ExactFDR: exact computation of false discovery rate estimate in case-control association studies

Genome-wide association studies require accurate and fast statistical methods to identify relevant signals from the background noise generated by a huge number of simultaneously tested hypotheses. It is now commonly accepted that exact computations of association probability value (P-value) are preferred to chi(2) and permutation-based approximations. Following the same principle, the ExactFDR software package improves speed and accuracy of the permutation-based false discovery rate (FDR) estimation method by replacing the permutation-based estimation of the null distribution by the generalization of the algorithm used for computing individual exact P-values. It provides a quick and accurate non-conservative estimator of the proportion of false positives in a given selection of markers, and is therefore an efficient and pragmatic tool for the analysis of genome-wide association studies.     

An unexpected influence of widely used significance thresholds on the distribution of reported P-values

We consider the problematic relationship between publication success and statistical significance in the light of analyses in which we examine the distribution of published probability (P) values across the statistical 'significance' range, below the 5% probability threshold. P-values are often judged according to whether they lie beneath traditionally accepted thresholds (< 0.05, < 0.01, < 0.001, < 0.0001); we examine how these thresholds influence the distribution of reported absolute P-values in published scientific papers, the majority in biological sciences. We collected published P-values from three leading journals, and summarized their distribution using the frequencies falling across and within these four threshold values between 0.05 and 0. These published frequencies were then fitted to three complementary null models which allowed us to predict the expected proportions of P-values in the top and bottom half of each inter-threshold interval (i.e. those lying below, as opposed to above, each P-value threshold). Statistical comparison of these predicted proportions, against those actually observed, provides the first empirical evidence for a remarkable excess of probability values being cited on, or just below, each threshold relative to the smoothed theoretical distributions. The pattern is consistent across thresholds and journals, and for whichever theoretical approach used to generate our expected proportions. We discuss this novel finding and its implications for solving the problems of publication bias and selective reporting in evolutionary biology.     

The Ranking Probability Approach and Its Usage in Design and Analysis of Large-Scale Studies

In experiments with many statistical tests there is need to balance type I and type II error rates while taking multiplicity into account. In the traditional approach, the nominal -level such as 0.05 is adjusted by the number of tests, , i.e., as 0.05/. Assuming that some proportion of tests represent “true signals”, that is, originate from a scenario where the null hypothesis is false, power depends on the number of true signals and the respective distribution of effect sizes. One way to define power is for it to be the probability of making at least one correct rejection at the assumed -level. We advocate an alternative way of establishing how “well-powered” a study is. In our approach, useful for studies with multiple tests, the ranking probability is controlled, defined as the probability of making at least correct rejections while rejecting hypotheses with smallest P-values. The two approaches are statistically related. Probability that the smallest P-value is a true signal (i.e., ) is equal to the power at the level , to an excellent approximation. Ranking probabilities are also related to the false discovery rate and to the Bayesian posterior probability of the null hypothesis. We study properties of our approach when the effect size distribution is replaced for convenience by a single “typical” value taken to be the mean of the underlying distribution. We conclude that its performance is often satisfactory under this simplification; however, substantial imprecision is to be expected when is very large and is small. Precision is largely restored when three values with the respective abundances are used instead of a single typical effect size value.     

Novel rank-based approaches for discovery and replication in genome-wide association studies

In recent years, genome-wide association studies (GWAS) have uncovered a large number of susceptibility variants. Nevertheless, GWAS findings provide only tentative evidence of association, and replication studies are required to establish their validity. Due to this uncertainty, researchers often focus on top-ranking SNPs, instead of considering strict significance thresholds to guide replication efforts. The number of SNPs for replication is often determined ad hoc. We show how the rank-based approach can be used for sample size allocation in GWAS as well as for deciding on a number of SNPs for replication. The basis of this approach is the "ranking probability": chances that at least j true associations will rank among top u SNPs, when SNPs are sorted by P-value. By employing simple but accurate approximations for ranking probabilities, we accommodate linkage disequilibrium (LD) and evaluate consequences of ignoring LD. Further, we relate ranking probabilities to the proportion of false discoveries among top u SNPs. A study-specific proportion can be estimated from P-values, and its expected value can be predicted for study design applications.     

