect possible associations between bipolar disease and a large number of single nucleotide polymorphisms on each chromosome based on data from a genome-wide association study. Numerical studies demonstrate the superior performance and high power of the proposed test across a wide spectrum of applications.

On Robust Association Testing for Quantitative Traits and Rare Variants

With the advance of sequencing technologies, it has become a routine practice to test for association between a quantitative trait and a set of rare variants (RVs). While a number of RV association tests have been proposed, there is a dearth of studies on the robustness of RV association testing for nonnormal distributed traits, e.g., due to skewness, which is ubiquitous in cohort studies. By extensive simulations, we demonstrate that commonly used RV tests, including sequence kernel association test (SKAT) and optimal unified SKAT (SKAT-O), are not robust to heavy-tailed or right-skewed trait distributions with inflated type I error rates; in contrast, the adaptive sum of powered score (aSPU) test is much more robust. Here we further propose a robust version of the aSPU test, called aSPUr. We conduct extensive simulations to evaluate the power of the tests, finding that for a larger number of RVs, aSPU is often more powerful than SKAT and SKAT-O, owing to its high data-adaptivity. We also compare different tests by conducting association analysis of triglyceride levels using the NHLBI ESP whole-exome sequencing data. The QQ plots for SKAT and SKAT-O were severely inflated (λ = 1.89 and 1.78, respectively), while those for aSPU and aSPUr behaved normally. Due to its relatively high robustness to outliers and high power of the aSPU test, we recommend its use complementary to SKAT and SKAT-O. If there is evidence of inflated type I error rate from the aSPU test, we would recommend the use of the more robust, but less powerful, aSPUr test.

An adaptive association test for microbiome data

There is increasing interest in investigating how the compositions of microbial communities are associated with human health and disease. Although existing methods have identified many associations, a proper choice of a phylogenetic distance is critical for the power of these methods. To assess an overall association between the composition of a microbial community and an outcome of interest, we present a novel multivariate testing method called aMiSPU, that is joint and highly adaptive over all observed taxa and thus high powered across various scenarios, alleviating the issue with the choice of a phylogenetic distance. Our simulations and real-data analyses demonstrated that the aMiSPU test was often more powerful than several competing methods while correctly controlling type I error rates. The R package MiSPU is available at https://github.com/ChongWu-Biostat/MiSPU and CRAN.

Adaptive gene- and pathway-trait association testing with GWAS summary statistics

BACKGROUND

Gene- and pathway-based analyses offer a useful alternative and complement to the usual single SNP-based analysis for GWAS. On the other hand, most existing gene- and pathway-based tests are not highly adaptive, and/or require the availability of individual-level genotype and phenotype data. It would be desirable to have highly adaptive tests applicable to summary statistics for single SNPs. This has become increasingly important given the popularity of large-scale meta-analyses of multiple GWASs and the practical availability of either single GWAS or meta-analyzed GWAS summary statistics for single SNPs.

RESULTS

We extend two adaptive tests for gene- and pathway-level association with a univariate trait to the case with GWAS summary statistics without individual-level genotype and phenotype data. We use the WTCCC GWAS data to evaluate and compare the proposed methods and several existing methods. We further illustrate their applications to a meta-analyzed dataset to identify genes and pathways associated with blood pressure, demonstrating the potential usefulness of the proposed methods. The methods are implemented in R package aSPU, freely and publicly available.

AVAILABILITY AND IMPLEMENTATION

https://cran.r-project.org/web/packages/aSPU/ CONTACT: weip@biostat.umn.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Powerful and Adaptive Testing for Multi-trait and Multi-SNP Associations with GWAS and Sequencing Data

