Joint tests for quantitative trait loci in experimental crosses

Selective genotyping is common because it can increase the expected correlation between QTL genotype and phenotype and thus increase the statistical power of linkage tests (i.e., regression-based tests). Linkage can also be tested by assessing whether the marginal genotypic distribution conforms to its expectation, a marginal-based test. We developed a class of joint tests that, by constraining intercepts in regression-based analyses, capitalize on the information available in both regression-based and marginal-based tests. We simulated data corresponding to the null hypothesis of no QTL effect and the alternative of some QTL effect at the locus for a backcross and an F2 intercross between inbred strains. Regression-based and marginal-based tests were compared to corresponding joint tests. We studied the effects of random sampling, selective sampling from a single tail of the phenotypic distribution, and selective sampling from both tails of the phenotypic distribution. Joint tests were nearly as powerful as all competing alternatives for random sampling and two-tailed selection under both backcross and F2 intercross situations. Joint tests were generally more powerful for one-tailed selection under both backcross and F2 intercross situations. However, joint tests cannot be recommended for one-tailed selective genotyping if segregation distortion is suspected.     

ArrayVigil: a methodology for statistical comparison of gene signatures using segregated-one-tailed (SOT) Wilcoxon's signed-rank test

Due to versatile diagnostic and prognostic fidelity molecular signatures or fingerprints are anticipated as the most powerful tools for cancer management in the near future. Notwithstanding the experimental advancements in microarray technology, methods for analyzing either whole arrays or gene signatures have not been firmly established. Recently, an algorithm, ArraySolver has been reported by Khan for two-group comparison of microarray gene expression data using two-tailed Wilcoxon signed-rank test. Most of the molecular signatures are composed of two sets of genes (hybrid signatures) wherein up-regulation of one set and down-regulation of the other set collectively define the purpose of a gene signature. Since the direction of a selected gene's expression (positive or negative) with respect to a particular disease condition is known, application of one-tailed statistics could be a more relevant choice. A novel method, ArrayVigil, is described for comparing hybrid signatures using segregated-one-tailed (SOT) Wilcoxon signed-rank test and the results compared with integrated-two-tailed (ITT) procedures (SPSS and ArraySolver). ArrayVigil resulted in lower P values than those obtained from ITT statistics while comparing real data from four signatures.     

Statistical Significance of Mutation Frequencies,and the Power of Statistical Testing,Using the Poisson Distribution

The Poisson distribution may be employed to test whether mutation frequencies differ from control frequencies. This paper describes how this testing procedure may be used for either one-tailed or two-tailed hypotheses. It is also shown how the power of the statistical test can be calculated, the power being the probability of correctly concluding the null hypothesis to be false.     

Assessing the relative contribution of functional divergence and guild aggregation to overall functional structure of species assemblages

The study of functional structure in species assemblages emphasizes the detection of significant guild aggregation patterns. Thus, protocols based on intensive resampling of empirical data have been proposed to assess guild structure. Such protocols obtain the frequency distribution of a given functional similarity metric, and identify a threshold value (often the 95th percentile) beyond which clusters in a functional dendrogram are considered as significant guilds (using one-tailed tests). An alternative approach sequentially searches for significant differences between clusters at decreasing levels of similarity in a dendrogram until one is detected, then assumes that all subsequent nodes should also be significant. Nevertheless, these protocols do not test both the significance and sign of deviations from random at all levels of functional similarity within a dendrogram. Here, we propose a new bootstrapping approach that: (1) overcomes such pitfalls by performing two-tailed tests for each node in a dendrogram of functional similarity after separately determining their respective sample distributions, and (2) enables the quantification of the relative contribution of guild aggregation and functional divergence to the overall functional structure of the entire assemblage. We exemplify this approach by using long-term data on guild dynamics in a vertebrate predator assemblage of central Chile. Finally, we illustrate how the interpretation of functional structure is improved by applying this new approach to the data set available.     

