Assessing significance in high-throughput experiments by sequential goodness of fit and q-value estimation

We developed a new multiple hypothesis testing adjustment called SGoF+ implemented as a sequential goodness of fit metatest which is a modification of a previous algorithm, SGoF, taking advantage of the information of the distribution of p-values in order to fix the rejection region. The new method uses a discriminant rule based on the maximum distance between the uniform distribution of p-values and the observed one, to set the null for a binomial test. This new approach shows a better power/pFDR ratio than SGoF. In fact SGoF+ automatically sets the threshold leading to the maximum power and the minimum false non-discovery rate inside the SGoF' family of algorithms. Additionally, we suggest combining the information provided by SGoF+ with the estimate of the FDR that has been committed when rejecting a given set of nulls. We study different positive false discovery rate, pFDR, estimation methods to combine q-value estimates jointly with the information provided by the SGoF+ method. Simulations suggest that the combination of SGoF+ metatest with the q-value information is an interesting strategy to deal with multiple testing issues. These techniques are provided in the latest version of the SGoF+ software freely available at http://webs.uvigo.es/acraaj/SGoF.htm.     

A new multitest correction (SGoF) that increases its statistical power when increasing the number of tests

Background  

The detection of true significant cases under multiple testing is becoming a fundamental issue when analyzing high-dimensional biological data. Unfortunately, known multitest adjustments reduce their statistical power as the number of tests increase. We propose a new multitest adjustment, based on a sequential goodness of fit metatest (SGoF), which increases its statistical power with the number of tests. The method is compared with Bonferroni and FDR-based alternatives by simulating a multitest context via two different kinds of tests: 1) one-sample t-test, and 2) homogeneity G-test.     

Bias compensated least squares estimate of the center of rotation

It is shown that a recently published least squares method for the estimation of the average center of rotation is biased. Consequently, a correction term is proposed, and an iterative algorithm is derived for finding a bias compensated solution to the least squares problem.The accuracy of the proposed bias compensated least squares method is compared to the previously proposed least squares method by Monte-Carlo simulations. The tests show that the new method gives a substantial improvement in accuracy.     

A new approach to account for the correlations among single nucleotide polymorphisms in genome: wide association studies

In genetic association studies, such as genome-wide association studies (GWAS), the number of single nucleotide polymorphisms (SNPs) can be as large as hundreds of thousands. Due to linkage disequilibrium, many SNPs are highly correlated; assuming they are independent is not valid. The commonly used multiple comparison methods, such as Bonferroni correction, are not appropriate and are too conservative when applied to GWAS. To overcome these limitations, many approaches have been proposed to estimate the so-called effective number of independent tests to account for the correlations among SNPs. However, many current effective number estimation methods are based on eigenvalues of the correlation matrix. When the dimension of the matrix is large, the numeric results may be unreliable or even unobtainable. To circumvent this obstacle and provide better estimates, we propose a new effective number estimation approach which is not based on the eigenvalues. We compare the new method with others through simulated and real data. The comparison results show that the proposed method has very good performance.     

Improved classification of Alzheimer's disease data via removal of nuisance variability

Diagnosis of Alzheimer's disease is based on the results of neuropsychological tests and available supporting biomarkers such as the results of imaging studies. The results of the tests and the values of biomarkers are dependent on the nuisance features, such as age and gender. In order to improve diagnostic power, the effects of the nuisance features have to be removed from the data. In this paper, four types of interactions between classification features and nuisance features were identified. Three methods were tested to remove these interactions from the classification data. In stratified analysis, a homogeneous subgroup was generated from a training set. Data correction method utilized linear regression model to remove the effects of nuisance features from data. The third method was a combination of these two methods. The methods were tested using all the baseline data from the Alzheimer's Disease Neuroimaging Initiative database in two classification studies: classifying control subjects from Alzheimer's disease patients and discriminating stable and progressive mild cognitive impairment subjects. The results show that both stratified analysis and data correction are able to statistically significantly improve the classification accuracy of several neuropsychological tests and imaging biomarkers. The improvements were especially large for the classification of stable and progressive mild cognitive impairment subjects, where the best improvements observed were 6% units. The data correction method gave better results for imaging biomarkers, whereas stratified analysis worked well with the neuropsychological tests. In conclusion, the study shows that the excess variability caused by nuisance features should be removed from the data to improve the classification accuracy, and therefore, the reliability of diagnosis making.     