Testing for genetic association with multiple traits has become increasingly important, not only because of its potential to boost statistical power, but also for its direct relevance to applications. For example, there is accumulating evidence showing that some complex neurodegenerative and psychiatric diseases like Alzheimer's disease are due to disrupted brain networks, for which it would be natural to identify genetic variants associated with a disrupted brain network, represented as a set of multiple traits, one for each of multiple brain regions of interest. In spite of its promise, testing for multivariate trait associations is challenging: if not appropriately used, its power can be much lower than testing on each univariate trait separately (with a proper control for multiple testing). Furthermore, differing from most existing methods for single-SNP-multiple-trait associations, we consider SNP set-based association testing to decipher complicated joint effects of multiple SNPs on multiple traits. Because the power of a test critically depends on several unknown factors such as the proportions of associated SNPs and of traits, we propose a highly adaptive test at both the SNP and trait levels, giving higher weights to those likely associated SNPs and traits, to yield high power across a wide spectrum of situations. We illuminate relationships among the proposed and some existing tests, showing that the proposed test covers several existing tests as special cases. We compare the performance of the new test with that of several existing tests, using both simulated and real data. The methods were applied to structural magnetic resonance imaging data drawn from the Alzheimer's Disease Neuroimaging Initiative to identify genes associated with gray matter atrophy in the human brain default mode network (DMN). For genome-wide association studies (GWAS), genes AMOTL1 on chromosome 11 and APOE on chromosome 19 were discovered by the new test to be significantly associated with the DMN. Notably, gene AMOTL1 was not detected by single SNP-based analyses. To our knowledge, AMOTL1 has not been highlighted in other Alzheimer's disease studies before, although it was indicated to be related to cognitive impairment. The proposed method is also applicable to rare variants in sequencing data and can be extended to pathway analysis.

Object-oriented regression for building predictive models with high dimensional omics data from translational studies

Maturing omics technologies enable researchers to generate high dimension omics data (HDOD) routinely in translational clinical studies. In the field of oncology, The Cancer Genome Atlas (TCGA) provided funding support to researchers to generate different types of omics data on a common set of biospecimens with accompanying clinical data and has made the data available for the research community to mine. One important application, and the focus of this manuscript, is to build predictive models for prognostic outcomes based on HDOD. To complement prevailing regression-based approaches, we propose to use an object-oriented regression (OOR) methodology to identify exemplars specified by HDOD patterns and to assess their associations with prognostic outcome. Through computing patient's similarities to these exemplars, the OOR-based predictive model produces a risk estimate using a patient's HDOD. The primary advantages of OOR are twofold: reducing the penalty of high dimensionality and retaining the interpretability to clinical practitioners. To illustrate its utility, we apply OOR to gene expression data from non-small cell lung cancer patients in TCGA and build a predictive model for prognostic survivorship among stage I patients, i.e., we stratify these patients by their prognostic survival risks beyond histological classifications. Identification of these high-risk patients helps oncologists to develop effective treatment protocols and post-treatment disease management plans. Using the TCGA data, the total sample is divided into training and validation data sets. After building up a predictive model in the training set, we compute risk scores from the predictive model, and validate associations of risk scores with prognostic outcome in the validation data (P-value=0.015).

Multiple SNP Set Analysis for Genome-Wide Association Studies Through Bayesian Latent Variable Selection

The power of genome-wide association studies (GWAS) for mapping complex traits with single-SNP analysis (where SNP is single-nucleotide polymorphism) may be undermined by modest SNP effect sizes, unobserved causal SNPs, correlation among adjacent SNPs, and SNP-SNP interactions. Alternative approaches for testing the association between a single SNP set and individual phenotypes have been shown to be promising for improving the power of GWAS. We propose a Bayesian latent variable selection (BLVS) method to simultaneously model the joint association mapping between a large number of SNP sets and complex traits. Compared with single SNP set analysis, such joint association mapping not only accounts for the correlation among SNP sets but also is capable of detecting causal SNP sets that are marginally uncorrelated with traits. The spike-and-slab prior assigned to the effects of SNP sets can greatly reduce the dimension of effective SNP sets, while speeding up computation. An efficient Markov chain Monte Carlo algorithm is developed. Simulations demonstrate that BLVS outperforms several competing variable selection methods in some important scenarios.

