Testing for Hardy–Weinberg equilibrium in structured populations using genotype or low‐depth next generation sequencing data

Testing for deviations from Hardy–Weinberg equilibrium (HWE) is a common practice for quality control in genetic studies. Variable sites violating HWE may be identified as technical errors in the sequencing or genotyping process, or they may be of particular evolutionary interest. Large‐scale genetic studies based on next‐generation sequencing (NGS) methods have become more prevalent as cost is decreasing but these methods are still associated with statistical uncertainty. The large‐scale studies usually consist of samples from diverse ancestries that make the existence of some degree of population structure almost inevitable. Precautions are therefore needed when analysing these data set, as population structure causes deviations from HWE. Here we propose a method that takes population structure into account in the testing for HWE, such that other factors causing deviations from HWE can be detected. We show the effectiveness of PCAngsd in low‐depth NGS data, as well as in genotype data, for both simulated and real data set, where the use of genotype likelihoods enables us to model the uncertainty.     

hw‐quickcheck: an easy‐to‐use computer program for checking genotypes for agreement with Hardy–Weinberg expectations

Deviations from Hardy–Weinberg expectations are frequently a sign of genotyping error. hw‐quickcheck is an easy‐to‐use computer program for detecting departures from Hardy–Weinberg equilibrium. hw‐quickcheck uses exact tests for all of its calculations. These tests include a global test for heterozygote excess/deficiency and genotype‐specific tests.     

A Confidence‐Limit‐Based Approach to the Assessment of Hardy–Weinberg Equilibrium

The classical χ²‐procedure for the assessment of Hardy–Weinberg equilibrium (HWE) is tailored for detecting violations of HWE. However, many applications in genetic epidemiology require approximate compatibility with HWE. In a previous contribution to the field (Wellek, S. (2004). Biometrics, 60 , 694–703), the methodology of statistical equivalence testing was exploited for the construction of tests for problems in which the assumption of approximate compatibility of a given genotype distribution with HWE plays the role of the alternative hypothesis one aims to establish. In this article, we propose a procedure serving the same purpose but relying on confidence limits rather than critical bounds of a significance test. Interval estimation relates to essentially the same parametric function that was previously chosen as the target parameter for constructing an exact conditional UMPU test for equivalence with a HWE conforming genotype distribution. This population parameter is shown to have a direct genetic interpretation as a measure of relative excess heterozygosity. Confidence limits are constructed using both asymptotic and exact methods. The new approach is illustrated by reanalyzing genotype distributions obtained from published genetic association studies, and detailed guidance for choosing the equivalence margin is provided. The methods have been implemented in freely available SAS macros.     

Network algorithm for the Exact Test of Hardy‐Weinberg Proportion for Multiple Alleles

We propose a new technique for the exact test of Hardy‐Weinberg proportion that considerably extends the bounds of computational feasibility. Our algorithm is constructed analogously to the network algorithm for Freeman‐Halton exact test in two‐way contingency tables. In this algorithm, the smallest and the largest values for the statistic are important and some interesting new theorems are proved for computing these values. Numerical examples are given to illustrate the practicality of our algorithm.     

The organizational–activational hypothesis as the foundation for a unified theory of sexual differentiation of all mammalian tissues

The 1959 publication of the paper by Phoenix et al. was a major turning point in the study of sexual differentiation of the brain. That study showed that sex differences in behavior, and by extension in the brain, were permanently sexually differentiated by testosterone, a testicular secretion, during an early critical period of development. The study placed the brain together in a class with other major sexually dimorphic tissues (external genitalia and genital tracts), and proposed an integrated hormonal theory of sexual differentiation for all of these non-gonadal tissues. Since 1959, the organizational–activational theory has been amended but survives as a central concept that explains many sex differences in phenotype, in diverse tissues and at all levels of analysis from the molecular to the behavioral. In the last two decades, however, sex differences have been found that are not explained by such gonadal hormonal effects, but rather because of the primary action of genes encoded on the sex chromosomes. To integrate the classic organizational and activational effects with the more recently discovered sex chromosome effects, we propose a unified theory of sexual differentiation that applies to all mammalian tissues.     

