Nonparametric Covariate-Adjusted Association Tests Based on the Generalized Kendall's Tau()

ULV: A robust statistical method for clustered data, with applications to multi-subject, single-cell omics data

Molecular and genomic technological advancements have greatly enhanced our understanding of biological processes by allowing us to quantify key biological variables such as gene expression, protein levels, and microbiome compositions. These breakthroughs have enabled us to achieve increasingly higher levels of resolution in our measurements, exemplified by our ability to comprehensively profile biological information at the single-cell level. However, the analysis of such data faces several critical challenges: limited number of individuals, non-normality, potential dropouts, outliers, and repeated measurements from the same individual. In this article, we propose a novel method, which we call U-statistic based latent variable (ULV). Our proposed method takes advantage of the robustness of rank-based statistics and exploits the statistical efficiency of parametric methods for small sample sizes. It is a computationally feasible framework that addresses all the issues mentioned above simultaneously. We show that our method controls false positives at desired significance levels. An additional advantage of ULV is its flexibility in modeling various types of single-cell data, including both RNA and protein abundance. The usefulness of our method is demonstrated in two studies: a single-cell proteomics study of acute myelogenous leukemia (AML) and a single-cell RNA study of COVID-19 symptoms. In the AML study, ULV successfully identified differentially expressed proteins that would have been missed by the pseudobulk version of the Wilcoxon rank-sum test. In the COVID-19 study, ULV identified genes associated with covariates such as age and gender, and genes that would be missed without adjusting for covariates. The differentially expressed genes identified by our method are less biased toward genes with high expression levels. Furthermore, ULV identified additional gene pathways likely contributing to the mechanisms of COVID-19 severity.

Multiple phenotype association tests based on sliced inverse regression

BACKGROUND

Joint analysis of multiple phenotypes in studies of biological systems such as Genome-Wide Association Studies is critical to revealing the functional interactions between various traits and genetic variants, but growth of data in dimensionality has become a very challenging problem in the widespread use of joint analysis. To handle the excessiveness of variables, we consider the sliced inverse regression (SIR) method. Specifically, we propose a novel SIR-based association test that is robust and powerful in testing the association between multiple predictors and multiple outcomes.

RESULTS

We conduct simulation studies in both low- and high-dimensional settings with various numbers of Single-Nucleotide Polymorphisms and consider the correlation structure of traits. Simulation results show that the proposed method outperforms the existing methods. We also successfully apply our method to the genetic association study of ADNI dataset. Both the simulation studies and real data analysis show that the SIR-based association test is valid and achieves a higher efficiency compared with its competitors.

CONCLUSION

Several scenarios with low- and high-dimensional responses and genotypes are considered in this paper. Our SIR-based method controls the estimated type I error at the pre-specified level α .

Pleiotropic genetic association analysis with multiple phenotypes using multivariate response best-subset selection

Genetic pleiotropy refers to the simultaneous association of a gene with multiple phenotypes. It is widely distributed in the whole genome and can help to understand the common genetic mechanism of diseases or traits. In this study, a multivariate response best-subset selection (MRBSS) model based pleiotropic association analysis method is proposed. Different from the traditional genetic association model, the high-dimensional genotypic data are viewed as response variables while the multiple phenotypic data as predictor variables. Moreover, the response best-subset selection procedure is converted into an 0-1 integer optimization problem by introducing a separation parameter and a tuning parameter. Furthermore, the model parameters are estimated by using the curve search under the modified Bayesian information criterion. Simulation experiments show that the proposed method MRBSS remarkably reduces the computational time, obtains higher statistical power under most of the considered scenarios, and controls the type I error rate at a low level. The application studies in the datasets of maize yield traits and pig lipid traits further verifies the effectiveness.