A Bayesian measure of the probability of false discovery in genetic epidemiology studies

In light of the vast amounts of genomic data that are now being generated, we propose a new measure, the Bayesian false-discovery probability (BFDP), for assessing the noteworthiness of an observed association. BFDP shares the ease of calculation of the recently proposed false-positive report probability (FPRP) but uses more information, has a noteworthy threshold defined naturally in terms of the costs of false discovery and nondiscovery, and has a sound methodological foundation. In addition, in a multiple-testing situation, it is straightforward to estimate the expected numbers of false discoveries and false nondiscoveries. We provide an in-depth discussion of FPRP, including a comparison with the q value, and examine the empirical behavior of these measures, along with BFDP, via simulation. Finally, we use BFDP to assess the association between 131 single-nucleotide polymorphisms and lung cancer in a case-control study.     

复杂疾病全基因组关联研究进展——遗传统计分析

2005年, Science杂志首次报道了有关人类年龄相关性黄斑变性的全基因组关联研究, 此后有关肥胖、2型糖尿病、冠心病、阿尔茨海默病等一系列复杂疾病的全基因组关联研究被陆续报道, 这一阶段被称为人类全基因组关联研究的第一次浪潮。文章分别介绍了全基因组关联研究统计分析的方法、软件和应用实例; 比较了关联分析中多重检验的P值调整方法, 包括Bonferroni、递减的Bonferroni校正法、模拟运算法和控制错误发现率的方法; 还讨论了人群混杂对关联分析结果可能产生的影响及原理, 以及全基因组关联研究中控制人群混杂的方法的研究进展和应用实例。在全基因组关联研究的第一次浪潮中, 应用经典的遗传统计方法发现了许多基因-表型之间的关联并且能够对这些关联做出解释, 其中包括许多基因组中的未知基因和染色体区域。然而, 全基因组关联研究的继续发展需要进一步阐述基因组内基因之间相互作用、基因-基因之间的复杂作用网络与环境因素的相互作用在复杂疾病发生中的作用, 现有的统计分析方法肯定不能满足需要, 开发更为高级的统计分析方法势在必行。最后, 文章还给出了全基因组关联研究统计分析软件的相关网站信息。     

Accounting for Population Structure in Gene-by-Environment Interactions in Genome-Wide Association Studies Using Mixed Models

Although genome-wide association studies (GWASs) have discovered numerous novel genetic variants associated with many complex traits and diseases, those genetic variants typically explain only a small fraction of phenotypic variance. Factors that account for phenotypic variance include environmental factors and gene-by-environment interactions (GEIs). Recently, several studies have conducted genome-wide gene-by-environment association analyses and demonstrated important roles of GEIs in complex traits. One of the main challenges in these association studies is to control effects of population structure that may cause spurious associations. Many studies have analyzed how population structure influences statistics of genetic variants and developed several statistical approaches to correct for population structure. However, the impact of population structure on GEI statistics in GWASs has not been extensively studied and nor have there been methods designed to correct for population structure on GEI statistics. In this paper, we show both analytically and empirically that population structure may cause spurious GEIs and use both simulation and two GWAS datasets to support our finding. We propose a statistical approach based on mixed models to account for population structure on GEI statistics. We find that our approach effectively controls population structure on statistics for GEIs as well as for genetic variants.     

A general population-genetic model for the production by population structure of spurious genotype-phenotype associations in discrete, admixed or spatially distributed populations

In linkage disequilibrium mapping of genetic variants causally associated with phenotypes, spurious associations can potentially be generated by any of a variety of types of population structure. However, mathematical theory of the production of spurious associations has largely been restricted to population structure models that involve the sampling of individuals from a collection of discrete subpopulations. Here, we introduce a general model of spurious association in structured populations, appropriate whether the population structure involves discrete groups, admixture among such groups, or continuous variation across space. Under the assumptions of the model, we find that a single common principle--applicable to both the discrete and admixed settings as well as to spatial populations--gives a necessary and sufficient condition for the occurrence of spurious associations. Using a mathematical connection between the discrete and admixed cases, we show that in admixed populations, spurious associations are less severe than in corresponding mixtures of discrete subpopulations, especially when the variance of admixture across individuals is small. This observation, together with the results of simulations that examine the relative influences of various model parameters, has important implications for the design and analysis of genetic association studies in structured populations.     

