Summary statistics-based association test for identifying the pleiotropic effects with set of genetic variants.

MOTIVATION: Traditional genome-wide association study focuses on testing one-to-one relationship between genetic variants and complex human diseases or traits. While its success in the past decade, this one-to-one paradigm lacks efficiency because it does not utilize the information of intrinsic genetic structure and pleiotropic effects. Due to privacy reasons, only summary statistics of current genome-wide association study data are publicly available. Existing summary statistics-based association tests do not consider covariates for regression model, while adjusting for covariates including population stratification factors is a routine issue. RESULTS: In this work, we first derive the correlation coefficients between summary Wald statistics obtained from linear regression model with covariates. Then, a new test is proposed by integrating three-level information including the intrinsic genetic structure, pleiotropy, and the potential information combinations. Extensive simulations demonstrate that the proposed test outperforms three other existing methods under most of the considered scenarios. Real data analysis of polyunsaturated fatty acids further shows that the proposed test can identify more genes than the compared existing methods. AVAILABILITY AND IMPLEMENTATION: Code is available at https://github.com/bschilder/ThreeWayTest.

A maximum kernel-based association test to detect the pleiotropic genetic effects on multiple phenotypes.

MOTIVATION: Testing the association between multiple phenotypes with a set of genetic variants simultaneously, rather than analyzing one trait at a time, is receiving increasing attention for its high statistical power and easy explanation on pleiotropic effects. The kernel-based association test (KAT), being free of data dimensions and structures, has proven to be a good alternative method for genetic association analysis with multiple phenotypes. However, KAT suffers from substantial power loss when multiple phenotypes have moderate to strong correlations. To handle this issue, we propose a maximum KAT (MaxKAT) and suggest using the generalized extreme value distribution to calculate its statistical significance under the null hypothesis. RESULTS: We show that MaxKAT reduces computational intensity greatly while maintaining high accuracy. Extensive simulations demonstrate that MaxKAT can properly control type I error rates and obtain remarkably higher power than KAT under most of the considered scenarios. Application to a porcine dataset used in biomedical experiments of human disease further illustrates its practical utility. AVAILABILITY AND IMPLEMENTATION: The R package MaxKAT that implements the proposed method is available on Github https://github.com/WangJJ-xrk/MaxKAT.

An adaptive direction-assisted test for microbiome compositional data.

MOTIVATION: Microbial communities have been shown to be associated with many complex diseases, such as cancers and cardiovascular diseases. The identification of differentially abundant taxa is clinically important. It can help understand the pathology of complex diseases, and potentially provide preventive and therapeutic strategies. Appropriate differential analyses for microbiome data are challenging due to its unique data characteristics including compositional constraint, excessive zeros and high dimensionality. Most existing approaches either ignore these data characteristics or only account for the compositional constraint by using log-ratio transformations with zero observations replaced by a pseudocount. However, there is no consensus on how to choose a pseudocount. More importantly, ignoring the characteristic of excessive zeros may result in poorly powered analyses and therefore yield misleading findings. RESULTS: We develop a novel microbiome-based direction-assisted test for the detection of overall difference in microbial relative abundances between two health conditions, which simultaneously incorporates the characteristics of relative abundance data. The proposed test (i) divides the taxa into two clusters by the directions of mean differences of relative abundances and then combines them at cluster level, in light of the compositional characteristic; and (ii) contains a burden type test, which collapses multiple taxa into a single one to account for excessive zeros. Moreover, the proposed test is an adaptive procedure, which can accommodate high-dimensional settings and yield high power against various alternative hypotheses. We perform extensive simulation studies across a wide range of scenarios to evaluate the proposed test and show its substantial power gain over some existing tests. The superiority of the proposed approach is further demonstrated with real datasets from two microbiome studies. AVAILABILITY AND IMPLEMENTATION: An R package for MiDAT is available at https://github.com/zhangwei0125/MiDAT. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Change point detection for high dimensional data via kernel measure with application to human aging brain data.

Identifying the existence and locations of change points has been a broadly encountered task in many statistical application areas. The existing change point detection methods may produce unsatisfactory results for high-dimensional data since certain distributional assumptions are made on data, which are hard to verify in practice. Moreover, some parameters (such as the number of change points) need to be estimated beforehand for some methods, making their powers sensitive to these values. Here, we propose a kernel-based U $$ U $$ -statistic to identify change points (KUCP) for high dimensional data, which is free of distributional assumptions and sup-parameter estimations. Specifically, we employ a kernel function to describe similarities among the subjects and construct a U $$ U $$ -statistic to test the existence of change point for a given location. The asymptotic properties of the U $$ U $$ -statistic are deduced. We also develop a procedure to locate the change points sequentially via a dichotomy algorithm. Extensive simulations demonstrate that KUCP has higher sensitivity in identifying existence of change points and higher accuracy in locating these change points than its counterparts. We further illustrate its practical utility by analyzing a gene expression data of human brain to detect the time point when gene expression profiles begin to change, which has been reported to be closely related with aging brain.