Quantitative trait locus mapping analysis of multiple traits when using genotype data with potential errors

Background

Quantitative trait locus (QTL) analysis aims to locate and estimate the effects of the genes influencing quantitative traits and infer the relationship between gene variants and changes in phenotypic characteristics using statistical methods. Some methods have been developed to map QTLs of multiple traits in the case of no genotype error in a given dataset. However, practical genetic data that people use may contain some potential errors because of the limitations of biotechnology. Common genetic data correction methods can only reduce errors, but cannot calculate the degree of error. In this paper, we propose a QTL mapping strategy for multiple traits in the presence of genotype errors.

Methods

The additive effect, dominant effect, recombination rate, error rate, and other parameters of QTLs can be simultaneously obtained using this new method in the framework of multiple-interval mapping.

Results

Our simulation results show that the accuracy of parameter estimation can be improved by considering the errors of marker genotypes during the analysis of genetic data. Real data analysis also shows that the new method proposed in this paper can map the QTLs of multiple traits more accurately.

COMPARATIVE ANALYSIS OF 2 BIOMETERS USING SWEPT-SOURCE OPTICAL COHERENCE TOMOGRAPHY TECHNOLOGY

PURPOSE

To report the repeatability, level of agreement and correlation of 2 swept-source optical coherence tomography (SS-OCT) biometers, the IOLMaster 700® (biometer A, Carl Zeiss, Germany) and the Anterion® (biometer B, Heidelberg Engineering GmbH, Heidelberg, Germany).

SETTING

Rothschild Foundation Hospital, Paris, France.

DESIGN

Prospective comparative case series.

METHODS

Consecutive patients who attended for cataract assessment had SS-OCT biometry performed with the reference and the biometer B. Axial length (AL), mean keratometry (mean K), central corneal thickness (CCT), anterior chamber depth (ACD), lens thickness (LT), and corneal diameter measurements (WTW) were measured. The intraoperator repeatability was calculated using ANOVA and repeatability limits. . Correlations were assessed and the level of agreement between the biometers was represented with the Bland-Altman method.

RESULTS

The study comprised 63 patients (125 eyes). There was a statistically significant difference between the 2 biometers in all measurements (P < .05). All repeatability measurements were very high as were the level of correlation and level of agreement between the biometer A and the biometer B for all parameters.

CONCLUSION

The biometer B provided good agreement and repeatability compared with the biometer A, however all parameters are not interchangeable in particular the WTW measurement and high keratometric values.

A novel association test for rare variants based on algebraic statistics

With the rapid growth of next-generation sequencing technology, more and more rare variants are available in the human genome. In recent years, the point of study has already changed direction to rare variants in genome-wide association studies (GWAS). Although a variety of approaches have been proposed to test associations between rare variants and phenotypes of interest, it is far from the end of this problem, and it is worth exploring new statistical methods based on special features of rare variants. As we all know, the most direct way is to evaluate the association in a two-way contingency table if the phenotype is a discrete variable. The numbers of observations are very close or equal to 0s for most of cells in the contingency table due to the extremely low mutation rates of rare variants. In this paper, we propose a novel association test for rare variants based on a generalization of Fisher's exact test, and the p-value of this exact test can be computed under the multivariate hypergeometric distribution in the framework of algebraic statistics. Simulation results show that our proposed method outperforms the existing methods, despite there is heterogeneity among causal variants. We also successfully apply our method into the genetic association study of coronary artery disease and hypertension from the Wellcome Trust Case Control Consortium.

Comparative analysis of 2 swept-source optical coherence tomography biometers

PURPOSE

To report the level of agreement, repeatability, and correlation of axial length (AL), mean keratometry, central corneal thickness, anterior chamber depth, lens thickness, and corneal diameter measurements of 2 swept-source optical coherence tomography (SS-OCT) biometers, the IOLMaster 700 (reference biometer) and the Argos (new biometer).

SETTING

Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom.

DESIGN

Retrospective case series.