Analytical correction for multiple testing in admixture mapping

Admixture mapping, using unrelated individuals from the admixture populations that result from recent mating between members of each parental population, is an efficient approach to localize disease-causing variants that differ in frequency between two or more historically separated populations. Recently, several methods have been proposed to test linkage between a susceptibility gene and a disease locus by using admixture-generated linkage disequilibrium (LD) for each of the genotyped markers. In a genome scan, admixture mapping usually tests 2,000 to 3,000 markers across the genome. Currently, either a very conservative Sidak (or Bonferroni) correction or a very time consuming simulation-based method is used to correct for the multiple tests and evaluate the overall p value. In this report, we propose a computationally efficient analytical approach for correction of the multiple tests and for calculating the overall p value for an admixture genome scan. Except for the Sidak (or Bonferroni) correction, our proposed method is the first analytical approach for correction of the multiple tests and for calculating the overall p value for a genome scan. Our simulation studies show that the proposed method gives correct overall type I error rates for genome scans in all cases, and is much more computationally efficient than simulation-based methods.     

Beyond Bonferroni: less conservative analyses for conservation genetics

Studies in conservation genetics often attempt to determine genetic differentiation between two or more temporally or geographically distinct sample collections. Pairwise p-values from Fisher’s exact tests or contingency Chi-square tests are commonly reported with a Bonferroni correction for multiple tests. While the Bonferroni correction controls the experiment-wise α, this correction is very conservative and results in greatly diminished power to detect differentiation among pairs of sample collections. An alternative is to control the false discovery rate (FDR) that provides increased power, but this method only maintains experiment-wise α when none of the pairwise comparisons are significant. Recent modifications to the FDR method provide a moderate approach to determining significance level. Simulations reveal that critical values of multiple comparison tests with both the Bonferroni method and a modified FDR method approach a minimum asymptote very near zero as the number of tests gets large, but the Bonferroni method approaches zero much more rapidly than the modified FDR method. I compared pairwise significance from three published studies using three critical values corresponding to Bonferroni, FDR, and modified FDR methods. Results suggest that the modified FDR method may provide the most biologically important critical value for evaluating significance of population differentiation in conservation genetics.␣Ultimately, more thorough reporting of statistical significance is needed to allow interpretation of biological significance of genetic differentiation among populations.An erratum to this article can be found at     

Correcting for measurement error in individual ancestry estimates in structured association tests

We present theoretical explanations and show through simulation that the individual admixture proportion estimates obtained by using ancestry informative markers should be seen as an error-contaminated measurement of the underlying individual ancestry proportion. These estimates can be used in structured association tests as a control variable to limit type I error inflation or reduce loss of power due to population stratification observed in studies of admixed populations. However, the inclusion of such error-containing variables as covariates in regression models can bias parameter estimates and reduce ability to control for the confounding effect of admixture in genetic association tests. Measurement error correction methods offer a way to overcome this problem but require an a priori estimate of the measurement error variance. We show how an upper bound of this variance can be obtained, present four measurement error correction methods that are applicable to this problem, and conduct a simulation study to compare their utility in the case where the admixed population results from the intermating between two ancestral populations. Our results show that the quadratic measurement error correction (QMEC) method performs better than the other methods and maintains the type I error to its nominal level.     