Group analysis of distance matrices.

Distance-based regression model has become a powerful approach to identifying phenotypic associations in many fields. It is found to be particularly useful for high-dimensional biological and genetic data with proper distance or similarity measures being available. The pseudo F statistic used in this model accumulates information and is effective when the signals, that is the variations represented by the eigenvalues of the similarity matrix, scatter evenly along the eigenvectors of the similarity matrix. However, it might lose power for the uneven signals. To deal with this issue, we propose a group analysis on the variations of signals along the eigenvalues of the similarity matrix and take the maximum among them. The new procedure can automatically choose an optimal grouping point on some given thresholds and thus can improve the power evidence. Extensive computer simulations and applications to a prostate cancer data and an aging human brain data illustrate the effectiveness of the proposed method.

Truncated tests for combining evidence of summary statistics.

To date, thousands of genetic variants to be associated with numerous human traits and diseases have been identified by genome-wide association studies (GWASs). The GWASs focus on testing the association between single trait and genetic variants. However, the analysis of multiple traits and single nucleotide polymorphisms (SNPs) might reflect physiological process of complex diseases and the corresponding study is called pleiotropy association analysis. Modern day GWASs report only summary statistics instead of individual-level phenotype and genotype data to avoid logistical and privacy issues. Existing methods for combining multiple phenotypes GWAS summary statistics mainly focus on low-dimensional phenotypes while lose power in high-dimensional cases. To overcome this defect, we propose two kinds of truncated tests to combine multiple phenotypes summary statistics. Extensive simulations show that the proposed methods are robust and powerful when the dimension of the phenotypes is high and only part of the phenotypes are associated with the SNPs. We apply the proposed methods to blood cytokines data collected from Finnish population. Results show that the proposed tests can identify additional genetic markers that are missed by single trait analysis.

A ROC-based test for evaluating the group difference with an application to neonatal audiology screening.

This article proposes a powerful method to compare two samples. The proposed method handles comparison of data by drawing inference from ROC curve model parameters. The method estimates parameters from a linear model framework on the empirical sensitivities and specificities. The consistent ROC parameters are then used to give a more powerful test than existing methods in several situations. In addition, we present a comprehensive statistic based on the Cauchy combination, which works well in all scenarios considered in this article. We also offer an efficient one-layer wild permutation procedure to calculate the P-value of our statistic. The method is particularly useful when the underlying continuous biomarker results are non-normal. We illustrate the proposed methods in a neonatal audiology diagnostic example.

k-Resolution sequential randomization procedure to improve covariates balance in a randomized experiment.

Balancing allocation of assigning units to two treatment groups to minimize the allocation differences is important in biomedical research. The complete randomization, rerandomization, and pairwise sequential randomization (PSR) procedures can be employed to balance the allocation. However, the first two do not allow a large number of covariates. In this article, we generalize the PSR procedure and propose a k-resolution sequential randomization (k-RSR) procedure by minimizing the Mahalanobis distance between both groups with equal group size. The proposed method can be used to achieve adequate balance and obtain a reasonable estimate of treatment effect. Compared to PSR, k-RSR is more likely to achieve the optimal value theoretically. Extensive simulation studies are conducted to show the superiorities of k-RSR and applications to the clinical synthetic data and GAW16 data further illustrate the methods.

A novel test by combining the maximum and minimum values among a large number of dependent Z-scores with application to genome wide association study.

In this article, we propose a novel test via combining the maximum and minimum values among a large number of dependent Z-scores for testing the hypothesis with sparse signals. The proposed test employs the information about different signs of maximum and minimum Z-scores and thus power is gained. Its asymptotic null distribution is derived under the null hypothesis and some regular conditions. Extensive simulation studies are conducted to show the advantages of the proposed test by comparing with two existing ones. A real application to the lipids genome wide association study further shows its performances.

Nonparametric estimation of distributions and diagnostic accuracy based on group-tested results with differential misclassification.

This article concerns the problem of estimating a continuous distribution in a diseased or nondiseased population when only group-based test results on the disease status are available. The problem is challenging in that individual disease statuses are not observed and testing results are often subject to misclassification, with further complication that the misclassification may be differential as the group size and the number of the diseased individuals in the group vary. We propose a method to construct nonparametric estimation of the distribution and obtain its asymptotic properties. The performance of the distribution estimator is evaluated under various design considerations concerning group sizes and classification errors. The method is exemplified with data from the National Health and Nutrition Examination Survey study to estimate the distribution and diagnostic accuracy of C-reactive protein in blood samples in predicting chlamydia incidence.