Polypeptide growth factors augment interleukin 1-induced release of prostaglandin E2 by rheumatoid arthritis synovial cells in vitro

When stimulated with increasing amounts of interleukin 1 beta (IL 1 beta) rheumatoid arthritis (RA), as compared with osteoarthritis (OA), synovial cells grown in RPMI plus fetal bovine serum (FBS), released significantly more prostaglandin E2 (PGE2) (p less than 0.05; paired t test, two-tailed). PGE2 release by IL 1 beta-stimulated RA synovial cells grown for 14 days in serum-free RPMI was significantly less than that released by the same cells grown in medium plus 10% FBS (p less than 0.03; two-tailed). Since these data suggest that growth factors present in FBS may augment the effects of IL 1 beta, experiments were conducted to study the influence of four polypeptide growth factors--transforming growth factor-beta (TGF-beta), platelet-derived growth factor (PDGF), epidermal growth factor (EGF), and basic fibroblast growth factor (bFGF), on IL 1 beta-induced release of PGE2 by cultured RA synovial cells. Both EGF and bFGF significantly enhanced IL 1 beta-induced release of PGE2 (p less than 0.05; paired t test, one-tailed), while PDGF was synergistic with IL 1 beta, significantly increasing release of PGE2 by these cultured cells (p less than 0.02; two-tailed). No such effect was seen when TGF-beta was added to the culture medium. Taken together, these data lend support to the concept that within the synovial micro-environment small quantities of individual growth factors may potentiate the effects of IL 1 beta to amplify intra-articular inflammation.     

REVERSIBILITY IN EVOLUTION: A MAXIMUM LIKELIHOOD APPROACH TO CHARACTER GAIN/LOSS BIAS IN PHYLOGENIES

Statistical methods are used to test the hypothesis that rate of gain is equal to rate of loss for a single character on a cladogram. Ancestral character states are used as input for maximum likelihood (ML) rate estimation. Two markovian models of character evolution are considered: one has equality of rate across branches; the other permits variation in rate according to predetermined weights for branches. ML estimates are derived for both models, and their properties in large and small trees are investigated. Bias and error are significant in small trees. Error is greatest for characters in which rate of gain is low, and is greater for the loss estimate than for the gain estimate. Likelihood ratio (LR) tests of the null hypothesis of equality of gain/loss rate are derived, and their properties investigated. The distribution of -2 log LR is close to χ² with 1 df with as few as 32 taxa. However, the power of the test is low unless the character is evolving rapidly. Methods for increasing power are examined, including selection of rapidly evolving subsets of characters, and pooling across characters. A goodness of fit test is presented to determine if pooling is justified. An example using published restriction site data on the Asteraceae demonstrates significant deviation from the null model in the direction predicted on the basis of the molecular biology of restriction enzyme site recognition, but only for one large subset of the data in which pooling is warranted.     

EDISON-WMW: Exact Dynamic Programing Solution of the Wilcoxon–Mann–Whitney Test

In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon–Mann–Whitney(WMW) test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calculate the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we presented different optimization strategies and developed a parallel solution. Using our program,the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molecular biomarkers for lung carcinoma and chronic obstructive pulmonary disease(COPD). We foundthat approximated P values were generally higher than the exact solution provided by EDISONWMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http://www.ccb.uni-saarland.de/software/wtest/.     

Abnormal clearance of postprandial Sf 100-400 plasma lipoproteins in insulin-dependent diabetes mellitus

Studies were carried out in three normolipidemic non-obese men with insulin-dependent diabetes mellitus (IDDM) and three normal men, to assess whether the clearance of postprandial Sf 100-400 lipoproteins is decreased in IDDM. Sf greater than 100 lipoproteins isolated from plasma 4.5 h after fat ingestion were labeled with 125I and injected into the same subject intravenously. ApoB radioactivity was measured over time in Sf greater than 400, Sf 100-400, and Sf 20-100 lipoproteins isolated from plasma and analyzed using a kinetic model that included both fast and slow delipidation cascades, where lipolysis and uptake of particles by the liver and other tissues were represented. Fractional catabolic rates of Sf 100-400 lipoproteins (min-1) were decreased in diabetic versus control subjects: fast = 0.170 +/- 0.126 versus 0.680 +/- 0.242 (mean +/- SD) (P less than 0.05, two-tailed) and slow = 0.011 +/- 0.006 versus 0.031 +/- 0.015 (P less than 0.05, one-tailed). Kinetic analysis showed that the data were consistent with decreased uptake by the tissues for the fast cascade (diabetic, 0.084 +/- 0.082, vs. control, 0.617 +/- 0.328, P less than 0.05, one-tailed). A similar trend was observed for the slow cascade. There were no significant differences between the two groups in the intraplasma lipolysis rates of Sf 100-400 particles. Analysis of the composition of the injected particles showed that they were total cholesterol (TC)- versus triglyceride (TG)-enriched (P less than 0.001, log-ratio analysis of composition) in IDDM subjects.(ABSTRACT TRUNCATED AT 250 WORDS)     