Highly adaptive tests for group differences in brain functional connectivity

Resting-state functional magnetic resonance imaging (rs-fMRI) and other technologies have been offering evidence and insights showing that altered brain functional networks are associated with neurological illnesses such as Alzheimer's disease. Exploring brain networks of clinical populations compared to those of controls would be a key inquiry to reveal underlying neurological processes related to such illnesses. For such a purpose, group-level inference is a necessary first step in order to establish whether there are any genuinely disrupted brain subnetworks. Such an analysis is also challenging due to the high dimensionality of the parameters in a network model and high noise levels in neuroimaging data. We are still in the early stage of method development as highlighted by Varoquaux and Craddock (2013) that “there is currently no unique solution, but a spectrum of related methods and analytical strategies” to learn and compare brain connectivity. In practice the important issue of how to choose several critical parameters in estimating a network, such as what association measure to use and what is the sparsity of the estimated network, has not been carefully addressed, largely because the answers are unknown yet. For example, even though the choice of tuning parameters in model estimation has been extensively discussed in the literature, as to be shown here, an optimal choice of a parameter for network estimation may not be optimal in the current context of hypothesis testing. Arbitrarily choosing or mis-specifying such parameters may lead to extremely low-powered tests. Here we develop highly adaptive tests to detect group differences in brain connectivity while accounting for unknown optimal choices of some tuning parameters.

The proposed tests combine statistical evidence against a null hypothesis from multiple sources across a range of plausible tuning parameter values reflecting uncertainty with the unknown truth. These highly adaptive tests are not only easy to use, but also high-powered robustly across various scenarios. The usage and advantages of these novel tests are demonstrated on an Alzheimer's disease dataset and simulated data.

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Rigorous testing for genuinely altered functional networks between two groups

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The proposed tests are high powered and general across a wide range of scenarios.

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Data-driven penalized network estimation

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Data-driven choice between correlations and partial correlations to describe association

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Some key differences between network estimation and testing are highlighted.

Approximate score-based testing with application to multivariate trait association analysis

For genome-wide association studies and DNA sequencing studies, several powerful score-based tests, such as kernel machine regression and sum of powered score tests, have been proposed in the last few years. However, extensions of these score-based tests to more complex models, such as mixed-effects models for analysis of multiple and correlated traits, have been hindered by the unavailability of the score vector, due to either no output from statistical software or no closed-form solution at all. We propose a simple and general method to asymptotically approximate the score vector based on an asymptotically normal and consistent estimate of a parameter vector to be tested and its (consistent) covariance matrix. The proposed method is applicable to both maximum-likelihood estimation and estimating function-based approaches. We use the derived approximate score vector to extend several score-based tests to mixed-effects models. We demonstrate the feasibility and possible power gains of these tests in association analysis of multiple and correlated quantitative or binary traits with both real and simulated data. The proposed method is easy to implement with a wide applicability.

A Powerful Pathway-Based Adaptive Test for Genetic Association with Common or Rare Variants

In spite of the success of genome-wide association studies (GWASs), only a small proportion of heritability for each complex trait has been explained by identified genetic variants, mainly SNPs. Likely reasons include genetic heterogeneity (i.e., multiple causal genetic variants) and small effect sizes of causal variants, for which pathway analysis has been proposed as a promising alternative to the standard single-SNP-based analysis. A pathway contains a set of functionally related genes, each of which includes multiple SNPs. Here we propose a pathway-based test that is adaptive at both the gene and SNP levels, thus maintaining high power across a wide range of situations with varying numbers of the genes and SNPs associated with a trait. The proposed method is applicable to both common variants and rare variants and can incorporate biological knowledge on SNPs and genes to boost statistical power. We use extensively simulated data and a WTCCC GWAS dataset to compare our proposal with several existing pathway-based and SNP-set-based tests, demonstrating its promising performance and its potential use in practice.