Associations of functional candidate genes derived from gene-expression profiles of prenatal porcine muscle tissue with meat quality and muscle deposition

Ten genes (ANK1, bR10D1, CA3, EPOR, HMGA2, MYPN, NME1, PDGFRA, ERC1, TTN), whose candidacy for meat-quality and carcass traits arises from their differential expression in prenatal muscle development, were examined for association in 1700 performance-tested fattening pigs of commercial purebred and crossbred herds of Duroc, Pietrain, Pietrain x (Landrace x Large White), Duroc x (Landrace x Large White) as well as in an experimental F(2) population based on a reciprocal cross of Duroc and Pietrain. Comparative sequencing revealed polymorphic sites segregating across commercial breeds. Genetic mapping results corresponded to pre-existing assignments to porcine chromosomes or current human-porcine comparative maps. Nine of these genes showed association with meat-quality and carcass traits at a nominal P-value of < or = 0.05; PDGFRA revealed no association reaching the P < or = 0.05 threshold. In particular, HMGA2, CA3, EPOR, NME1 and TTN were associated with meat colour, pH and conductivity of loin 24 h postmortem; CA3 and MYPN exhibited association with ham weight and lean content (FOM) respectively at P-values of < 0.003 that correspond to false discovery rates of < 0.05. However, none of the genes showed significant associations for a particular trait across all populations. The study revealed statistical-genetic evidence for association of the functional candidate genes with traits related to meat quality and muscle deposition. The polymorphisms detected are not likely causal, but markers were identified that are in linkage disequilibrium with causal genetic variation within particular populations.     

Computing exact P-values for DNA motifs

MOTIVATION: Many heuristic algorithms have been designed to approximate P-values of DNA motifs described by position weight matrices, for evaluating their statistical significance. They often significantly deviate from the true P-value by orders of magnitude. Exact P-value computation is needed for ranking the motifs. Furthermore, surprisingly, the complexity of the problem is unknown. RESULTS: We show the problem to be NP-hard, and present MotifRank, software based on dynamic programming, to calculate exact P-values of motifs. We define the exact P-value on a general and more precise model. Asymptotically, MotifRank is faster than the best exact P-value computing algorithm, and is in fact practical. Our experiments clearly demonstrate that MotifRank significantly improves the accuracy of existing approximation algorithms. AVAILABILITY: MotifRank is available from http://bio.dlg.cn. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Type I error and the power of the s-test: old lessons from a new,analytically justified statistical test for phylogenies

We present a new procedure for assessing the statistical significance of the most likely unrooted dichotomous topology inferrable from four DNA sequences. The procedure calculates directly a P-value for the support given to this topology by the informative sites congruent with it, assuming the most likely star topology as the null hypothesis. Informative sites are crucial in the determination of the maximum likelihood dichotomous topology and are therefore an obvious target for a statistical test of phylogenies. Our P-value is the probability of producing through parallel substitutions on the branches of the star topology at least as much support as that given to the maximum likelihood dichotomous topology by the aforementioned informative sites, for any of the three possible dichotomous topologies. The degree of statistical significance is simply the complement of this P-value. Ours is therefore an a posteriori testing approach, in which no dichotomous topology is specified in advance. We implement the test for the case in which all sites behave identically and the substitution model has a single parameter. Under these conditions, the P-value can be easily calculated on the basis of the probabilities of change on the branches of the most likely star topology, because under these assumptions, each site can become informative independently from every other site; accordingly, the total number of informative sites of each kind is binomially distributed. We explore the test's type I error by applying it to data produced in star topologies having all branches equally long, or having two short and two long branches, and various degrees of homoplasy. The test is conservative but we demonstrate, by means of a discreteness correction and progressively assumption-free calculations of the P-values, that (1) the conservativeness is mostly due to the discrete nature of informative sites and (2) the P-values calculated empirically are moreover mostly quite accurate in absolute terms. Applying the test to data produced in dichotomous topologies with increasing internal branch length shows that, despite the test's "conservativeness," its power is much higher than that of the bootstrap, especially when the relevant informative sites are few.     