Optimal tests for rare variant effects in sequencing association studies

With development of massively parallel sequencing technologies, there is a substantial need for developing powerful rare variant association tests. Common approaches include burden and non-burden tests. Burden tests assume all rare variants in the target region have effects on the phenotype in the same direction and of similar magnitude. The recently proposed sequence kernel association test (SKAT) (Wu, M. C., and others, 2011. Rare-variant association testing for sequencing data with the SKAT. The American Journal of Human Genetics 89, 82-93], an extension of the C-alpha test (Neale, B. M., and others, 2011. Testing for an unusual distribution of rare variants. PLoS Genetics 7, 161-165], provides a robust test that is particularly powerful in the presence of protective and deleterious variants and null variants, but is less powerful than burden tests when a large number of variants in a region are causal and in the same direction. As the underlying biological mechanisms are unknown in practice and vary from one gene to another across the genome, it is of substantial practical interest to develop a test that is optimal for both scenarios. In this paper, we propose a class of tests that include burden tests and SKAT as special cases, and derive an optimal test within this class that maximizes power. We show that this optimal test outperforms burden tests and SKAT in a wide range of scenarios. The results are illustrated using simulation studies and triglyceride data from the Dallas Heart Study. In addition, we have derived sample size/power calculation formula for SKAT with a new family of kernels to facilitate designing new sequence association studies.     

Lung volume and spirometric standards for healthy female lifetime nonsmokers

The FRC, RV, VC, TLC, RV/TLC (%), FVC, FEV1.0, FEF25-75%, and FEV1.0/FVC (%) were measured in 161 South Australian females aged 18.4-81.2 yr using a Stead-Wells spirometer and helium analyzer. Multiple regression equations were generated to predict these lung volume and spirometric parameters from the best weighted combination of age, mass, standing height, and various other anthropometric variables (FRC: R = 0.715, SEE = 387 ml; RV: R = 0.684, SEE = 256 ml; VC: R = 0.815, SEE = 383 ml; TLC: R = 0.754, SEE = 468 ml; RV/TLC: R = 0.780, SEE = 4.2%; FVC: R = 0.839, SEE = 375 ml; FEV1.0: R = 0.869, SEE = 326 ml; FEV1.0/FVC: R = 0.644, SEE = 5.7%; FEF25-75%: R = 0.753, SEE = 802 ml/s). The range of normality for the lung volumes was defined as the predicted value plus or minus the 95% confidence interval (two-tailed test), and the lower limit of normality for the spirometric variables was designated as the predicted value minus the 95% confidence interval (one-tailed test). Cross-validation of other equations in the literature indicates that they are of limited use for the sample and instrumentation used in this study.     

Statistical Methods for Integrating Randomized Clinical Studies for Evaluation of Combination Treatment Therapy

In regulatory applications, evaluation of a combination drug at a fixed dose is based on pairwise comparisons of the combination with its component drugs. These comparisons generate the least expected gain of the combination relative to its components as the key effect parameter for evaluation. Two test methods are developed for the evaluation to combine multiple clinical studies that are deemed combinable. One test method is based on a linear combination of the Min tests from individual studies. In the other test method, weighted estimators are first derived for the pairwise comparisons between the combination and the respective components by combining the studies. A Min test is then applied to these estimators. The latter test method tends to be more powerful than the former test method. A test-based confidence interval is constructed for the least expected gain of the combination relative to its components. A test for heterogeneity across studies is also developed.     

Testing for a treatment effect in the presence of nonresponders

Good (1979, Biometrics 35, 483-489) introduced a new randomization test for the two-sample problem where a proportion 1 - p of the treatment group does not respond to the treatment, and suggested that the Wilcoxon test is not effective for this situation. We show to the contrary that the Wilcoxon test is quite useful when p greater than or equal to .6 and point out an error in his definition of a one-tailed randomization test.     

