Gene-Based Association Analysis for Censored Traits Via Fixed Effect Functional Regressions

Genetic heterogeneity: Challenges, impacts, and methods through an associative lens

Genetic heterogeneity describes the occurrence of the same or similar phenotypes through different genetic mechanisms in different individuals. Robustly characterizing and accounting for genetic heterogeneity is crucial to pursuing the goals of precision medicine, for discovering novel disease biomarkers, and for identifying targets for treatments. Failure to account for genetic heterogeneity may lead to missed associations and incorrect inferences. Thus, it is critical to review the impact of genetic heterogeneity on the design and analysis of population level genetic studies, aspects that are often overlooked in the literature. In this review, we first contextualize our approach to genetic heterogeneity by proposing a high-level categorization of heterogeneity into "feature," "outcome," and "associative" heterogeneity, drawing on perspectives from epidemiology and machine learning to illustrate distinctions between them. We highlight the unique nature of genetic heterogeneity as a heterogeneous pattern of association that warrants specific methodological considerations. We then focus on the challenges that preclude effective detection and characterization of genetic heterogeneity across a variety of epidemiological contexts. Finally, we discuss systems heterogeneity as an integrated approach to using genetic and other high-dimensional multi-omic data in complex disease research.

Gene-level association analysis of ordinal traits with functional ordinal logistic regressions

In this paper, we develop functional ordinal logistic regression (FOLR) models to perform gene-based analysis of ordinal traits. In the proposed FOLR models, genetic variant data are viewed as stochastic functions of physical positions and the genetic effects are treated as a function of physical positions. The FOLR models are built upon functional data analysis which can be revised to analyze the ordinal traits and high dimension genetic data. The proposed methods are capable of dealing with dense genotype data which is usually encountered in analyzing the next-generation sequencing data. The methods are flexible and can analyze three types of genetic data: (1) rare variants only, (2) common variants only, and (3) a combination of rare and common variants. Simulation studies show that the likelihood ratio test statistics of the FOLR models control type I errors well and have good power performance. The proposed methods achieve the goals of analyzing ordinal traits directly, reducing high dimensionality of dense genetic variants, being computationally manageable, facilitating model convergence, properly controlling type I errors, and maintaining high power levels. The FOLR models are applied to analyze Age-Related Eye Disease Study data, in which two genes are found to strongly associate with four ordinal traits.

Gene-based analysis of bi-variate survival traits via functional regressions with applications to eye diseases

Genetic studies of two related survival outcomes of a pleiotropic gene are commonly encountered but statistical models to analyze them are rarely developed. To analyze sequencing data, we propose mixed effect Cox proportional hazard models by functional regressions to perform gene-based joint association analysis of two survival traits motivated by our ongoing real studies. These models extend fixed effect Cox models of univariate survival traits by incorporating variations and correlation of multivariate survival traits into the models. The associations between genetic variants and two survival traits are tested by likelihood ratio test statistics. Extensive simulation studies suggest that type I error rates are well controlled and power performances are stable. The proposed models are applied to analyze bivariate survival traits of left and right eyes in the age-related macular degeneration progression.

Gene-Based Association Testing of Dichotomous Traits With Generalized Functional Linear Mixed Models Using Extended Pedigrees: Applications to Age-Related Macular Degeneration

Genetics plays a role in age-related macular degeneration (AMD), a common cause of blindness in the elderly. There is a need for powerful methods for carrying out region-based association tests between a dichotomous trait like AMD and genetic variants on family data. Here, we apply our new generalized functional linear mixed models (GFLMM) developed to test for gene-based association in a set of AMD families. Using common and rare variants, we observe significant association with two known AMD genes: CFH and ARMS2. Using rare variants, we find suggestive signals in four genes: ASAH1, CLEC6A, TMEM63C, and SGSM1. Intriguingly, ASAH1 is down-regulated in AMD aqueous humor, and ASAH1 deficiency leads to retinal inflammation and increased vulnerability to oxidative stress. These findings were made possible by our GFLMM which model the effect of a major gene as a fixed mean, the polygenic contributions as a random variation, and the correlation of pedigree members by kinship coefficients. Simulations indicate that the GFLMM likelihood ratio tests (LRTs) accurately control the Type I error rates. The LRTs have similar or higher power than existing retrospective kernel and burden statistics. Our GFLMM-based statistics provide a new tool for conducting family-based genetic studies of complex diseases. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Gene-based association analysis for bivariate time-to-event data through functional regression with copula models