Powerful Tukey's One Degree-of-Freedom Test for Detecting Gene-Gene and Gene-Environment Interactions

Genome-wide association studies (GWASs) have identified thousands of single nucleotide polymorphisms (SNPs) robustly associated with hundreds of complex human diseases including cancers. However, the large number of GWAS-identified genetic loci only explains a small proportion of the disease heritability. This “missing heritability” problem has been partly attributed to the yet-to-be-identified gene–gene (G × G) and gene–environment (G × E) interactions. In spite of the important roles of G × G and G × E interactions in understanding disease mechanisms and filling in the missing heritability, straightforward GWAS scanning for such interactions has very limited statistical power, leading to few successes. Here we propose a two-step statistical approach to test G × G/G × E interactions: the first step is to perform principal component analysis (PCA) on the multiple SNPs within a gene region, and the second step is to perform Tukey’s one degree-of-freedom (1-df) test on the leading PCs. We derive a score test that is computationally fast and numerically stable for the proposed Tukey’s 1-df interaction test. Using extensive simulations we show that the proposed approach, which combines the two parsimonious models, namely, the PCA and Tukey’s 1-df form of interaction, outperforms other state-of-the-art methods. We also demonstrate the utility and efficiency gains of the proposed method with applications to testing G × G interactions for Crohn’s disease using the Wellcome Trust Case Control Consortium (WTCCC) GWAS data and testing G × E interaction using data from a case–control study of pancreatic cancer.

Testing in Microbiome-Profiling Studies with MiRKAT, the Microbiome Regression-Based Kernel Association Test

High-throughput sequencing technology has enabled population-based studies of the role of the human microbiome in disease etiology and exposure response. Distance-based analysis is a popular strategy for evaluating the overall association between microbiome diversity and outcome, wherein the phylogenetic distance between individuals' microbiome profiles is computed and tested for association via permutation. Despite their practical popularity, distance-based approaches suffer from important challenges, especially in selecting the best distance and extending the methods to alternative outcomes, such as survival outcomes. We propose the microbiome regression-based kernel association test (MiRKAT), which directly regresses the outcome on the microbiome profiles via the semi-parametric kernel machine regression framework. MiRKAT allows for easy covariate adjustment and extension to alternative outcomes while non-parametrically modeling the microbiome through a kernel that incorporates phylogenetic distance. It uses a variance-component score statistic to test for the association with analytical p value calculation. The model also allows simultaneous examination of multiple distances, alleviating the problem of choosing the best distance. Our simulations demonstrated that MiRKAT provides correctly controlled type I error and adequate power in detecting overall association. "Optimal" MiRKAT, which considers multiple candidate distances, is robust in that it suffers from little power loss in comparison to when the best distance is used and can achieve tremendous power gain in comparison to when a poor distance is chosen. Finally, we applied MiRKAT to real microbiome datasets to show that microbial communities are associated with smoking and with fecal protease levels after confounders are controlled for.

Testing for polygenic effects in genome-wide association studies

To confirm associations with a large number of single nucleotide polymorphisms (SNPs), each with only a small effect size, as hypothesized in the polygenic theory for schizophrenia, the International Schizophrenia Consortium (2009, Nature 460:748-752) proposed a polygenic risk score (PRS) test and demonstrated its effectiveness when applied to psychiatric disorders. The basic idea of the PRS test is to use a half of the sample to select and up-weight those more likely to be associated SNPs, and then use the other half of the sample to test for aggregated effects of the selected SNPs. Intrigued by the novelty and increasing use of the PRS test, we aimed to evaluate and improve its performance for GWAS data. First, by an analysis of the PRS test, we point out its connection with the Sum test [Chapman and Whittaker, Genet Epidemiol 32:560-566; Pan, Genet Epidemiol 33:497-507]; given the known advantages and disadvantages of the Sum test, this connection motivated the development of several other polygenic tests, some of which may be more powerful than the PRS test under certain situations. Second, more importantly, to overcome the low statistical efficiency of the data-splitting strategy as adopted in the PRS test, we reformulate and thus modify the PRS test, obtaining several adaptive tests, which are closely related to the adaptive sum of powered score (SPU) test studied in the context of rare variant analysis [Pan et al., 2014, Genetics 197:1081-1095]. We use both simulated data and a real GWAS dataset of alcohol dependence to show dramatically improved power of the new tests over the PRS test; due to its superior performance and simplicity, we recommend the whole sample-based adaptive SPU test for polygenic testing. We hope to raise the awareness of the limitations of the PRS test and potential power gain of the adaptive SPU test.