Cross‐sectional human immunodeficiency virus incidence estimation accounting for heterogeneity across communities

Accurate estimation of human immunodeficiency virus (HIV) incidence rates is crucial for the monitoring of HIV epidemics, the evaluation of prevention programs, and the design of prevention studies. Traditional cohort approaches to measure HIV incidence require repeatedly testing large cohorts of HIV‐uninfected individuals with an HIV diagnostic test (eg, enzyme‐linked immunosorbent assay) for long periods of time to identify new infections, which can be prohibitively costly, time‐consuming, and subject to loss to follow‐up. Cross‐sectional approaches based on the usual HIV diagnostic test and biomarkers of recent infection offer important advantages over standard cohort approaches, in terms of time, cost, and attrition. Cross‐sectional samples usually consist of individuals from different communities. However, small sample sizes limit the ability to estimate community‐specific incidence and existing methods typically ignore heterogeneity in incidence across communities. We propose a permutation test for the null hypothesis of no heterogeneity in incidence rates across communities, develop a random‐effects model to account for this heterogeneity and to estimate community‐specific incidence, and provide one way to estimate the coefficient of variation. We evaluate the performance of the proposed methods through simulation studies and apply them to the data from the National Institute of Mental Health Project ACCEPT, a phase 3 randomized controlled HIV prevention trial in Sub‐Saharan Africa, to estimate the overall and community‐specific HIV incidence rates.     

Study on constant–step stress accelerated life tests in white organic light‐emitting diodes

In order to obtain reliability information for a white organic light‐emitting diode (OLED), two constant and one step stress tests were conducted with its working current increased. The Weibull function was applied to describe the OLED life distribution, and the maximum likelihood estimation (MLE) and its iterative flow chart were used to calculate shape and scale parameters. Furthermore, the accelerated life equation was determined using the least squares method, a Kolmogorov–Smirnov test was performed to assess if the white OLED life follows a Weibull distribution, and self‐developed software was used to predict the average and the median lifetimes of the OLED. The numerical results indicate that white OLED life conforms to a Weibull distribution, and that the accelerated life equation completely satisfies the inverse power law. The estimated life of a white OLED may provide significant guidelines for its manufacturers and customers. Copyright © 2014 John Wiley & Sons, Ltd.     

A universal and reliable assay for molecular sex identification of three‐spined sticklebacks (Gasterosteus aculeatus)

In heterogametic species, biological differences between the two sexes are ubiquitous, and hence, errors in sex identification can be a significant source of noise and bias in studies where sex‐related sources of variation are of interest or need to be controlled for. We developed and validated a universal multimarker assay for reliable sex identification of three‐spined sticklebacks (Gasterosteus aculeatus). The assay makes use of genotype scores from three sex‐linked loci and utilizes Bayesian probabilistic inference to identify sex of the genotyped individuals. The results, validated with 286 phenotypically sexed individuals from six populations of sticklebacks representing all major genetic lineages (cf. Pacific, Atlantic and Japan Sea), indicate that in contrast to commonly used single‐marker‐based sex identification assays, the developed multimarker assay should be 100% accurate. As the markers in the assay can be scored from agarose gels, it provides a quick and cost‐efficient tool for universal sex identification of three‐spined sticklebacks. The general principle of combining information from multiple markers to improve the reliability of sex identification is transferable and can be utilized to develop and validate similar assays for other species.     

Correction: Simultaneous confidence regions for closed tests,including Holm‐, Hochberg‐, and Hommel‐related procedures

Algorithm 1 in Guilbaud (2012, p. 327) in Biometrical Journal (DOI: 10.1002/bimj.201100123 ) reproduced a recently detected index error in a theorem concerning a shortcut for rejection decisions for certain multiple‐testing procedures as it was stated in Bernhard et al. (2004, p. 8) in Statistical Papers (DOI: 10.1007/BF02778266 ). This short article provides: (i) the correction to be made to Algorithm 1 and (ii) a brief discussion of the consequences. Although the theoretical developments in Guilbaud (2012) are not affected, the numerical illustrations in Section 7 are affected. A corrected version of that section is given in the Supporting Information.     

On Distance‐Based Permutation Tests for Between‐Group Comparisons

Summary Permutation tests based on distances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo‐F tests arising from a distance‐based extension of multivariate analysis of variance. In this article, we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data.     

Plug‐in tests for nonequivalence of means of independent normal populations

In this paper, we consider the problem of testing nonequivalence of several independent normal population means. It is a well‐known problem to test the equality of several means using the analysis of variance (ANOVA). Instead of determining the equality, one may consider more flexible homogeneity, which allows a predetermined level of difference. This problem is known as testing nonequivalence of populations. We propose the plug‐in statistics for two different measures of variability: the sum of the absolute deviations and the maximum of the absolute deviations. For each test, the least favorable configuration (LFC) to ensure the maximum rejection probability under the null hypothesis is investigated. Furthermore, we demonstrate the numerical studies based on both simulation and real data to evaluate the plug‐in tests and compare these with the range test.     