Order-restricted inference for clustered ROC data with application to fingerprint matching accuracy.

Receiver operating characteristic (ROC) curve is commonly used to evaluate and compare the accuracy of classification methods or markers. Estimating ROC curves has been an important problem in various fields including biometric recognition and diagnostic medicine. In real applications, classification markers are often developed under two or more ordered conditions, such that a natural stochastic ordering exists among the observations. Incorporating such a stochastic ordering into estimation can improve statistical efficiency (Davidov and Herman, 2012). In addition, clustered and correlated data arise when multiple measurements are gleaned from the same subject, making estimation of ROC curves complicated due to within-cluster correlations. In this article, we propose to model the ROC curve using a weighted empirical process to jointly account for the order constraint and within-cluster correlation structure. The algebraic properties of resulting summary statistics of the ROC curve such as its area and partial area are also studied. The algebraic expressions reduce to the ones by Davidov and Herman (2012) for independent observations. We derive asymptotic properties of the proposed order-restricted estimators and show that they have smaller mean-squared errors than the existing estimators. Simulation studies also demonstrate better performance of the newly proposed estimators over existing methods for finite samples. The proposed method is further exemplified with the fingerprint matching data from the National Institute of Standards and Technology Special Database 4.

Incorporating retesting outcomes for estimation of disease prevalence.

Group testing has been widely used as a cost-effective strategy to screen for and estimate the prevalence of a rare disease. While it is well-recognized that retesting is necessary for identifying infected subjects, it is not required for estimating the prevalence. For a test without misclassification, gains in statistical efficiency are expected from incorporating retesting results in the estimation of the prevalence. However, when the test is subject to misclassification, it is not clear how much gain should be expected. There are a number of theoretical challenges in addressing this issue, including (1) enumerating the potential test results from retesting individual subjects in a group, (2) the dependence among these test results and the test result from testing at the group level, and (3) differential misclassification due to pooling of biospecimens. Overcoming some of these challenges, we show that retesting subjects in either positive or negative groups can substantially improve the efficiency of the estimation and that retesting positive groups yields higher efficiency than retesting a same number or proportion of negative groups.

A powerful test for ordinal trait genetic association analysis.

Response selective sampling design is commonly adopted in genetic epidemiologic study because it can substantially reduce time cost and increase power of identifying deleterious genetic variants predispose to human complex disease comparing with prospective design. The proportional odds model (POM) can be used to fit data obtained by this design. Unlike the logistic regression model, the estimated genetic effect based on POM by taking data as being enrolled prospectively is inconsistent. So the power of resulted Wald test is not satisfactory. The modified POM is suitable to fit this type of data, however, the corresponding Wald test is not optimal when the genetic effect is small. Here, we propose a new association test to handle this issue. Simulation studies show that the proposed test can control the type I error rate correctly and is more powerful than two existing methods. Finally, we applied three tests to Anticyclic Citrullinated Protein Antibody data from Genetic Workshop 16.

A cluster-adjusted rank-based test for a clinical trial concerning multiple endpoints with application to dietary intervention assessment.

Multiple endpoints are often naturally clustered based on their scientific interpretations. Tests that compare these clustered outcomes between independent groups may lose efficiency if the cluster structures are not properly accounted for. For the two-sample generalized Behrens-Fisher hypothesis concerning multiple endpoints we propose a cluster-adjusted multivariate test procedure for the comparison and demonstrate its gain in efficiency over test procedures that ignore the clusters. Data from a dietary intervention trial are used to illustrate the methods.

GATE: an efficient procedure in study of pleiotropic genetic associations.

BACKGROUND: The association studies on human complex traits are admittedly propitious to identify deleterious genetic markers. Compared to single-trait analyses, multiple-trait analyses can arguably make better use of the information on both traits and markers, and thus improve statistical power of association tests prominently. Principal component analysis (PCA) is a well-known useful tool in multivariate analysis and can be applied to this task. Generally, PCA is first performed on all traits and then a certain number of top principal components (PCs) that explain most of the trait variations are selected to construct the test statistics. However, under some situations, only utilizing these top PCs would lead to a loss of important evidences from discarded PCs and thus makes the capability compromised. METHODS: To overcome this drawback while keeping the advantages of using the top PCs, we propose a group accumulated test evidence (GATE) procedure. By dividing the PCs which is sorted in the descending order according to the corresponding eigenvalues into a few groups, GATE integrates the information of traits at the group level. RESULTS: Simulation studies demonstrate the superiority of the proposed approach over several existing methods in terms of statistical power. Sometimes, the increase of power can reach 25%. These methods are further illustrated using the Heterogeneous Stock Mice data which is collected from a quantitative genome-wide association study. CONCLUSIONS: Overall, GATE provides a powerful test for pleiotropic genetic associations.