Test a clade in phylogenetic trees

We develop a new method for testing a portion of a tree (called a clade) based on multiple tests of many 4-taxon trees in this paper. This is particularly useful when the phylogenetic tree constructed by other methods have a clade that is difficult to explain from a biological point of view. The statement about the test of the clade can be made through the multiple P values from these individual tests. By controlling the familywise error rate or the false discovery rate (FDR), 4 different tree test methods are evaluated through simulation methods. It shows that the combination of the approximately unbiased (AU) test and the FDR-controlling procedure provides strong power along with reasonable type I error rate and less heavy computation.     

Correcting for toxic inhibition in quantification of genotoxic response in the umuC test.

An improved procedure for quantification of results from the umuC tests for genotoxicity is presented. The calculation method better separates toxic growth inhibition (cytotoxicity) from genotoxic effects than currently used methods and therefore, greatly extends the applicability of genotoxicity tests on environmental samples. The basic principle is to normalize the genotoxic response compensating for both decreasing biomass and growth rate reduction that results from cytotoxicity. The improved method and the currently used method was compared for umuC tests on the pure compounds: methylmethanesulfonate (MMS), N-methyl-N'-nitro-N-nitroguanidine (MNNG), sodium azide (NaN3), and 4-nitroquinoline-1-oxide (4-NQO). For compounds with no or low cytotoxicity, the two calculation methods gave practically identical results, while for highly cytotoxic compounds, the traditional method overestimated genotoxicity. umuC tests were also carried out on leachate polluted groundwater sampled downgradient of a landfill (Grindsted, Denmark). All polluted samples showed high cytotoxicity concomitant with high genotoxicity when the results were quantified in the traditional way. The new method showed that these results were in fact false positive, as the apparent genotoxicity was a result of cytotoxicity. Based on the mathematical analysis leading to the improved procedure for correction for cytotoxicity, it is suggested to alter the present test design of the umuC test in order to obtain well-defined exposure concentrations as well as mathematical consistency in the quantification of genotoxicity.     

Rapid simulation of P values for product methods and multiple-testing adjustment in association studies

A major aim of association studies is the identification of polymorphisms (usually SNPs) associated with a trait. Tests of association may be based on individual SNPs or on sets of neighboring SNPs, by use of (for example) a product P value method or Hotelling's T test. Linkage disequilibrium, the nonindependence of SNPs in physical proximity, causes problems for all these tests. First, multiple-testing correction for individual-SNP tests or for multilocus tests either leads to conservative P values (if Bonferroni correction is used) or is computationally expensive (if permutation is used). Second, calculation of product P values usually requires permutation. Here, we present the direct simulation approach (DSA), a method that accurately approximates P values obtained by permutation but is much faster. It may be used whenever tests are based on score statistics--for example, with Armitage's trend test or its multivariate analogue. The DSA can be used with binary, continuous, or count traits and allows adjustment for covariates. We demonstrate the accuracy of the DSA on real and simulated data and illustrate how it might be used in the analysis of a whole-genome association study.     

Algorithmic Optimisation Method for Improving Use Case Points Estimation

This paper presents a new size estimation method that can be used to estimate size level for software engineering projects. The Algorithmic Optimisation Method is based on Use Case Points and on Multiple Least Square Regression. The method is derived into three phases. The first phase deals with calculation Use Case Points and correction coefficients values. Correction coefficients are obtained by using Multiple Least Square Regression. New project is estimated in the second and third phase. In the second phase Use Case Points parameters for new estimation are set up and in the third phase project estimation is performed. Final estimation is obtained by using newly developed estimation equation, which used two correction coefficients. The Algorithmic Optimisation Method performs approximately 43% better than the Use Case Points method, based on their magnitude of relative error score. All results were evaluated by standard approach: visual inspection, goodness of fit measure and statistical significance.     