Several gene-based association tests for time-to-event traits have been proposed recently to detect whether a gene region (containing multiple variants), as a set, is associated with the survival outcome. However, for bivariate survival outcomes, to the best of our knowledge, there is no statistical method that can be directly applied for gene-based association analysis. Motivated by a genetic study to discover the gene regions associated with the progression of a bilateral eye disease, age-related macular degeneration (AMD), we implement a novel functional regression (FR) method under the copula framework. Specifically, the effects of variants within a gene region are modeled through a functional linear model, which then contributes to the marginal survival functions within the copula. Generalized score test statistics are derived to test for the association between bivariate survival traits and the genetic region. Extensive simulation studies are conducted to evaluate the type I error control and power performance of the proposed approach, with comparisons to several existing methods for a single survival trait, as well as the marginal Cox FR model using the robust sandwich estimator for bivariate survival traits. Finally, we apply our method to a large AMD study, the Age-related Eye Disease Study, and to identify the gene regions that are associated with AMD progression.

Gene-based association analysis of survival traits via functional regression-based mixed effect cox models for related samples

The importance to integrate survival analysis into genetics and genomics is widely recognized, but only a small number of statisticians have produced relevant work toward this study direction. For unrelated population data, functional regression (FR) models have been developed to test for association between a quantitative/dichotomous/survival trait and genetic variants in a gene region. In major gene association analysis, these models have higher power than sequence kernel association tests. In this paper, we extend this approach to analyze censored traits for family data or related samples using FR based mixed effect Cox models (FamCoxME). The FamCoxME model effect of major gene as fixed mean via functional data analysis techniques, the local gene or polygene variations or both as random, and the correlation of pedigree members by kinship coefficients or genetic relationship matrix or both. The association between the censored trait and the major gene is tested by likelihood ratio tests (FamCoxME FR LRT). Simulation results indicate that the LRT control the type I error rates accurately/conservatively and have good power levels when both local gene or polygene variations are modeled. The proposed methods were applied to analyze a breast cancer data set from the Consortium of Investigators of Modifiers of BRCA1 and BRCA2 (CIMBA). The FamCoxME provides a new tool for gene-based analysis of family-based studies or related samples.

Linear mixed models for association analysis of quantitative traits with next-generation sequencing data

We develop linear mixed models (LMMs) and functional linear mixed models (FLMMs) for gene-based tests of association between a quantitative trait and genetic variants on pedigrees. The effects of a major gene are modeled as a fixed effect, the contributions of polygenes are modeled as a random effect, and the correlations of pedigree members are modeled via inbreeding/kinship coefficients. F -statistics and χ 2 likelihood ratio test (LRT) statistics based on the LMMs and FLMMs are constructed to test for association. We show empirically that the F -distributed statistics provide a good control of the type I error rate. The F -test statistics of the LMMs have similar or higher power than the FLMMs, kernel-based famSKAT (family-based sequence kernel association test), and burden test famBT (family-based burden test). The F -statistics of the FLMMs perform well when analyzing a combination of rare and common variants. For small samples, the LRT statistics of the FLMMs control the type I error rate well at the nominal levels α = 0.01 and 0.05 . For moderate/large samples, the LRT statistics of the FLMMs control the type I error rates well. The LRT statistics of the LMMs can lead to inflated type I error rates. The proposed models are useful in whole genome and whole exome association studies of complex 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.

Meta-analysis of quantitative pleiotropic traits for next-generation sequencing with multivariate functional linear models

To analyze next-generation sequencing data, multivariate functional linear models are developed for a meta-analysis of multiple studies to connect genetic variant data to multiple quantitative traits adjusting for covariates. The goal is to take the advantage of both meta-analysis and pleiotropic analysis in order to improve power and to carry out a unified association analysis of multiple studies and multiple traits of complex disorders. Three types of approximate F -distributions based on Pillai-Bartlett trace, Hotelling-Lawley trace, and Wilks's Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants. Simulation analysis is performed to evaluate false-positive rates and power of the proposed tests. The proposed methods are applied to analyze lipid traits in eight European cohorts. It is shown that it is more advantageous to perform multivariate analysis than univariate analysis in general, and it is more advantageous to perform meta-analysis of multiple studies instead of analyzing the individual studies separately. The proposed models require individual observations. The value of the current paper can be seen at least for two reasons: (a) the proposed methods can be applied to studies that have individual genotype data; (b) the proposed methods can be used as a criterion for future work that uses summary statistics to build test statistics to meta-analyze the data.