METHODS

Each patient had SS-OCT biometry with the reference biometer and new biometer. In addition to reporting the statistical results derived from both eyes, this study included a subgroup analysis of right eyes and left eyes. The level of agreement between the biometers was represented with the Bland-Altman method. Power vector analysis of the J0 (Jackson cross-cylinder, axes at 0 degrees and 90 degrees) and J45 (Jackson cross-cylinder, axes at 45 degrees and 135 degrees) vectorial components of astigmatism was performed. Internal consistency was assessed with the Cronbach α coefficient of reliability. The dispersion of probability distribution was computed with the coefficient of variation. The intraoperator repeatability was calculated using the intraclass correlation coefficient (ICC).

RESULTS

The study comprised 112 patients (218 eyes). There was a statistically significant difference between the 2 biometers in all measurements (P < .05) except AL. The level of correlation between the reference biometer and the new biometer was very high for all the parameters except corneal diameter, and the agreement was high. The ICC and internal consistency were excellent with both biometers.

CONCLUSION

The new biometer provided good agreement and repeatability compared with the reference biometer.

A nonparametric test for association with multiple loci in the retrospective case-control study

The genome-wide association studies aim at identifying common or rare variants associated with common diseases and explaining more heritability. It is well known that common diseases are influenced by multiple single nucleotide polymorphisms (SNPs) that are usually correlated in location or function. In order to powerfully detect association signals, it is highly desirable to take account of correlations or linkage disequilibrium (LD) information among multiple SNPs in testing for association. In this article, we propose a test SLIDE that depicts the difference of the average multi-locus genotypes between cases and controls and derive its variance-covariance matrix in the retrospective design. This matrix is composed of the pairwise LD between SNPs. Thus SLIDE can borrow the strength from an external database in the population of interest with a few thousands to hundreds of thousands individuals to improve the power for detecting association. Extensive simulations show that SLIDE has apparent superiority over the existing methods, especially in the situation involving both common and rare variants, both protective and deleterious variants. Furthermore, the efficiency of the proposed method is demonstrated in the application to the data from the Wellcome Trust Case Control Consortium.

Modeling Hybrid Traits for Comorbidity and Genetic Studies of Alcohol and Nicotine Co-Dependence

We propose a novel multivariate model for analyzing hybrid traits and identifying genetic factors for comorbid conditions. Comorbidity is a common phenomenon in mental health in which an individual suffers from multiple disorders simultaneously. For example, in the Study of Addiction: Genetics and Environment (SAGE), alcohol and nicotine addiction were recorded through multiple assessments that we refer to as hybrid traits. Statistical inference for studying the genetic basis of hybrid traits has not been well-developed. Recent rank-based methods have been utilized for conducting association analyses of hybrid traits but do not inform the strength or direction of effects. To overcome this limitation, a parametric modeling framework is imperative. Although such parametric frameworks have been proposed in theory, they are neither well-developed nor extensively used in practice due to their reliance on complicated likelihood functions that have high computational complexity. Many existing parametric frameworks tend to instead use pseudo-likelihoods to reduce computational burdens. Here, we develop a model fitting algorithm for the full likelihood. Our extensive simulation studies demonstrate that inference based on the full likelihood can control the type-I error rate, and gains power and improves the effect size estimation when compared with several existing methods for hybrid models. These advantages remain even if the distribution of the latent variables is misspecified. After analyzing the SAGE data, we identify three genetic variants (rs7672861, rs958331, rs879330) that are significantly associated with the comorbidity of alcohol and nicotine addiction at the chromosome-wide level. Moreover, our approach has greater power in this analysis than several existing methods for hybrid traits.Although the analysis of the SAGE data motivated us to develop the model, it can be broadly applied to analyze any hybrid responses.

Conditional independence test by generalized Kendall's tau with generalized odds ratio

Determining conditional dependence is a challenging but important task in both model building and in applications such as genetic association studies and graphical models. Research on this topic has focused on kernel-based methods or has used categorical conditioning variables because of the challenge of the curse of dimensionality. To overcome this challenge, we propose a class of tests for conditional independence without any restriction on the distribution of the conditioning variables. The proposed test statistic can be treated as a generalized weighted Kendall's tau, in which the generalized odds ratio is utilized as a weight function to account for the distance between different values of the conditioning variables. The test procedure has desirable asymptotic properties and is easy to implement. We evaluate the finite sample performance of the proposed test through simulation studies and illustrate it using two real data examples.