Comparison of type I error for multiple test corrections in large single-nucleotide polymorphism studies using principal components versus haplotype blocking algorithms

Although permutation testing has been the gold standard for assessing significance levels in studies using multiple markers, it is time-consuming. A Bonferroni correction to the nominal p-value that uses the underlying pair-wise linkage disequilibrium (LD) structure among the markers to determine the number of effectively independent tests has recently been proposed. We propose using the number of independent LD blocks plus the number of independent single-nucleotide polymorphisms for correction. Using the Collaborative Study on the Genetics of Alcoholism LD data for chromosome 21, we simulated 1,000 replicates of parent-child trio data under the null hypothesis with two levels of LD: moderate and high. Assuming haplotype blocks were independent, we calculated the number of independent statistical tests using 3 haplotype blocking algorithms. We then compared the type I error rates using a principal components-based method, the three blocking methods, a traditional Bonferroni correction, and the unadjusted p-values obtained from FBAT. Under high LD conditions, the PC method and one of the blocking methods were slightly conservative, whereas the 2 other blocking methods exceeded the target type I error rate. Under conditions of moderate LD, we show that the blocking algorithm corrections are closest to the desired type I error, although still slightly conservative, with the principal components-based method being almost as conservative as the traditional Bonferroni correction.     

北京市土地利用生态分类方法

本文从国内外土地利用分类体系的现状分析入手,分析了当前土地利用分类体系与生态保护存在的矛盾,提出进行土地利用生态分类。首先,将北京市的土地利用现状类型分析归并为9个一级类15个二级类,确定各土地利用类型基准生态服务价值,然后提出各土地利用类型生态系统服务价值的区位修正方法,在对各种土地利用类型生态系统服务价值进行区位修正的基础上,划分出6个一级生态用地类型。其次,对北京市进行生态适宜性评价,生成生态适宜性分布图,将已生成的土地利用生态一级分类图与生态适宜性分布图进行叠加,对一级生态用地类型进行了二级划分,得到6个大类、18个亚类的北京市土地利用生态用地类型。最后,以北京市2007年的土地利用现状图为例,对北京市的土地利用生态分类方法进行应用,得到了2007年北京市土地利用生态分类图并分析了各土地利用生态用地类型的分布状况。     

Comparing the performances of Diggle's tests of spatial randomness for small samples with and without edge-effect correction: application to ecological data

Diggle's tests of spatial randomness based on empirical distributions of interpoint distances can be performed with and without edge-effect correction. We present here numerical results illustrating that tests without the edge-effect correction proposed by Diggle (1979, Biometrics 35, 87-101) have a higher power for small sample sizes than those with correction. Ignoring the correction enables detection of departure from spatial randomness with smaller samples (down to 10 points vs. 30 points for the tests with correction). These results are confirmed by an example with ecological data consisting of maps of two species of trees in a West African savanna. Tree numbers per species per map were often less than 20. For one of the species, for which maps strongly suggest an aggregated pattern, tests without edge-effect correction enabled rejection of the null hypothesis on three plots out of five vs. on only one for the tests with correction.     

Bootstrap method of interior-branch test for phylogenetic trees

Statistical properties of the bootstrap test of interior branch lengths of phylogenetic trees have been studied and compared with those of the standard interior-branch test in computer simulations. Examination of the properties of the tests under the null hypothesis showed that both tests for an interior branch of a predetermined topology are quite reliable when the distribution of the branch length estimate approaches a normal distribution. Unlike the standard interior-branch test, the bootstrap test appears to retain this property even when the substitution rate varies among sites. In this case, the distribution of the branch length estimate deviates from a normal distribution, and the standard interior-branch test gives conservative confidence probability values. A simple correction method was developed for both interior- branch tests to be applied for testing the reliability of tree topologies estimated from sequence data. This correction for the standard interior-branch test appears to be as effective as that obtained in our previous study, though it is much simpler. The bootstrap and standard interior-branch tests for estimated topologies become conservative as the number of sequence groups in a star-like tree increases.      