Comparison of statistical tests for group differences in brain functional networks

Brain functional connectivity has been studied by analyzing time series correlations in regional brain activities based on resting-state fMRI data. Brain functional connectivity can be depicted as a network or graph defined as a set of nodes linked by edges. Nodes represent brain regions and an edge measures the strength of functional correlation between two regions. Most of existing work focuses on estimation of such a network. A key but inadequately addressed question is how to test for possible differences of the networks between two subject groups, say between healthy controls and patients. Here we illustrate and compare the performance of several state-of-the-art statistical tests drawn from the neuroimaging, genetics, ecology and high-dimensional data literatures. Both real and simulated data were used to evaluate the methods. We found that Network Based Statistic (NBS) performed well in many but not all situations, and its performance critically depends on the choice of its threshold parameter, which is unknown and difficult to choose in practice. Importantly, two adaptive statistical tests called adaptive sum of powered score (aSPU) and its weighted version (aSPUw) are easy to use and complementary to NBS, being higher powered than NBS in some situations. The aSPU and aSPUw tests can also be applied to adjust for covariates. Between the aSPU and aSPUw tests, they often, but not always, performed similarly with neither one as a uniform winner. On the other hand, Multivariate Matrix Distance Regression (MDMR) has been applied to detect group differences for brain connectivity; with the usual choice of the Euclidean distance, MDMR is a special case of the aSPU test. Consequently NBS, aSPU and aSPUw tests are recommended to test for group differences in functional connectivity.

Functional logistic regression approach to detecting gene by longitudinal environmental exposure interaction in a case-control study

Most complex human diseases are likely the consequence of the joint actions of genetic and environmental factors. Identification of gene-environment (G × E) interactions not only contributes to a better understanding of the disease mechanisms, but also improves disease risk prediction and targeted intervention. In contrast to the large number of genetic susceptibility loci discovered by genome-wide association studies, there have been very few successes in identifying G × E interactions, which may be partly due to limited statistical power and inaccurately measured exposures. Although existing statistical methods only consider interactions between genes and static environmental exposures, many environmental/lifestyle factors, such as air pollution and diet, change over time, and cannot be accurately captured at one measurement time point or by simply categorizing into static exposure categories. There is a dearth of statistical methods for detecting gene by time-varying environmental exposure interactions. Here, we propose a powerful functional logistic regression (FLR) approach to model the time-varying effect of longitudinal environmental exposure and its interaction with genetic factors on disease risk. Capitalizing on the powerful functional data analysis framework, our proposed FLR model is capable of accommodating longitudinal exposures measured at irregular time points and contaminated by measurement errors, commonly encountered in observational studies. We use extensive simulations to show that the proposed method can control the Type I error and is more powerful than alternative ad hoc methods. We demonstrate the utility of this new method using data from a case-control study of pancreatic cancer to identify the windows of vulnerability of lifetime body mass index on the risk of pancreatic cancer as well as genes that may modify this association.

Analytical strategies for discovery and replication of genetic effects in pharmacogenomic studies

In the past decade, the pharmaceutical industry and biomedical research sector have devoted considerable resources to pharmacogenomics (PGx) with the hope that understanding genetic variation in patients would deliver on the promise of personalized medicine. With the advent of new technologies and the improved collection of DNA samples, the roadblock to advancements in PGx discovery is no longer the lack of high-density genetic information captured on patient populations, but rather the development, adaptation, and tailoring of analytical strategies to effectively harness this wealth of information. The current analytical paradigm in PGx considers the single-nucleotide polymorphism (SNP) as the genomic feature of interest and performs single SNP association tests to discover PGx effects – ie, genetic effects impacting drug response. While it can be straightforward to process single SNP results and to consider how this information may be extended for use in downstream patient stratification, the rate of replication for single SNP associations has been low and the desired success of producing clinically and commercially viable biomarkers has not been realized. This may be due to the fact that single SNP association testing is suboptimal given the complexities of PGx discovery in the clinical trial setting, including: 1) relatively small sample sizes; 2) diverse clinical cohorts within and across trials due to genetic ancestry (potentially impacting the ability to replicate findings); and 3) the potential polygenic nature of a drug response. Subsequently, a shift in the current paradigm is proposed: to consider the gene as the genomic feature of interest in PGx discovery. The proof-of-concept study presented in this manuscript demonstrates that genomic region-based association testing has the potential to improve the power of detecting single SNP or complex PGx effects in the discovery stage (by leveraging the underlying genetic architecture and reducing the multiplicity burden), and it can also improve power in the replication stage.