A nonparametric method to test for associations between rare variants and multiple traits

More and more rare genetic variants are being detected in the human genome, and it is believed that besides common variants, some rare variants also explain part of the phenotypic variance for human diseases. Due to the importance of rare variants, many statistical methods have been proposed to test for associations between rare variants and human traits. However, in existing studies, most methods only test for associations between multiple loci and one trait; therefore, the joint information of multiple traits has not been considered simultaneously and sufficiently. In this article, we present a study of testing for associations between rare variants and multiple traits, where trait value can be binary, ordinal, quantitative and/or any mixture of them. Based on the method of generalized Kendall’s τ, a nonparametric method called NM-RV is proposed. A new kernel function for U-statistic, which could incorporate the information of each rare variant itself, is also presented and is expected to enhance the power of rare variant analysis. We further consider the asymptotic distribution of the proposed association test statistic. Our simulation work suggests that the proposed method is more powerful and robust than existing methods in testing for associations between rare variants and multiple traits,especially for multivariate ordinal traits.

Modeling Multiple Responses via Bootstrapping Margins with an Application to Genetic Association Testing

The need for analysis of multiple responses arises from many applications. In behavioral science, for example, comorbidity is a common phenomenon where multiple disorders occur in the same person. The advantage of jointly analyzing multiple correlated responses has been examined and documented. Due to the difficulties of modeling multiple responses, nonparametric tests such as generalized Kendall's Tau have been developed to assess the association between multiple responses and risk factors. These procedures have been applied to genomewide association studies of multiple complex traits. Unfortunately, those nonparametric tests only provide the significance of the association but not the magnitude. We propose a Gaussian copula model with discrete margins for modeling multivariate binary responses. This model separates marginal effects from between-trait correlations. We use a bootstrapping margins approach to constructing Wald's statistic for the association test. Although our derivation is based on the fully parametric Gaussian copula framework for simplicity, the underlying assumptions to apply our method can be weakened. The bootstrapping margins approach only requires the correct specification of the model margins. Our simulation and real data analysis demonstrate that our proposed method not only increases power over some existing association tests, but also provides further insight into genetic association studies of multivariate traits.

A powerful nonparametric statistical framework for family-based association analyses

Family-based study design is commonly used in genetic research. It has many ideal features, including being robust to population stratification (PS). With the advance of high-throughput technologies and ever-decreasing genotyping cost, it has become common for family studies to examine a large number of variants for their associations with disease phenotypes. The yield from the analysis of these family-based genetic data can be enhanced by adopting computationally efficient and powerful statistical methods. We propose a general framework of a family-based U-statistic, referred to as family-U, for family-based association studies. Unlike existing parametric-based methods, the proposed method makes no assumption of the underlying disease models and can be applied to various phenotypes (e.g., binary and quantitative phenotypes) and pedigree structures (e.g., nuclear families and extended pedigrees). By using only within-family information, it can offer robust protection against PS. In the absence of PS, it can also utilize additional information (i.e., between-family information) for power improvement. Through simulations, we demonstrated that family-U attained higher power over a commonly used method, family-based association tests, under various disease scenarios. We further illustrated the new method with an application to large-scale family data from the Framingham Heart Study. By utilizing additional information (i.e., between-family information), family-U confirmed a previous association of CHRNA5 with nicotine dependence.

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.