Power of the Wilcoxon–Mann–Whitney test for non‐inferiority in the presence of death‐censored observations

In clinical trials with patients in a critical state, death may preclude measurement of a quantitative endpoint of interest, and even early measurements, for example for intention‐to‐treat analysis, may not be available. For example, a non‐negligible proportion of patients with acute pulmonary embolism will die before 30 day measurements on the efficacy of thrombolysis can be obtained. As excluding such patients may introduce bias, alternative analyses, and corresponding means for sample size calculation are needed. We specifically consider power analysis in a randomized clinical trial setting in which the goal is to demonstrate noninferiority of a new treatment as compared to a reference treatment. Also, a nonparametric approach may be needed due to the distribution of the quantitative endpoint of interest. While some approaches have been developed in a composite endpoint setting, our focus is on the continuous endpoint affected by death‐related censoring, for which no approach for noninferiority is available. We propose a solution based on ranking the quantitative outcome and assigning worst rank scores to the patients without quantitative outcome because of death. Based on this, we derive power formulae for a noninferiority test in the presence of death‐censored observations, considering settings with and without ties. The approach is illustrated for an exemplary clinical trial in pulmonary embolism. The results there show a substantial effect of death on power, also depending on differential effects in the two trial arms. Therefore, use of the proposed formulae is advisable whenever there is death to be expected before measurement of a quantitative primary outcome of interest.     

Sizes of interface residues account for cross‐class binding affinity patterns in Eph receptor–ephrin families

Eph receptors comprise the largest known family of receptor tyrosine kinases in mammals. They bind members of a second family, the ephrins. As both Eph receptors and ephrins are membrane bound, interactions permit unusual bidirectional cell–cell signaling. Eph receptors and ephrins each form two classes, A and B, based on sequences, structures, and patterns of affinity: Class A Eph receptors bind class A ephrins, and class B Eph receptors bind class B ephrins. The only known exceptions are the receptor EphA4, which can bind ephrinB2 and ephrinB3 in addition to the ephrin‐As (Bowden et al., Structure 2009;17:1386–1397); and EphB2, which can bind ephrin‐A5 in addition to the ephrin‐Bs (Himanen et al., Nat Neurosci 2004;7:501–509). A crystal structure is available of the interacting domains of the EphA4‐ephrin B2 complex (wwPDB entry 2WO2) (Bowden et al., Structure 2009;17:1386–1397). In this complex, the ligand‐binding domain of EphA4 adopts an EphB‐like conformation. To understand why other cross‐class EphA receptor–ephrinB complexes do not form, we modeled hypothetical complexes between (1) EphA4–ephrinB1, (2) EphA4–ephrinB3, and (3) EphA2–ephrinB2. We identify particular residues in the interface region, the size variations of which cause steric clashes that prevent formation of the unobserved complexes. The sizes of the sidechains of residues at these positions correlate with the pattern of binding affinity. Proteins 2014; 82:349–353. © 2013 Wiley Periodicals, Inc.     

Order‐restricted Scores Test for the Evaluation of Population‐based Case–control Studies when the Genetic Model is Unknown

The Cochran–Armitage (CA) linear trend test for proportions is often used for genotype‐based analysis of candidate gene association. Depending on the underlying genetic mode of inheritance, the use of model‐specific scores maximises the power. Commonly, the underlying genetic model, i.e. additive, dominant or recessive mode of inheritance, is a priori unknown. Association studies are commonly analysed using permutation tests, where both inference and identification of the underlying mode of inheritance are important. Especially interesting are tests for case–control studies, defined by a maximum over a series of standardised CA tests, because such a procedure has power under all three genetic models. We reformulate the test problem and propose a conditional maximum test of scores‐specific linear‐by‐linear association tests. For maximum‐type, sum and quadratic test statistics the asymptotic expectation and covariance can be derived in a closed form and the limiting distribution is known. Both the limiting distribution and approximations of the exact conditional distribution can easily be computed using standard software packages. In addition to these technical advances, we extend the area of application to stratified designs, studies involving more than two groups and the simultaneous analysis of multiple loci by means of multiplicity‐adjusted p‐values for the underlying multiple CA trend tests. The new test is applied to reanalyse a study investigating genetic components of different subtypes of psoriasis. A new and flexible inference tool for association studies is available both theoretically as well as practically since already available software packages can be easily used to implement the suggested test procedures.