Testing for association with multiple traits in generalized estimation equations, with application to neuroimaging data

There is an increasing need to develop and apply powerful statistical tests to detect multiple traits-single locus associations, as arising from neuroimaging genetics and other studies. For example, in the Alzheimer's Disease Neuroimaging Initiative (ADNI), in addition to genome-wide single nucleotide polymorphisms (SNPs), thousands of neuroimaging and neuropsychological phenotypes as intermediate phenotypes for Alzheimer's disease, have been collected. Although some classic methods like MANOVA and newly proposed methods may be applied, they have their own limitations. For example, MANOVA cannot be applied to binary and other discrete traits. In addition, the relationships among these methods are not well understood. Importantly, since these tests are not data adaptive, depending on the unknown association patterns among multiple traits and between multiple traits and a locus, these tests may or may not be powerful. In this paper we propose a class of data-adaptive weights and the corresponding weighted tests in the general framework of generalized estimation equations (GEE). A highly adaptive test is proposed to select the most powerful one from this class of the weighted tests so that it can maintain high power across a wide range of situations. Our proposed tests are applicable to various types of traits with or without covariates. Importantly, we also analytically show relationships among some existing and our proposed tests, indicating that many existing tests are special cases of our proposed tests. Extensive simulation studies were conducted to compare and contrast the power properties of various existing and our new methods. Finally, we applied the methods to an ADNI dataset to illustrate the performance of the methods. We conclude with the recommendation for the use of the GEE-based Score test and our proposed adaptive test for their high and complementary performance.

GWAS to Sequencing: Divergence in Study Design and Analysis

The success of genome-wide association studies (GWAS) in uncovering genetic risk factors for complex traits has generated great promise for the complete data generated by sequencing. The bumpy transition from GWAS to whole-exome or whole-genome association studies (WGAS) based on sequencing investigations has highlighted important differences in analysis and interpretation. We show how the loss in power due to the allele frequency spectrum targeted by sequencing is difficult to compensate for with realistic effect sizes and point to study designs that may help. We discuss several issues in interpreting the results, including a special case of the winner's curse. Extrapolation and prediction using rare SNPs is complex, because of the selective ascertainment of SNPs in case-control studies and the low amount of information at each SNP, and naive procedures are biased under the alternative. We also discuss the challenges in tuning gene-based tests and accounting for multiple testing when genes have very different sets of SNPs. The examples we emphasize in this paper highlight the difficult road we must travel for a two-letter switch.

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.

On multi-marker tests for association in case-control studies

Genome-wide association studies (GWAs) have identified thousands of DNA loci associated with a variety of traits. Statistical inference is almost always based on single marker hypothesis tests of association and the respective p-values with Bonferroni correction. Since commercially available genomic arrays interrogate hundreds of thousands or even millions of loci simultaneously, many causal yet undetected loci are believed to exist because the conditional power to achieve a genome-wide significance level can be low, in particular for markers with small effect sizes and low minor allele frequencies and in studies with modest sample size. However, the correlation between neighboring markers in the human genome due to linkage disequilibrium (LD) resulting in correlated marker test statistics can be incorporated into multi-marker hypothesis tests, thereby increasing power to detect association. Herein, we establish a theoretical benchmark by quantifying the maximum power achievable for multi-marker tests of association in case-control studies, achievable only when the causal marker is known. Using that genotype correlations within an LD block translate into an asymptotically multivariate normal distribution for score test statistics, we develop a set of weights for the markers that maximize the non-centrality parameter, and assess the relative loss of power for other approaches. We find that the method of Conneely and Boehnke (2007) based on the maximum absolute test statistic observed in an LD block is a practical and powerful method in a variety of settings. We also explore the effect on the power that prior biological or functional knowledge used to narrow down the locus of the causal marker can have, and conclude that this prior knowledge has to be very strong and specific for the power to approach the maximum achievable level, or even beat the power observed for methods such as the one proposed by Conneely and Boehnke (2007).