False discovery rate, sensitivity and sample size for microarray studies

MOTIVATION: In microarray data studies most researchers are keenly aware of the potentially high rate of false positives and the need to control it. One key statistical shift is the move away from the well-known P-value to false discovery rate (FDR). Less discussion perhaps has been spent on the sensitivity or the associated false negative rate (FNR). The purpose of this paper is to explain in simple ways why the shift from P-value to FDR for statistical assessment of microarray data is necessary, to elucidate the determining factors of FDR and, for a two-sample comparative study, to discuss its control via sample size at the design stage. RESULTS: We use a mixture model, involving differentially expressed (DE) and non-DE genes, that captures the most common problem of finding DE genes. Factors determining FDR are (1) the proportion of truly differentially expressed genes, (2) the distribution of the true differences, (3) measurement variability and (4) sample size. Many current small microarray studies are plagued with large FDR, but controlling FDR alone can lead to unacceptably large FNR. In evaluating a design of a microarray study, sensitivity or FNR curves should be computed routinely together with FDR curves. Under certain assumptions, the FDR and FNR curves coincide, thus simplifying the choice of sample size for controlling the FDR and FNR jointly.     

A new exact and more powerful unconditional test of no treatment effect from binary matched pairs

Summary .   We consider the problem of testing for a difference in the probability of success from matched binary pairs. Starting with three standard inexact tests, the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization, producing what I call an E+M P-value. The E+M P-value based on McNemar's statistic is shown numerically to dominate previous suggestions, including partially maximized P-values as described in Berger and Sidik (2003, Statistical Methods in Medical Research 12, 91–108). The latter method, however, may have computational advantages for large samples.     

Estimation and control of multiple testing error rates for microarray studies

The analysis of microarray data often involves performing a large number of statistical tests, usually at least one test per queried gene. Each test has a certain probability of reaching an incorrect inference; therefore, it is crucial to estimate or control error rates that measure the occurrence of erroneous conclusions in reporting and interpreting the results of a microarray study. In recent years, many innovative statistical methods have been developed to estimate or control various error rates for microarray studies. Researchers need guidance choosing the appropriate statistical methods for analysing these types of data sets. This review describes a family of methods that use a set of P-values to estimate or control the false discovery rate and similar error rates. Finally, these methods are classified in a manner that suggests the appropriate method for specific applications and diagnostic procedures that can identify problems in the analysis are described.     

CYP3A4-V and prostate cancer in African Americans: causal or confounding association because of population stratification?

CYP3A4-V, an A to G promoter variant associated with prostate cancer in African Americans, exhibits large differences in allele frequency between populations. Given that the African American population is genetically heterogeneous because of its African ancestry and subsequent admixture with European Americans, case-control studies with African Americans are highly susceptible to spurious associations. To test for association with prostate cancer, we genotyped CYP3A4-V in 1376 (2 N) chromosomes from prostate cancer patients and age- and ethnicity-matched controls representing African Americans, Nigerians, and European Americans. To detect population stratification among the African American samples, 10 unlinked genetic markers were genotyped. To correct for the stratification, the uncorrected association statistic was divided by the average of association statistics across the 10 unlinked markers. Sharp differences in CYP3A4-V frequencies were observed between Nigerian and European American controls (0.87 and 0.10, respectively; P<0.0001). African Americans were intermediate (0.66). An association uncorrected for stratification was observed between CYP3A4-V and prostate cancer in African Americans (P=0.007). A nominal association was also observed among European Americans (P=0.02) but not Nigerians. In addition, the unlinked genetic marker test provided strong evidence of population stratification among African Americans. Because of the high level of stratification, the corrected P-value was not significant (P=0.25). Follow-up studies on a larger dataset will be needed to confirm whether the association is indeed spurious; however, these results reveal the potential for confounding of association studies by using African Americans and the need for study designs that take into account substructure caused by differences in ancestral proportions between cases and controls.     

