Score-based Test Research Articles

A Semiparametric Approach to Test for the Presence of INAR: Simulations and Empirical Applications

The present paper explores the application of bootstrap methods in testing for serial dependence in observed driven Integer-AutoRegressive (models) considering Poisson arrivals (P-INAR). To this end, a new semiparametric and restricted bootstrap algorithm is developed to ameliorate the performance of the score-based test statistic, especially when the time series present small or moderately small lengths. The performance of the proposed bootstrap test, in terms of empirical size and power, is investigated through a simulation study even considering deviation from Poisson assumptions for innovations, i.e., overdispersion and underdispersion. Under non-Poisson innovations, the semiparametric bootstrap seems to “restore” inference, while the asymptotic test usually fails. Finally, the usefulness of this approach is shown via three empirical applications.

A powerful global test for spliceQTL effects.

Statistical methods to test for effects of single nucleotide polymorphisms (SNPs) on exon inclusion exist but often rely on testing of associations between multiple exon-SNP pairs, with sometimes subsequent summarization of results at the gene level. Such approaches require heavy multiple testing corrections and detect mostly events with large effect sizes. We propose here a test to find spliceQTL (splicing quantitative trait loci) effects that takes all exons and all SNPs into account simultaneously. For any chosen gene, this score-based test looks for an association between the set of exon expressions and the set of SNPs, via a random-effects model framework. It is efficient to compute and can be used if the number of SNPs is larger than the number of samples. In addition, the test is powerful in detecting effects that are relatively small for individual exon-SNP pairs but are observed for many pairs. Furthermore, test results are more often replicated across datasets than pairwise testing results. This makes our test more robust to exon-SNP pair-specific effects, which do not extend to multiple pairs within the same gene. We conclude that the test we propose here offers more power and better replicability in the search for spliceQTLeffects.

An Evaluation of DIF Tests in Multistage Tests for Continuous Covariates

Multistage tests are a widely used and efficient type of test presentation that aims to provide accurate ability estimates while keeping the test relatively short. Multistage tests typically rely on the psychometric framework of item response theory. Violations of item response models and other assumptions underlying a multistage test, such as differential item functioning, can lead to inaccurate ability estimates and unfair measurements. There is a practical need for methods to detect problematic model violations to avoid these issues. This study compares and evaluates three methods for the detection of differential item functioning with regard to continuous person covariates in data from multistage tests: a linear logistic regression test and two adaptations of a recently proposed score-based DIF test. While all tests show a satisfactory Type I error rate, the score-based tests show greater power against three types of DIF effects.

Family-based gene-environment interaction using sequence kernel association test (FGE-SKAT) for complex quantitative traits

After the genome-wide association studies (GWAS) era, whole-genome sequencing is highly engaged in identifying the association of complex traits with rare variations. A score-based variance-component test has been proposed to identify common and rare genetic variants associated with complex traits while quickly adjusting for covariates. Such kernel score statistic allows for familial dependencies and adjusts for random confounding effects. However, the etiology of complex traits may involve the effects of genetic and environmental factors and the complex interactions between genes and the environment. Therefore, in this research, a novel method is proposed to detect gene and gene-environment interactions in a complex family-based association study with various correlated structures. We also developed an R function for the Fast Gene-Environment Sequence Kernel Association Test (FGE-SKAT), which is freely available as supplementary material for easy GWAS implementation to unveil such family-based joint effects. Simulation studies confirmed the validity of the new strategy and the superior statistical power. The FGE-SKAT was applied to the whole genome sequence data provided by Genetic Analysis Workshop 18 (GAW18) and discovered concordant and discordant regions compared to the methods without considering gene by environment interactions.

Novel score test to increase power in association test by integrating external controls.