Kernel machine SNP-set testing under multiple candidate kernels

Joint testing for the cumulative effect of multiple single-nucleotide polymorphisms grouped on the basis of prior biological knowledge has become a popular and powerful strategy for the analysis of large-scale genetic association studies. The kernel machine (KM)-testing framework is a useful approach that has been proposed for testing associations between multiple genetic variants and many different types of complex traits by comparing pairwise similarity in phenotype between subjects to pairwise similarity in genotype, with similarity in genotype defined via a kernel function. An advantage of the KM framework is its flexibility: choosing different kernel functions allows for different assumptions concerning the underlying model and can allow for improved power. In practice, it is difficult to know which kernel to use a priori because this depends on the unknown underlying trait architecture and selecting the kernel which gives the lowest P-value can lead to inflated type I error. Therefore, we propose practical strategies for KM testing when multiple candidate kernels are present based on constructing composite kernels and based on efficient perturbation procedures. We demonstrate through simulations and real data applications that the procedures protect the type I error rate and can lead to substantially improved power over poor choices of kernels and only modest differences in power vs. using the best candidate kernel.

Adjustment for population stratification via principal components in association analysis of rare variants

For unrelated samples, principal component (PC) analysis has been established as a simple and effective approach to adjusting for population stratification in association analysis of common variants (CVs, with minor allele frequencies MAF > 5%). However, it is less clear how it would perform in analysis of low-frequency variants (LFVs, MAF between 1% and 5%), or of rare variants (RVs, MAF < 5%). Furthermore, with next-generation sequencing data, it is unknown whether PCs should be constructed based on CVs, LFVs, or RVs. In this study, we used the 1000 Genomes Project sequence data to explore the construction of PCs and their use in association analysis of LFVs or RVs for unrelated samples. It is shown that a few top PCs based on either CVs or LFVs could separate two continental groups, European and African samples, but those based on only RVs performed less well. When applied to several association tests in simulated data with population stratification, using PCs based on either CVs or LFVs was effective in controlling Type I error rates, while nonadjustment led to inflated Type I error rates. Perhaps the most interesting observation is that, although the PCs based on LFVs could better separate the two continental groups than those based on CVs, the use of the former could lead to overadjustment in the sense of substantial power loss in the absence of population stratification; in contrast, we did not see any problem with the use of the PCs based on CVs in all our examples.

SNP-set analysis replicates acute lung injury genetic risk factors

BACKGROUND

We used a gene - based replication strategy to test the reproducibility of prior acute lung injury (ALI) candidate gene associations.

METHODS

We phenotyped 474 patients from a prospective severe trauma cohort study for ALI. Genomic DNA from subjects' blood was genotyped using the IBC chip, a multiplex single nucleotide polymorphism (SNP) array. Results were filtered for 25 candidate genes selected using prespecified literature search criteria and present on the IBC platform. For each gene, we grouped SNPs according to haplotype blocks and tested the joint effect of all SNPs on susceptibility to ALI using the SNP-set kernel association test. Results were compared to single SNP analysis of the candidate SNPs. Analyses were separate for genetically determined ancestry (African or European).

RESULTS

We identified 4 genes in African ancestry and 2 in European ancestry trauma subjects which replicated their associations with ALI. Ours is the first replication of IL6, IL10, IRAK3, and VEGFA associations in non-European populations with ALI. Only one gene - VEGFA - demonstrated association with ALI in both ancestries, with distinct haplotype blocks in each ancestry driving the association. We also report the association between trauma-associated ALI and NFKBIA in European ancestry subjects.