A comparison study of multivariate fixed models and Gene Association with Multiple Traits (GAMuT) for next-generation sequencing

In this paper, extensive simulations are performed to compare two statistical methods to analyze multiple correlated quantitative phenotypes: (1) approximate F-distributed tests of multivariate functional linear models (MFLM) and additive models of multivariate analysis of variance (MANOVA), and (2) Gene Association with Multiple Traits (GAMuT) for association testing of high-dimensional genotype data. It is shown that approximate F-distributed tests of MFLM and MANOVA have higher power and are more appropriate for major gene association analysis (i.e., scenarios in which some genetic variants have relatively large effects on the phenotypes); GAMuT has higher power and is more appropriate for analyzing polygenic effects (i.e., effects from a large number of genetic variants each of which contributes a small amount to the phenotypes). MFLM and MANOVA are very flexible and can be used to perform association analysis for (i) rare variants, (ii) common variants, and (iii) a combination of rare and common variants. Although GAMuT was designed to analyze rare variants, it can be applied to analyze a combination of rare and common variants and it performs well when (1) the number of genetic variants is large and (2) each variant contributes a small amount to the phenotypes (i.e., polygenes). MFLM and MANOVA are fixed effect models that perform well for major gene association analysis. GAMuT can be viewed as an extension of sequence kernel association tests (SKAT). Both GAMuT and SKAT are more appropriate for analyzing polygenic effects and they perform well not only in the rare variant case, but also in the case of a combination of rare and common variants. Data analyses of European cohorts and the Trinity Students Study are presented to compare the performance of the two methods.

A Comparison Study of Fixed and Mixed Effect Models for Gene Level Association Studies of Complex Traits

In association studies of complex traits, fixed-effect regression models are usually used to test for association between traits and major gene loci. In recent years, variance-component tests based on mixed models were developed for region-based genetic variant association tests. In the mixed models, the association is tested by a null hypothesis of zero variance via a sequence kernel association test (SKAT), its optimal unified test (SKAT-O), and a combined sum test of rare and common variant effect (SKAT-C). Although there are some comparison studies to evaluate the performance of mixed and fixed models, there is no systematic analysis to determine when the mixed models perform better and when the fixed models perform better. Here we evaluated, based on extensive simulations, the performance of the fixed and mixed model statistics, using genetic variants located in 3, 6, 9, 12, and 15 kb simulated regions. We compared the performance of three models: (i) mixed models that lead to SKAT, SKAT-O, and SKAT-C, (ii) traditional fixed-effect additive models, and (iii) fixed-effect functional regression models. To evaluate the type I error rates of the tests of fixed models, we generated genotype data by two methods: (i) using all variants, (ii) using only rare variants. We found that the fixed-effect tests accurately control or have low false positive rates. We performed simulation analyses to compare power for two scenarios: (i) all causal variants are rare, (ii) some causal variants are rare and some are common. Either one or both of the fixed-effect models performed better than or similar to the mixed models except when (1) the region sizes are 12 and 15 kb and (2) effect sizes are small. Therefore, the assumption of mixed models could be satisfied and SKAT/SKAT-O/SKAT-C could perform better if the number of causal variants is large and each causal variant contributes a small amount to the traits (i.e., polygenes). In major gene association studies, we argue that the fixed-effect models perform better or similarly to mixed models in most cases because some variants should affect the traits relatively large. In practice, it makes sense to perform analysis by both the fixed and mixed effect models and to make a comparison, and this can be readily done using our R codes and the SKAT packages.

Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models

We developed generalized functional linear models (GFLMs) to perform a meta-analysis of multiple case-control studies to evaluate the relationship of genetic data to dichotomous traits adjusting for covariates. Unlike the previously developed meta-analysis for sequence kernel association tests (MetaSKATs), which are based on mixed-effect models to make the contributions of major gene loci random, GFLMs are fixed models; i.e., genetic effects of multiple genetic variants are fixed. Based on GFLMs, we developed chi-squared-distributed Rao's efficient score test and likelihood-ratio test (LRT) statistics to test for an association between a complex dichotomous trait and multiple genetic variants. We then performed extensive simulations to evaluate the empirical type I error rates and power performance of the proposed tests. The Rao's efficient score test statistics of GFLMs are very conservative and have higher power than MetaSKATs when some causal variants are rare and some are common. When the causal variants are all rare [i.e., minor allele frequencies (MAF) < 0.03], the Rao's efficient score test statistics have similar or slightly lower power than MetaSKATs. The LRT statistics generate accurate type I error rates for homogeneous genetic-effect models and may inflate type I error rates for heterogeneous genetic-effect models owing to the large numbers of degrees of freedom and have similar or slightly higher power than the Rao's efficient score test statistics. GFLMs were applied to analyze genetic data of 22 gene regions of type 2 diabetes data from a meta-analysis of eight European studies and detected significant association for 18 genes (P < 3.10 × 10(-6)), tentative association for 2 genes (HHEX and HMGA2; P ≈ 10(-5)), and no association for 2 genes, while MetaSKATs detected none. In addition, the traditional additive-effect model detects association at gene HHEX. GFLMs and related tests can analyze rare or common variants or a combination of the two and can be useful in whole-genome and whole-exome association studies.