Haplotype reconstruction from SNP fragments by minimum error correction

MOTIVATION: Haplotype reconstruction based on aligned single nucleotide polymorphism (SNP) fragments is to infer a pair of haplotypes from localized polymorphism data gathered through short genome fragment assembly. An important computational model of this problem is the minimum error correction (MEC) model, which has been mentioned in several literatures. The model retrieves a pair of haplotypes by correcting minimum number of SNPs in given genome fragments coming from an individual's DNA. RESULTS: In the first part of this paper, an exact algorithm for the MEC model is presented. Owing to the NP-hardness of the MEC model, we also design a genetic algorithm (GA). The designed GA is intended to solve large size problems and has very good performance. The strength and weakness of the MEC model are shown using experimental results on real data and simulation data. In the second part of this paper, to improve the MEC model for haplotype reconstruction, a new computational model is proposed, which simultaneously employs genotype information of an individual in the process of SNP correction, and is called MEC with genotype information (shortly, MEC/GI). Computational results on extensive datasets show that the new model has much higher accuracy in haplotype reconstruction than the pure MEC model.     

Aberration-corrected ultrafine analysis of miRNA reads at single-base resolution: a k-mer lattice approach

Raw sequencing reads of miRNAs contain machine-made substitution errors, or even insertions and deletions (indels). Although the error rate can be low at 0.1%, precise rectification of these errors is critically important because isoform variation analysis at single-base resolution such as novel isomiR discovery, editing events understanding, differential expression analysis, or tissue-specific isoform identification is very sensitive to base positions and copy counts of the reads. Existing error correction methods do not work for miRNA sequencing data attributed to miRNAs’ length and per-read-coverage properties distinct from DNA or mRNA sequencing reads. We present a novel lattice structure combining kmers, (k – 1)mers and (k + 1)mers to address this problem. The method is particularly effective for the correction of indel errors. Extensive tests on datasets having known ground truth of errors demonstrate that the method is able to remove almost all of the errors, without introducing any new error, to improve the data quality from every-50-reads containing one error to every-1300-reads containing one error. Studies on experimental miRNA sequencing datasets show that the errors are often rectified at the 5′ ends and the seed regions of the reads, and that there are remarkable changes after the correction in miRNA isoform abundance, volume of singleton reads, overall entropy, isomiR families, tissue-specific miRNAs, and rare-miRNA quantities.     

A simple method for in vivo measurement of implant rod three-dimensional geometry during scoliosis surgery

Scoliosis is defined as a spinal pathology characterized as a three-dimensional deformity of the spine combined with vertebral rotation. Treatment for severe scoliosis is achieved when the scoliotic spine is surgically corrected and fixed using implanted rods and screws. Several studies performed biomechanical modeling and corrective forces measurements of scoliosis correction. These studies were able to predict the clinical outcome and measured the corrective forces acting on screws, however, they were not able to measure the intraoperative three-dimensional geometry of the spinal rod. In effect, the results of biomechanical modeling might not be so realistic and the corrective forces during the surgical correction procedure were intra-operatively difficult to measure. Projective geometry has been shown to be successful in the reconstruction of a three-dimensional structure using a series of images obtained from different views. In this study, we propose a new method to measure the three-dimensional geometry of an implant rod using two cameras. The reconstruction method requires only a few parameters, the included angle θ between the two cameras, the actual length of the rod in mm, and the location of points for curve fitting. The implant rod utilized in spine surgery was used to evaluate the accuracy of the current method. The three-dimensional geometry of the rod was measured from the image obtained by a scanner and compared to the proposed method using two cameras. The mean error in the reconstruction measurements ranged from 0.32 to 0.45 mm. The method presented here demonstrated the possibility of intra-operatively measuring the three-dimensional geometry of spinal rod. The proposed method could be used in surgical procedures to better understand the biomechanics of scoliosis correction through real-time measurement of three-dimensional implant rod geometry in vivo.