CONCLUSIONS

Prior ALI genetic associations are reproducible and replicate in a trauma cohort. Kernel - based SNP-set analysis is a more powerful method to detect ALI association than single SNP analysis, and thus may be more useful for replication testing. Further, gene-based replication can extend candidate gene associations to diverse ethnicities.

U-statistics in genetic association studies

Many common human diseases are complex and are expected to be highly heterogeneous, with multiple causative loci and multiple rare and common variants at some of the causative loci contributing to the risk of these diseases. Data from the genome-wide association studies (GWAS) and metadata such as known gene functions and pathways provide the possibility of identifying genetic variants, genes and pathways that are associated with complex phenotypes. Single-marker-based tests have been very successful in identifying thousands of genetic variants for hundreds of complex phenotypes. However, these variants only explain very small percentages of the heritabilities. To account for the locus- and allelic-heterogeneity, gene-based and pathway-based tests can be very useful in the next stage of the analysis of GWAS data. U-statistics, which summarize the genomic similarity between pair of individuals and link the genomic similarity to phenotype similarity, have proved to be very useful for testing the associations between a set of single nucleotide polymorphisms and the phenotypes. Compared to single marker analysis, the advantages afforded by the U-statistics-based methods is large when the number of markers involved is large. We review several formulations of U-statistics in genetic association studies and point out the links of these statistics with other similarity-based tests of genetic association. Finally, potential application of U-statistics in analysis of the next-generation sequencing data and rare variants association studies are discussed.

A powerful test for multiple rare variants association studies that incorporates sequencing qualities

Next-generation sequencing data will soon become routinely available for association studies between complex traits and rare variants. Sequencing data, however, are characterized by the presence of sequencing errors at each individual genotype. This makes it especially challenging to perform association studies of rare variants, which, due to their low minor allele frequencies, can be easily perturbed by genotype errors. In this article, we develop the quality-weighted multivariate score association test (qMSAT), a new procedure that allows powerful association tests between complex traits and multiple rare variants under the presence of sequencing errors. Simulation results based on quality scores from real data show that the qMSAT often dominates over current methods, that do not utilize quality information. In particular, the qMSAT can dramatically increase power over existing methods under moderate sample sizes and relatively low coverage. Moreover, in an obesity data study, we identified using the qMSAT two functional regions (MGLL promoter and MGLL 3′-untranslated region) where rare variants are associated with extreme obesity. Due to the high cost of sequencing data, the qMSAT is especially valuable for large-scale studies involving rare variants, as it can potentially increase power without additional experimental cost. qMSAT is freely available at http://qmsat.sourceforge.net/.

Comparison of statistical tests for disease association with rare variants

In anticipation of the availability of next-generation sequencing data, there is increasing interest in investigating association between complex traits and rare variants (RVs). In contrast to association studies for common variants (CVs), due to the low frequencies of RVs, common wisdom suggests that existing statistical tests for CVs might not work, motivating the recent development of several new tests for analyzing RVs, most of which are based on the idea of pooling/collapsing RVs. However, there is a lack of evaluations of, and thus guidance on the use of, existing tests. Here we provide a comprehensive comparison of various statistical tests using simulated data. We consider both independent and correlated rare mutations, and representative tests for both CVs and RVs. As expected, if there are no or few non-causal (i.e. neutral or non-associated) RVs in a locus of interest while the effects of causal RVs on the trait are all (or mostly) in the same direction (i.e. either protective or deleterious, but not both), then the simple pooled association tests (without selecting RVs and their association directions) and a new test called kernel-based adaptive clustering (KBAC) perform similarly and are most powerful; KBAC is more robust than simple pooled association tests in the presence of non-causal RVs; however, as the number of non-causal CVs increases and/or in the presence of opposite association directions, the winners are two methods originally proposed for CVs and a new test called C-alpha test proposed for RVs, each of which can be regarded as testing on a variance component in a random-effects model. Interestingly, several methods based on sequential model selection (i.e. selecting causal RVs and their association directions), including two new methods proposed here, perform robustly and often have statistical power between those of the above two classes.