A family-based robust multivariate association test using maximum statistic

For characterizing the genetic mechanisms of complex diseases familial data with multiple correlated quantitative traits are usually collected in genetic studies. To analyze such data, various multivariate tests have been proposed to investigate the association between the underlying disease genes and the multiple traits. Although these multivariate association tests may have better power performance than the univariate association tests, they suffer from loss of testing power when the genetic models of the putative genes are misspecified. To address the problem, in this paper we aim to develop a family-based robust multivariate association test. We will first establish the optimal multivariate score tests for the recessive, additive, and dominant genetic models. Based on these optimal tests, a maximum-type robust multivariate association test is then obtained. Simulations are conducted to compare the power of our method with that of other existing multivariate methods. The results show that the robust multivariate test does manifest the robustness in power over all plausible genetic models. A practical data set is applied to demonstrate the applicability of our approach. The results suggest that the robust multivariate test is more powerful than the robust univariate test when dealing with multiple quantitative traits.

Identifying Genetic Variants for Addiction via Propensity Score Adjusted Generalized Kendall's Tau

Identifying replicable genetic variants for addiction has been extremely challenging. Besides the common difficulties with genome-wide association studies (GWAS), environmental factors are known to be critical to addiction, and comorbidity is widely observed. Despite the importance of environmental factors and comorbidity for addiction study, few GWAS analyses adequately considered them due to the limitations of the existing statistical methods. Although parametric methods have been developed to adjust for covariates in association analysis, difficulties arise when the traits are multivariate because there is no ready-to-use model for them. Recent nonparametric development includes U-statistics to measure the phenotype-genotype association weighted by a similarity score of covariates. However, it is not clear how to optimize the similarity score. Therefore, we propose a semiparametric method to measure the association adjusted by covariates. In our approach, the nonparametric U-statistic is adjusted by parametric estimates of propensity scores using the idea of inverse probability weighting. The new measurement is shown to be asymptotically unbiased under our null hypothesis while the previous non-weighted and weighted ones are not. Simulation results show that our test improves power as opposed to the non-weighted and two other weighted U-statistic methods, and it is particularly powerful for detecting gene-environment interactions. Finally, we apply our proposed test to the Study of Addiction: Genetics and Environment (SAGE) to identify genetic variants for addiction. Novel genetic variants are found from our analysis, which warrant further investigation in the future.

Nonparametric tests of associations with disease based on U-statistics

In case-control studies, association analysis was designed to test whether genetic variants were associated with human diseases. To evaluate the association, analysing one genetic marker at a time suffered from weak power, because of the correction for multiple testing and possibly small genetic effects. An alternative strategy was to test simultaneous effects of multiple markers, which was believed to be more powerful. However, when the number of markers under investigation was large, they would be subjected to weak power as well, because of the greater degrees of freedom. To conquer these limitations in case-control studies, we proposed a novel method that could test joint association of several loci (i.e. haplotype), with only a single degree of freedom. In this research, we developed a nonparametric approach, which was based on U-statistics. We also introduced a new kernel for U-statistic, which could combine the haplotype structure information, and was expected to enhance the power. Simulations indicated that our proposed approach offered merits in identifying the associations between diseases and haplotypes. Application of our method to a study of candidate genes for internalising disorder illustrated its virtue in utility and interpretation, and provided an excellent result in detecting the associations.

A nonparametric regression method for multiple longitudinal phenotypes using multivariate adaptive splines

In genetic studies of complex diseases, particularly mental illnesses, and behavior disorders, two distinct characteristics have emerged in some data sets. First, genetic data sets are collected with a large number of phenotypes that are potentially related to the complex disease under study. Second, each phenotype is collected from the same subject repeatedly over time. In this study, we present a nonparametric regression approach to study multivariate and time-repeated phenotypes together by using the technique of the multivariate adaptive regression splines for analysis of longitudinal data (MASAL), which makes it possible to identify genes, gene-gene and gene-environment, including time, interactions associated with the phenotypes of interest. Furthermore, we propose a permutation test to assess the associations between the phenotypes and selected markers. Through simulation, we demonstrate that our proposed approach has advantages over the existing methods that examine each longitudinal phenotype separately or analyze the summarized values of phenotypes by compressing them into one-time-point phenotypes. Application of the proposed method to the Framingham Heart Study illustrates that the use of multivariate longitudinal phenotypes enhanced the significance of the association test.