Integration of Mouse and Human Genome-Wide Association Data Identifies KCNIP4 as an Asthma Gene

Asthma is a common chronic respiratory disease characterized by airway hyperresponsiveness (AHR). The genetics of asthma have been widely studied in mouse and human, and homologous genomic regions have been associated with mouse AHR and human asthma-related phenotypes. Our goal was to identify asthma-related genes by integrating AHR associations in mouse with human genome-wide association study (GWAS) data. We used Efficient Mixed Model Association (EMMA) analysis to conduct a GWAS of baseline AHR measures from males and females of 31 mouse strains. Genes near or containing SNPs with EMMA p-values <0.001 were selected for further study in human GWAS. The results of the previously reported EVE consortium asthma GWAS meta-analysis consisting of 12,958 diverse North American subjects from 9 study centers were used to select a subset of homologous genes with evidence of association with asthma in humans. Following validation attempts in three human asthma GWAS (i.e., Sepracor/LOCCS/LODO/Illumina, GABRIEL, DAG) and two human AHR GWAS (i.e., SHARP, DAG), the Kv channel interacting protein 4 (KCNIP4) gene was identified as nominally associated with both asthma and AHR at a gene- and SNP-level. In EVE, the smallest KCNIP4 association was at rs6833065 (P-value 2.9e-04), while the strongest associations for Sepracor/LOCCS/LODO/Illumina, GABRIEL, DAG were 1.5e-03, 1.0e-03, 3.1e-03 at rs7664617, rs4697177, rs4696975, respectively. At a SNP level, the strongest association across all asthma GWAS was at rs4697177 (P-value 1.1e-04). The smallest P-values for association with AHR were 2.3e-03 at rs11947661 in SHARP and 2.1e-03 at rs402802 in DAG. Functional studies are required to validate the potential involvement of KCNIP4 in modulating asthma susceptibility and/or AHR. Our results suggest that a useful approach to identify genes associated with human asthma is to leverage mouse AHR association data.     

A genome-wide association study for quantitative trait loci of show-jumping in Hanoverian warmblood horses

Show-jumping is an economically important breeding goal in Hanoverian warmblood horses. The aim of this study was a genome-wide association study (GWAS) for quantitative trait loci (QTL) for show-jumping in Hanoverian warmblood horses, employing the Illumina equine SNP50 Beadchip. For our analyses, we genotyped 115 stallions of the National State stud of Lower Saxony. The show-jumping talent of a horse includes style and ability in free-jumping. To control spurious associations based on population stratification, two different mixed linear animal model (MLM) approaches were employed, besides linear models with fixed effects only and adaptive permutations for correcting multiple testing. Population stratification was explained best in the MLM considering Hanoverian, Thoroughbred, Trakehner and Holsteiner genes and the marker identity-by-state relationship matrix. We identified six QTL for show-jumping on horse chromosomes (ECA) 1, 8, 9 and 26 (-log(10) P-value >5) and further putative QTL with -log(10) P-values of 3-5 on ECA1, 3, 11, 17 and 21. Within six QTL regions, we identified human performance-related genes including PAPSS2 on ECA1, MYL2 on ECA8, TRHR on ECA9 and GABPA on ECA26 and within the putative QTL regions NRAP on ECA1, and TBX4 on ECA11. The results of our GWAS suggest that genes involved in muscle structure, development and metabolism are crucial for elite show-jumping performance. Further studies are required to validate these QTL in larger data sets and further horse populations.     

Batch effects in a multiyear sequencing study: False biological trends due to changes in read lengths

High‐throughput sequencing is a powerful tool, but suffers biases and errors that must be accounted for to prevent false biological conclusions. Such errors include batch effects; technical errors only present in subsets of data due to procedural changes within a study. If overlooked and multiple batches of data are combined, spurious biological signals can arise, particularly if batches of data are correlated with biological variables. Batch effects can be minimized through randomization of sample groups across batches. However, in long‐term or multiyear studies where data are added incrementally, full randomization is impossible, and batch effects may be a common feature. Here, we present a case study where false signals of selection were detected due to a batch effect in a multiyear study of Alpine ibex (Capra ibex). The batch effect arose because sequencing read length changed over the course of the project and populations were added incrementally to the study, resulting in nonrandom distributions of populations across read lengths. The differences in read length caused small misalignments in a subset of the data, leading to false variant alleles and thus false SNPs. Pronounced allele frequency differences between populations arose at these SNPs because of the correlation between read length and population. This created highly statistically significant, but biologically spurious, signals of selection and false associations between allele frequencies and the environment. We highlight the risk of batch effects and discuss strategies to reduce the impacts of batch effects in multiyear high‐throughput sequencing studies.