Recent advances in genotyping and sequencing technologies have enabled genetic association studies to leverage high-quality genotyped data to identify variants accounting for a substantial portion of disease risk. The usage of external controls, whose genomes have already been genotyped and are publicly available, could be a cost-effective approach to increase the power of association testing. There has been recent effort to integrate external controls while adjusting for possible batch effects, such as the integrating External Controls into Association Test (iECAT). The original iECAT test, however, cannot adjust for covariates such as age, gender, and so forth. Hence, based on the insight of iECAT, we propose a novel score-based test that allows for covariate adjustment and constructs a shrinkage score statistic that is a weighted sum of the score statistics using exclusively internal samples and uses both internal and external control samples. We assess the existence of batch effect at a variant by comparing control samples of internal and external sources. We show by simulation studies that our method has increased power over the original iECAT while controlling for type I error rates. We present the application of our method to the association studies of age-related macular degeneration (AMD) utilizing data from the International AMD Genomics Consortiumand Michigan Genomics Initiative. Through the incorporation of the score test approach, we extend the use of iECAT to adjust for covariates and improve power, further honing the statistical methods needed to identify disease-causing variants within the human genome.

Genome-wide association study for multiple phenotype analysis

Genome-wide association studies often collect multiple phenotypes for complex diseases. Multivariate joint analyses have higher power to detect genetic variants compared with the marginal analysis of each phenotype and are also able to identify loci with pleiotropic effects. We extend the unified score-based association test to incorporate family structure, apply different approaches to analyze multiple traits in GAW20 real samples, and compare the results. Through simulation studies, we confirm that the Type I error rate of the pedigree-based unified score association test is appropriately controlled. In marginalanalysis of triglyceride levels, we found 1 subgenome-wide significant variant on chromosome 6. Joint analyses identified several suggestive genome-wide significant signals, with the pedigree-based unified score association test yielding the greatest number of significant results.

Abstract 244: Pathway analysis of OncoArray data identifies biological pathways involved in lung cancer development

Abstract Background:Genome-wide association studies (GWAS) have identified susceptible loci associated with lung cancer development. However, these variants only account for a small proportion of lung cancer heritability. With the aim to identify the missing heritability, we propose to conduct pathway analysis to test the joint effects of rare and common variants using the OncoArray data. By grouping SNPs into genes and pathways, we may shed light into the underlying mechanisms for lung cancer development and identify novel candidate genes and pathways.Methods:We applied sequence kernel association test (SKAT) to the OncoArray data of the Transdisciplinary Research of Cancer in lung of the International Lung Cancer Consortium (TRICL-ILCCO) that includes 34,432 individuals (19,028 cases and 15,404 controls) across over twenty lung cancer studies. A total of 403 KEGG and Biocarta pathways containing 5,555 genes and 58,717 SNPs were included in the study. As a score-based variance-component test, SKAT calculated p values for each pathway set by fitting the null model containing only age, gender, smoking, and first three PCAs. Results:KEGG neuroactive ligand receptor interaction (p=1.18×10-4, FDR=0.0285) and KEGG pancreatic cancer pathways (p=1.41×10-4, FDR=0.0285) were significantly associated with lung cancer. Gene-based analyses found that the most significant genes on the KEGG neuroactive ligand receptor interaction pathway to be CHRNA5 (p=2.33×10-8, FDR=0.0003), CHRNA3 (p=2.85×10-7, FDR=0.0019), and CHRNB4 (p=7.49×10-7, FDR=0.0034), while the most significant genes for KEGG pancreatic cancer pathway to be BRCA2 (p=2.23×10-5, FDR=0.0505). Stratified analyses highlighted five pathways (KEGG intestinal immune network for IGA production, KEGG leishmania infection, KEGG bladder cancer, KEGG pancreatic cancer, and KEGG axon guidance) for squamous cell carcinoma and one pathway (Biocarta ACH pathway) for adenocarcinoma with FWER<0.05. Noteworthy, the most significant gene on ACH pathway for adenocarcinoma was TERT gene, whereas the top two significant pathways for squamous carcinoma shared the most significant HLA-DQA1 gene, along with 11 other HLA genes at 6p21.Conclusion:The results suggest that the underlying pathways differ by cancer cell types and further research should be conducted to investigate the effects of immune pathways and HLA genes on squamous cell carcinoma etiology. Citation Format: Zhihui Wang, Ruyang Zhang, Li Su, Rayjean Hung, Christopher Amos, David C. Christiani. Pathway analysis of OncoArray data identifies biological pathways involved in lung cancer development [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 244.

A Powerful Test for SNP Effects on Multivariate Binary Outcomes using Kernel Machine Regression.