Group-combined P-values with applications to genetic association studies.

MOTIVATION: In large-scale genetic association studies with tens of hundreds of single nucleotide polymorphisms (SNPs) genotyped, the traditional statistical framework of logistic regression using maximum likelihood estimator (MLE) to infer the odds ratios of SNPs may not work appropriately. This is because a large number of odds ratios need to be estimated, and the MLEs may be not stable when some of the SNPs are in high linkage disequilibrium. Under this situation, the P-value combination procedures seem to provide good alternatives as they are constructed on the basis of single-marker analysis. RESULTS: The commonly used P-value combination methods (such as the Fisher's combined test, the truncated product method, the truncated tail strength and the adaptive rank truncated product) may lose power when the significance level varies across SNPs. To tackle this problem, a group combined P-value method (GCP) is proposed, where the P-values are divided into multiple groups and then are combined at the group level. With this strategy, the significance values are integrated at different levels, and the power is improved. Simulation shows that the GCP can effectively control the type I error rates and have additional power over the existing methods-the power increase can be as high as over 50% under some situations. The proposed GCP method is applied to data from the Genetic Analysis Workshop 16. Among all the methods, only the GCP and ARTP can give the significance to identify a genomic region covering gene DSC3 being associated with rheumatoid arthritis, but the GCP provides smaller P-value. AVAILABILITY AND IMPLEMENTATION: http://www.statsci.amss.ac.cn/yjscy/yjy/lqz/201510/t20151027_313273.html CONTACT: liqz@amss.ac.cn SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A two-phase procedure for non-normal quantitative trait genetic association study.

BACKGROUND: The nonparametric trend test (NPT) is well suitable for identifying the genetic variants associated with quantitative traits when the trait values do not satisfy the normal distribution assumption. If the genetic model, defined according to the mode of inheritance, is known, the NPT derived under the given genetic model is optimal. However, in practice, the genetic model is often unknown beforehand. The NPT derived from an uncorrected model might result in loss of power. When the underlying genetic model is unknown, a robust test is preferred to maintain satisfactory power. RESULTS: We propose a two-phase procedure to handle the uncertainty of the genetic model for non-normal quantitative trait genetic association study. First, a model selection procedure is employed to help choose the genetic model. Then the optimal test derived under the selected model is constructed to test for possible association. To control the type I error rate, we derive the joint distribution of the test statistics developed in the two phases and obtain the proper size. CONCLUSIONS: The proposed method is more robust than existing methods through the simulation results and application to gene DNAH9 from the Genetic Analysis Workshop 16 for associated with Anti-cyclic citrullinated peptide antibody further demonstrate its performance.

Incorporating Hardy-Weinberg Equilibrium Law to Enhance the Association Strength for Ordinal Trait Genetic Study.

The conventional method to examine whether genetic variants are associated with the ordinal traits is the proportional odds model. Such analyses are often conducted by assuming an additive genetic mode of inheritance. However, how the genetic variants influence the risk of occurrence of a disease is impossible to know in practice. Using an improper model might result in a low-power test, thus it reduces the probability of detecting the deleterious genetic markers. To address these concerns, we propose a two-phase procedure (TPP) for ordinal trait genetic studies. In the first phase, we used a linear combination to weight the Hardy-Weinberg equilibrium tests in case groups and formed an omnibus test to classify the genetic models. Then based on the chosen model, the corresponding score test was used to identify the associations. To control the false positive rate, we derived the joint distribution of the test used for selecting the genetic model and that used for identifying the associations. We also obtained the closed forms of two other robust tests, MAX3 and CHI2. Extensive computer simulations were carried out and the results showed that the true selection rates of genetic models are satisfactory and the proposed TPP is more robust than MAX3 and CHI2. Finally, we demonstrated the advantage of our proposed method by applying it to analyse the antibody reactivity to cyclic citrullinated peptides data.

Genetic risks and genetic model specification.

Genetic risks and genetic models are often used in design and analysis of genetic epidemiology studies. A genetic model is defined in terms of two genetic risk measures: genotype relative risk and odds ratio. The impacts of choosing a risk measure on the resulting genetic models are studied in the power to detect association and deviation from Hardy-Weinberg equilibrium in cases using genetic relative risk. Extensive simulations demonstrate that the power of a study to detect associations using odds ratio is lower than that using relative risk with the same value when other parameters are fixed. When the Hardy-Weinberg equilibrium holds in the general population, the genetic model can be inferred by the deviation from Hardy-Weinberg equilibrium in only cases. Furthermore, it is more efficient than that based on the deviation from Hardy-Weinberg equilibrium in all cases and controls.

Least squares regression methods for clustered ROC data with discrete covariates.

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods.