Adaptive testing for multiple traits in a proportional odds model with applications to detect SNP‐brain network associations

There has been increasing interest in developing more powerful and flexible statistical tests to detect genetic associations with multiple traits, as arising from neuroimaging genetic studies. Most of existing methods treat a single trait or multiple traits as response while treating an SNP as a predictor coded under an additive inheritance mode. In this paper, we follow an earlier approach in treating an SNP as an ordinal response while treating traits as predictors in a proportional odds model (POM). In this way, it is not only easier to handle mixed types of traits, e.g., some quantitative and some binary, but it is also potentially more robust to the commonly adopted additive inheritance mode. More importantly, we develop an adaptive test in a POM so that it can maintain high power across many possible situations. Compared to the existing methods treating multiple traits as responses, e.g., in a generalized estimating equation (GEE) approach, the proposed method can be applied to a high dimensional setting where the number of phenotypes (p) can be larger than the sample size (n), in addition to a usual small P setting. The promising performance of the proposed method was demonstrated with applications to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, in which either structural MRI driven phenotypes or resting‐state functional MRI (rs‐fMRI) derived brain functional connectivity measures were used as phenotypes. The applications led to the identification of several top SNPs of biological interest. Furthermore, simulation studies showed competitive performance of the new method, especially for .     

X chromosome association testing in genome wide association studies

Genome wide association studies (GWAS) have revealed many fascinating insights into complex diseases even from simple, single-marker statistical tests. Most of these tests are designed for testing of associations between a phenotype and an autosomal genotype and are therefore not applicable to X chromosome data. Testing for association on the X chromosome raises unique challenges that have motivated the development of X-specific statistical tests in the literature. However, to date there has been no study of these methods under a wide range of realistic study designs, allele frequencies and disease models to assess the size and power of each test. To address this, we have performed an extensive simulation study to investigate the effects of the sex ratios in the case and control cohorts, as well as the allele frequencies, on the size and power of eight test statistics under three different disease models that each account for X-inactivation. We show that existing, but under-used, methods that make use of both male and female data are uniformly more powerful than popular methods that make use of only female data. In particular, we show that Clayton's one degree of freedom statistic [Clayton, 2008] is robust and powerful across a wide range of realistic simulation parameters. Our results provide guidance on selecting the most appropriate test statistic to analyse X chromosome data from GWAS and show that much power can be gained by a more careful analysis of X chromosome GWAS data.     

Resampling-based multiple hypothesis testing procedures for genetic case-control association studies

In case-control studies of unrelated subjects, gene-based hypothesis tests consider whether any tested feature in a candidate gene--single nucleotide polymorphisms (SNPs), haplotypes, or both--are associated with disease. Standard statistical tests are available that control the false-positive rate at the nominal level over all polymorphisms considered. However, more powerful tests can be constructed that use permutation resampling to account for correlations between polymorphisms and test statistics. A key question is whether the gain in power is large enough to justify the computational burden. We compared the computationally simple Simes Global Test to the min P test, which considers the permutation distribution of the minimum p-value from marginal tests of each SNP. In simulation studies incorporating empirical haplotype structures in 15 genes, the min P test controlled the type I error, and was modestly more powerful than the Simes test, by 2.1 percentage points on average. When disease susceptibility was conferred by a haplotype, the min P test sometimes, but not always, under-performed haplotype analysis. A resampling-based omnibus test combining the min P and haplotype frequency test controlled the type I error, and closely tracked the more powerful of the two component tests. This test achieved consistent gains in power (5.7 percentage points on average), compared to a simple Bonferroni test of Simes and haplotype analysis. Using data from the Shanghai Biliary Tract Cancer Study, the advantages of the newly proposed omnibus test were apparent in a population-based study of bile duct cancer and polymorphisms in the prostaglandin-endoperoxide synthase 2 (PTGS2) gene.     

Multilocus association testing with penalized regression

In multilocus association analysis, since some markers may not be associated with a trait, it seems attractive to use penalized regression with the capability of automatic variable selection. On the other hand, in spite of a rapidly growing body of literature on penalized regression, most focus on variable selection and outcome prediction, for which penalized methods are generally more effective than their nonpenalized counterparts. However, for statistical inference, i.e. hypothesis testing and interval estimation, it is less clear how penalized methods would perform, or even how to best apply them, largely due to lack of studies on this topic. In our motivating data for a cohort of kidney transplant recipients, it is of primary interest to assess whether a group of genetic variants are associated with a binary clinical outcome, acute rejection at 6 months. In this article, we study some technical issues and alternative implementations of hypothesis testing in Lasso penalized logistic regression, and compare their performance with each other and with several existing global tests, some of which are specifically designed as variance component tests for high-dimensional data. The most interesting, and perhaps surprising, conclusion of this study is that, for low to moderately high-dimensional data, statistical tests based on Lasso penalized regression are not necessarily more powerful than some existing global tests. In addition, in penalized regression, rather than building a test based on a single selected "best" model, combining multiple tests, each of which is built on a candidate model, might be more promising.     

XM: association testing on the X-chromosome in case-control samples with related individuals

Genetic variants on the X-chromosome could potentially play an important role in some complex traits. However, development of methods for detecting association with X-linked markers has lagged behind that for autosomal markers. We propose methods for case-control association testing with X-chromosome markers in samples with related individuals. Our method, XM, appropriately adjusts for both correlation among relatives and male-female allele copy number differences. Features of XM include: (1) it is applicable to and computationally feasible for completely general combinations of family and case-control designs; (2) it allows for both unaffected controls and controls of unknown phenotype to be included in the same analysis; (3) it can incorporate phenotype information on relatives with missing genotype data; and (4) it adjusts for sex-specific trait prevalence values. We propose two other tests, Xχ and XW, which can also be useful in certain contexts. We derive the best linear unbiased estimator of allele frequency, and its variance, for X-linked markers. In simulation studies with related individuals, we demonstrate the power and validity of the proposed methods. We apply the methods to X-chromosome association analysis of (1) asthma in a Hutterite sample and (2) alcohol dependence in the GAW 14 COGA data. In analysis (1), we demonstrate computational feasibility of XM and the applicability of our robust variance estimator. In analysis (2), we detect significant association, after Bonferroni correction, between alcohol dependence and single nucleotide polymorphism rs979606 in the monoamine oxidases A gene, where this gene has previously been found to be associated with substance abuse and antisocial behavior.     

An Adaptive Association Test for Multiple Phenotypes with GWAS Summary Statistics

We study the problem of testing for single marker‐multiple phenotype associations based on genome‐wide association study (GWAS) summary statistics without access to individual‐level genotype and phenotype data. For most published GWASs, because obtaining summary data is substantially easier than accessing individual‐level phenotype and genotype data, while often multiple correlated traits have been collected, the problem studied here has become increasingly important. We propose a powerful adaptive test and compare its performance with some existing tests. We illustrate its applications to analyses of a meta‐analyzed GWAS dataset with three blood lipid traits and another with sex‐stratified anthropometric traits, and further demonstrate its potential power gain over some existing methods through realistic simulation studies. We start from the situation with only one set of (possibly meta‐analyzed) genome‐wide summary statistics, then extend the method to meta‐analysis of multiple sets of genome‐wide summary statistics, each from one GWAS. We expect the proposed test to be useful in practice as more powerful than or complementary to existing methods.     

Permutation and Bayesian tests for testing random effects in linear mixed-effects models

In many applications of linear mixed-effects models to longitudinal and multilevel data especially from medical studies, it is of interest to test for the need of random effects in the model. It is known that classical tests such as the likelihood ratio, Wald, and score tests are not suitable for testing random effects because they suffer from testing on the boundary of the parameter space. Instead, permutation and bootstrap tests as well as Bayesian tests, which do not rely on the asymptotic distributions, avoid issues with the boundary of the parameter space. In this paper, we first develop a permutation test based on the likelihood ratio test statistic, which can be easily used for testing multiple random effects and any subset of them in linear mixed-effects models. The proposed permutation test would be an extension to two existing permutation tests. We then aim to compare permutation tests and Bayesian tests for random effects to find out which test is more powerful under which situation. Nothing is known about this in the literature, although this is an important practical problem due to the usefulness of both methods in tackling the challenges with testing random effects. For this, we consider a Bayesian test developed using Bayes factors, where we also propose a new alternative computation for this Bayesian test to avoid some computational issue it encounters in testing multiple random effects. Extensive simulations and a real data analysis are used for evaluation of the proposed permutation test and its comparison with the Bayesian test. We find that both tests perform well, albeit the permutation test with the likelihood ratio statistic tends to provide a relatively higher power when testing multiple random effects.     

Log-linear non-uniform association models for agreement between two ratings on an ordinal scale

In agreement studies, when objects are rated independently by two raters (or twice by the same rater), an association between their ratings on two categories arises, reflecting the distinguishability of these two categories for these raters. When ratings are performed on an ordinal scale, this association between ratings on two categories increases when the distance between these categories increases on the ordinal scale. Goodman's log-linear models derived for the analysis of agreement between two raters on an ordinal scale assume that distinguishabilities between adjacent categories are either constant, or a priori fixed. Log-non-linear models that allow variations of the distinguishabilities between adjacent categories along the scale, may lead to difficulties in parameter estimation.This paper describes a new class of log-linear non-uniform association models. These models extend the log-linear uniform association model by allowing variations of distinguishability between adjacent categories (along the scale). These new models are used to analyse ordinal agreement between dermatologists when assessing the severity of different cutaneous signs of ageing on women faces.     

Family-based association test for time-to-onset data with time-dependent differences between the hazard functions

In genetic association studies, the differences between the hazard functions for the individual genotypes are often time-dependent. We address the non-proportional hazards data by using the weighted logrank approach by Fleming and Harrington [1981]:Commun Stat-Theor M 10:763-794. We introduce a weighted FBAT-Logrank whose weights are based on a non-parametric estimator for the genetic marker distribution function under the alternative hypothesis. We show that the computation of the marker distribution under the alternative does not bias the significance level of any subsequently computed FBAT-statistic. Hence, we use the estimated marker distribution to select the Fleming-Harrington weights so that the power of the weighted FBAT-Logrank test is maximized. In simulation studies and applications to an asthma study, we illustrate the practical relevance of the new methodology. In addition to power increases of 100% over the original FBAT-Logrank test, we also gain insight into the age at which a genotype exerts the greatest influence on disease risk.     

Adaptive trimmed t-statistics for identifying predominantly high expression in a microarray experiment

Often, interesting candidate tumor markers are not only genes that show homogeneously higher expression (HHE) in tumor samples compared to control samples, but also genes with only predominantly higher expression (PHE), i.e. genes which exhibit higher expression in at least 80 per cent of tumor samples. Standard parametric test statistics used in the analysis of microarray experiments may fail with PHE as a consequence of the mixture of distributions present in the tumor group. As alternative we consider trimmed t-statistics which compare group mean values after removing outliers in each group. The trimming proportion can be chosen adaptively, either based on a boxplot outlier detection rule or by optimization over a series of tests with varying trimming proportions. The trimmed t-statistics can be plugged into the 'significance analysis of microarrays' (SAM) procedure, yielding the modified boxplot rule test (modBox) and the modified optimization test (modOpt), respectively. By means of simulation of microarray experiments, we show that modOpt is superior to contenders in detecting PHE, while there is only little loss in efficiency under HHE compared to SAM. Analysis of a real microarray experiment revealed that, out of nearly 29 000 genes, about 417 genes exhibiting PHE are detected by modOpt but missed by SAM.     

Generalized estimating equations for genome‐wide association studies using longitudinal phenotype data

Many longitudinal cohort studies have both genome‐wide measures of genetic variation and repeated measures of phenotypes and environmental exposures. Genome‐wide association study analyses have typically used only cross‐sectional data to evaluate quantitative phenotypes and binary traits. Incorporation of repeated measures may increase power to detect associations, but also requires specialized analysis methods. Here, we discuss one such method—generalized estimating equations (GEE)—in the contexts of analysis of main effects of rare genetic variants and analysis of gene‐environment interactions. We illustrate the potential for increased power using GEE analyses instead of cross‐sectional analyses. We also address challenges that arise, such as the need for small‐sample corrections when the minor allele frequency of a genetic variant and/or the prevalence of an environmental exposure is low. To illustrate methods for detection of gene‐drug interactions on a genome‐wide scale, using repeated measures data, we conduct single‐study analyses and meta‐analyses across studies in three large cohort studies participating in the Cohorts for Heart and Aging Research in Genomic Epidemiology consortium—the Atherosclerosis Risk in Communities study, the Cardiovascular Health Study, and the Rotterdam Study. Copyright © 2014 John Wiley & Sons, Ltd.     

The impact of diagnostic error on testing genetic association in case-control studies

In case-control studies, subjects in the case group may be recruited from suspected patients who are diagnosed positively with disease. While many statistical methods have been developed for measurement error or misclassification of exposure variables in epidemiological studies, no studies have been reported on the effect of errors in diagnosing disease on testing genetic association in case-control studies. We study the impact of using the original Cochran-Armitage trend test assuming no diagnostic error when, in fact, cases and controls may be clinically diagnosed by an imperfect gold standard or a reference test. The type I error, sample size and asymptotic power of trend tests are examined under a family of genetic models in the presence of diagnostic error. The empirical powers of the trend tests are also compared by simulation studies under various genetic models.     

Human biomonitoring reference values: Differences and similarities between approaches for identifying unusually high exposure of pollutants in humans

In exposure and risk assessment, the indication of unusually high exposure levels in humans to chemicals has been considered as an important objective for decades. To realize this objective, reference values (RV) need to be derived. However, while there is a tendency towards using the 95th percentile as a basis for deriving these reference values there is still no consensus. Moreover, side approaches have evolved including deriving RVs based on other percentiles, reporting multiple RVs or only reporting percentiles. The purpose of this article is to give an overview of the current literature, to point out differences and similarities between existing approaches, and to highlight important criteria for the derivation of RVs. We observe the majority of studies to base RVs on the 95th percentile and its 95% confidence interval which can been justified by statistical paradigms, present arguments for a single defined reference value, and discuss characteristics which call for more consistency. To conclude, our overview provides a first step towards a more homogenous and standardized derivation procedure to identify unusually high exposures in exposure science.     

Adapting the logical basis of tests for Hardy‐Weinberg Equilibrium to the real needs of association studies in human and medical genetics

The standard procedure to assess genetic equilibrium is a χ² test of goodness‐of‐fit. As is the case with any statistical procedure of that type, the null hypothesis is that the distribution underlying the data is in agreement with the model. Thus, a significant result indicates incompatibility of the observed data with the model, which is clearly at variance with the aim in the majority of applications: to exclude the existence of gross violations of the equilibrium condition. In current practice, we try to avoid this basic logical difficulty by increasing the significance bound to the P‐value (e.g. from 5 to 10%) and inferring compatibility of the data with Hardy Weinberg Equilibrium (HWE) from an insignificant result. Unfortunately, such direct inversion of a statistical testing procedure fails to produce a valid test of the hypothesis of interest, namely, that the data are in sufficiently good agreement with the model under which the P‐value is calculated. We present a logically unflawed solution to the problem of establishing (approximate) compatibility of an observed genotype distribution with HWE. The test is available in one‐ and two‐sided versions. For both versions, we provide tools for exact power calculation. We demonstrate the merits of the new approach through comparison with the traditional χ² goodness‐of‐fit test in 2×60 genotype distributions from 43 published genetic studies of complex diseases where departure from HWE was noted in either the case or control sample. In addition, we show that the new test is useful for the analysis of genome‐wide association studies. Genet. Epidemiol. 33:569–580, 2009. © 2009 Wiley‐Liss, Inc.     

Comparing HLA antigen frequencies between two groups of patients

For diseases that involve the immune system, the alleles of the human leukocyte antigen (HLA) complex can play a major role. For example, if responsiveness to therapy is immunologically mediated, one would think that responders and non-responders might tend to have different HLA alleles. However, comparing the frequencies between the two groups of patients at each allele can introduce a substantial multiple comparisons problem as the number of alleles is large. This paper proposes an efficient two-stage procedure for identifying alleles that may mediate response. In the first-stage, the distribution of all alleles for the patients are compared to a reference population and a few alleles are selected. These candidate alleles are then compared between the two groups of patients using a modest Bonferroni correction. The two-stage procedure strongly controls the type I error rate as the first-stage selection is statistically independent of the second-stage tests. We analyse a cohort of patients with bone marrow failure who are classified as responders or non-responders to immunosuppressive therapy. Published in 2003 by John Wiley & Sons, Ltd.     

An improved score test for genetic association studies

Large-scale genome-wide association studies (GWAS) have become feasible recently because of the development of bead and chip technology. However, the success of GWAS partially depends on the statistical methods that are able to manage and analyze this sort of large-scale data. Currently, the commonly used tests for GWAS include the Cochran-Armitage trend test, the allelic χ(2) test, the genotypic χ(2) test, the haplotypic χ(2) test, and the multi-marker genotypic χ(2) test among others. From a methodological point of view, it is a great challenge to improve the power of commonly used tests, since these tests are commonly used precisely because they are already among the most powerful tests. In this article, we propose an improved score test that is uniformly more powerful than the score test based on the generalized linear model. Since the score test based on the generalized linear model includes the aforementioned commonly used tests as its special cases, our proposed improved score test is thus uniformly more powerful than these commonly used tests. We evaluate the performance of the improved score test by simulation studies and application to a real data set. Our results show that the power increases of the improved score test over the score test cannot be neglected in most cases.     

Multiplicity adjustments in testing for bioequivalence

Bioequivalence of two drugs is usually demonstrated by rejecting two one‐sided null hypotheses using the two one‐sided tests for pharmacokinetic parameters: area under the concentration‐time curve (AUC) and maximum concentration (Cmax). By virtue of the intersection–union test, there is no need for multiplicity adjustment in testing the two one‐sided null hypotheses within each parameter. However, the decision rule for bioequivalence often requires equivalence to be achieved simultaneously on both parameters that contain four one‐sided null hypotheses together; without adjusting for multiplicity, the family wise error rate (FWER) could fail to be controlled at the nominal type‐I error rate α. The multiplicity issue for bioequivalence in this regard is scarcely discussed in the literature. To address this issue, we propose two approaches including a closed test procedure that controls FWER for the simultaneous AUC and Cmax bioequivalence and requires no adjustment of the type‐I error, and an alpha‐adaptive sequential testing (AAST) that controls FWER by pre‐specifying the significance level on AUC (α₁) and obtaining it for Cmax (α₂) adaptively after testing of AUC. While both methods control FWER, the closed test requires testing of eight intersection null hypotheses each at α, and AAST is at times accomplished through a slight deduction in α₁ and no deduction in α₂ relative to α. The latter considers equivalence reached in AUC a higher importance than that in Cmax. Illustrated with published data, the two approaches, although operate differently, can lead to the same substantive conclusion and are better than a traditional method like Bonferroni adjustment. Copyright © 2014 John Wiley & Sons, Ltd.     

New joint covariance- and marginal-based tests for association and linkage for quantitative traits for random and non-random sampling

We develop novel statistical tests for transmission disequilibrium testing (tests of linkage in the presence of association) for quantitative traits using parents and offspring. These joint tests utilize information in both the covariance (or more generally, dependency) between genotype and phenotype and the marginal distribution of genotype. Using computer simulation we test the validity (Type I error rate control) and power of the proposed methods, for additive, dominant, and recessive modes of inheritance, locus-specific heritability of the trait 0.05, 0.1, 0.2 with allele frequencies of P=0.2 and 0.4, and sample sizes of 500, 200, and 100 trios. Both random sampling and extreme sampling schemes were investigated. A multinomial logistic joint test provides the highest overall power irrespective of sample size, allele frequency, heritability, and modes of inheritance.