Evaluating multiple binary outcomes is common in genetic studies of complex diseases. These outcomes are often correlated because they are collected from the same individual and they may share common marker effects. In this paper, we propose a procedure to test for effect of a SNP-set on multiple, possibly correlated, binary responses. We develop a score-based test using a nonparametric modeling framework that jointly models the global effect of the marker set. We account for the nonlinear effects and potentially complicated interaction between markers using reproducing kernels. Our testing procedure only requires estimation under the null hypothesis and we use multivariate generalized estimating equations (GEEs) to estimate the model components to account for the correlation among the outcomes. We evaluate finite sample performance of our test via simulation study and demonstrated our methods using the CATIE antibody study data and the CoLaus Study data.

Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models

This article develops a systematic inference procedure for heavy-tailed and multiple-threshold double autoregressive (MTDAR) models. We first study its quasi-maximum exponential likelihood estimator (QMELE). It is shown that the estimated thresholds are n-consistent, each of which converges weakly to the smallest minimizer of a two-sided compound Poisson process. The remaining parameters are -consistent and asymptotically normal. Based on this theory, a score-based test is developed to identify the number of thresholds in the model. Furthermore, we construct a mixed sign-based portmanteau test for model checking. Simulation study is carried out to access the performance of our procedure and a real example is given.

On a Threshold Double Autoregressive Model

This article first proposes a score-based test for a double autoregressive model against a threshold double autoregressive (AR) model. It is an asymptotically distribution-free test and is easy to implement in practice. The article further studies the quasi-maximum likelihood estimation of a threshold double autoregressive model. It is shown that the estimated threshold is n-consistent and converges weakly to a functional of a two-sided compound Poisson process and the remaining parameters are asymptotically normal. Our results include the asymptotic theory of the estimator for threshold AR models with autoregressive conditional heteroscedastic (ARCH) errors and threshold ARCH models as special cases, each of which is also new in literature. Two portmanteau-type statistics are also derived for checking the adequacy of fitted model when either the error is nonnormal or the threshold is unknown. Simulation studies are conducted to assess the performance of the score-based test and the estimator in finite samples. The results are illustrated with an application to the weekly closing prices of Hang Seng Index. This article also includes the weak convergence of a score-marked empirical process on the space under an α-mixing assumption, which is independent of interest.

USAT: A Unified Score-Based Association Test for Multiple Phenotype-Genotype Analysis.

Genome-wide association studies (GWASs) for complex diseases often collect data on multiple correlated endo-phenotypes. Multivariate analysis of these correlated phenotypes can improve the power to detect genetic variants. Multivariate analysis of variance (MANOVA) can perform such association analysis at a GWAS level, but the behavior of MANOVA under different trait models has not been carefully investigated. In this paper, we show that MANOVA is generally very powerful for detecting association but there are situations, such as when a genetic variant is associated with all the traits, where MANOVA may not have any detection power. In these situations, marginal model based methods, however, perform much better than multivariate methods. We investigate the behavior of MANOVA, both theoretically and using simulations, and derive the conditions where MANOVA loses power. Based on our findings, we propose a unified score-based test statistic USAT that can perform better than MANOVA in such situations and nearly as well as MANOVA elsewhere. Our proposed test reports an approximate asymptotic P-value for association and is computationally very efficient to implement at a GWAS level. We have studied through extensive simulations the performance of USAT, MANOVA, and other existing approaches and demonstrated the advantage of using the USAT approach to detect association between a genetic variant and multivariate phenotypes. We applied USAT to data from three correlated traits collected on 5, 816 Caucasian individuals from the Atherosclerosis Risk in Communities (ARIC, The ARIC Investigators []) Study and detected some interesting associations.

Testing against changing correlation

A test for time-varying correlation is developed within the framework of a dynamic conditional score (DCS) model for both Gaussian and Student t-distributions. The test may be interpreted as a Lagrange multiplier test and modified to allow for the estimation of models for time-varying volatility in the individual series. Unlike standard moment-based tests, the score-based test statistic includes information on the level of correlation under the null hypothesis and local power arguments indicate the benefits of doing so. A simulation study shows that the performance of the score-based test is strong relative to existing tests across a range of data generating processes. An application to the Hong Kong and South Korean equity markets shows that the new test reveals changes in correlation that are not detected by the standard moment-based test.

Asymptotic inference in multiple-threshold double autoregressive models

This paper investigates a class of multiple-threshold models, called Multiple Threshold Double AR (MTDAR) models. A sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first-order MTDAR model. We study the Quasi-Maximum Likelihood Estimator (QMLE) of the MTDAR model. The estimated thresholds are shown to be n-consistent, asymptotically independent, and to converge weakly to the smallest minimizer of a two-sided compound Poisson process. The remaining parameters are n-consistent and asymptotically multivariate normal. In particular, these results apply to the multiple threshold ARCH model, with or without AR part, and to the multiple threshold AR models with ARCH errors. A score-based test is also presented to determine the number of thresholds in MTDAR models. The limiting distribution is shown to be distribution-free and is easy to implement in practice. Simulation studies are conducted to assess the performance of the QMLE and our score-based test in finite samples. The results are illustrated with an application to the quarterly US real GNP data over the period 1947–2013.

Local Score Tests in Mixture Exponential Family with Fixed Mean

Abstract In this paper, the testing problem for homogeneity is considered in the mixture exponential density or probability distribution family {f(x|θ1, θ2, λ,) = (1 - λ)fθ1(x) + λfθ2(x)} where {fθ(x) = f0(x)exp(xθ - c(θ))} belongs to a standard one-parameter exponential family for |θ| ≤ K (>0). Assuming the mean is fixed and unknown, a local score-based test is proposed which naturally generalizes Neyman and Scott's C(α)-test. Simulation results show that the proposed test improves C(α)-test in certain cases. The test does not involve the boundedness problem of the mean parameter space and the results continue the work of Wu and Gupta (2003).

Testing for unusual aggregation of health risk in semiparametric models

We present a method for surface estimation over some area of interest using spatial multilevel semiparametric models, in which the spatial correlation is modeled through splines with random coefficients associated with a set of knots. Multiple sets of random effects are associated with partitions of the entire area of interest that allow flexibility for testing unusual rates within sub-regions of larger areas. To test departures from the null value of no unusual rates, we derive a score-based test statistic, partially by using some of the results available for singular information problems. The test is robust in that it does not require specifying the joint distribution of the random effect. In an extensive simulation study this overall general test shows correct levels, and it is highly sensitive to clustering across all the scenarios considered. Once a departure is detected, a second, finer grid of knots can be superimposed on the existing grid, and the proposed procedure can be applied to test the homogeneity within two or more sub-areas. The proposed model is applied to lung cancer deaths in South Carolina in the year 2000 and to data on airborne mercury in vegetation around a solid waste incinerator in Oxford, New Jersey.

Confidence Intervals for the Variance Component of Random-effects Linear Models

We present the postestimation command xtvc to provide confidence intervals for the variance components of random-effects linear regression models. This command must be used after xtreg with option mle. Confidence intervals are based on the inversion of a score-based test (Bottai 2003).

Multipoint linkage detection in the presence of heterogeneity.

Linkage heterogeneity is common for complex diseases. It is well known that loss of statistical power for detecting linkage will result if one assumes complete homogeneity in the presence of linkage heterogeneity. To this end, Smith (1963, Annals of Human Genetics 27, 175-182) proposed an admixture model to account for linkage heterogeneity. It is well known that for this model, the conventional chi-squared approximation to the likelihood ratio test for no linkage does not apply even when the sample size is large. By dealing with nuclear families and one marker at a time for genetic diseases with simple modes of inheritance, score-based test statistics (Liang and Rathouz, 1999, Biometrics 55, 65-74) and likelihood-ratio-based test statistics (Lemdani and Pons, 1995, Biometrics 51, 1033-1041) have been proposed which have a simple large-sample distribution under the null hypothesis of linkage. In this paper, we extend their work to more practical situations that include information from multiple markers and multi-generational pedigrees while allowing for a class of general genetic models. Three different approaches are proposed to eliminate the nuisance parameters in these test statistics. We show that all three approaches lead to the same asymptotic distribution under the null hypothesis of no linkage. Simulation results show that the proposed test statistics have adequate power to detect linkage and that the performances of these two classes of test statistics are quite comparable. We have applied the proposed method to a family study of asthma (Barnes et al., 1996), in which the score-based test shows evidence of linkage with p-value <0.0001 in the region of interest on chromosome 12. Additionally, we have implemented this score-based test within the frequently used computer package GENEHUNTER.