Are molecular haplotypes worth the time and expense? A cost-effective method for applying molecular haplotypes

Because current molecular haplotyping methods are expensive and not amenable to automation, many researchers rely on statistical methods to infer haplotype pairs from multilocus genotypes, and subsequently treat these inferred haplotype pairs as observations. These procedures are prone to haplotype misclassification. We examine the effect of these misclassification errors on the false-positive rate and power for two association tests. These tests include the standard likelihood ratio test (LRTstd) and a likelihood ratio test that employs a double-sampling approach to allow for the misclassification inherent in the haplotype inference procedure (LRTae). We aim to determine the cost-benefit relationship of increasing the proportion of individuals with molecular haplotype measurements in addition to genotypes to raise the power gain of the LRTae over the LRTstd. This analysis should provide a guideline for determining the minimum number of molecular haplotypes required for desired power. Our simulations under the null hypothesis of equal haplotype frequencies in cases and controls indicate that (1) for each statistic, permutation methods maintain the correct type I error; (2) specific multilocus genotypes that are misclassified as the incorrect haplotype pair are consistently misclassified throughout each entire dataset; and (3) our simulations under the alternative hypothesis showed a significant power gain for the LRTae over the LRTstd for a subset of the parameter settings. Permutation methods should be used exclusively to determine significance for each statistic. For fixed cost, the power gain of the LRTae over the LRTstd varied depending on the relative costs of genotyping, molecular haplotyping, and phenotyping. The LRTae showed the greatest benefit over the LRTstd when the cost of phenotyping was very high relative to the cost of genotyping. This situation is likely to occur in a replication study as opposed to a whole-genome association study.     

Bayesian sample size determination for prevalence and diagnostic test studies in the absence of a gold standard test

Planning studies involving diagnostic tests is complicated by the fact that virtually no test provides perfectly accurate results. The misclassification induced by imperfect sensitivities and specificities of diagnostic tests must be taken into account, whether the primary goal of the study is to estimate the prevalence of a disease in a population or to investigate the properties of a new diagnostic test. Previous work on sample size requirements for estimating the prevalence of disease in the case of a single imperfect test showed very large discrepancies in size when compared to methods that assume a perfect test. In this article we extend these methods to include two conditionally independent imperfect tests, and apply several different criteria for Bayesian sample size determination to the design of such studies. We consider both disease prevalence studies and studies designed to estimate the sensitivity and specificity of diagnostic tests. As the problem is typically nonidentifiable, we investigate the limits on the accuracy of parameter estimation as the sample size approaches infinity. Through two examples from infectious diseases, we illustrate the changes in sample sizes that arise when two tests are applied to individuals in a study rather than a single test. Although smaller sample sizes are often found in the two-test situation, they can still be prohibitively large unless accurate information is available about the sensitivities and specificities of the tests being used.     

Directional and anteroposterior asymmetry of common white markings in the legs of the Arabian horse: response to selection

Arabian bay horses manifest, on the average, more common white markings in their hind legs than their forelegs (anteroposterior asymmetry) and more common white markings in their left legs than their right legs (directional asymmetry). To determine if genetic variation exists for these types of asymmetry, the phenotypic response was studied in bay foals when their dams and sires were selected for the directions of fore-hind and left-right differences. In the fore-hind studies, the quantitative shifts in the bay foals were in the direction specified by the selection scheme and the observed deviations were all statistically significant. The shifts were also consistently in the direction favored by selection in the left-right studies, but only two of six observed deviations were statistically significant using a one-tailed test of significance. Thus, only marginal statistical evidence is available to support the observed consistent responses to selection in the left-right studies. These differential responses are reflected in the magnitudes of the heritability estimates. Based on the overall results, it is concluded that both types of asymmetry have a genetic basis in the Arabian horse, but much more genetic variation is present for anteroposterior asymmetry than for directional asymmetry. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Two-Tailed P-Value for Fisher's Exact Test

A two-tailed P-value is presented for a significance test in two by two contingency tables. There is no extraneous quasi-observation such as is needed in the exact randomized uniformly most powerful unbiased (UMPU) test of the hypothesis of independence. The proposed P-value can never exceed unity and is always two-tailed, unlike other P-values proposed in the literature     

Maximizing gain per effort by using clonal replicates in genetic tests

Summary Models for predicting cummulative genetic gain from recurrent selection applicable to predominantly outcrossing plant species are derived to include the effect of observations on clonal replicates (ramets) in addition to observations on individuals and family means. Such models are discussed with special reference to forest trees. The consequence of redistributing effort from individuals to ramets is investigated for several conditions with a fixed number of families and fixed total test size. Factors that affect the distribution of variance among sources and factors that affect individual selection intensity are the primary determinants of the optimum distribution of effort. The optimum number of ramets ranged from 1 to 6 for the conditions tested and the efficiency of redistribution (ratio of gain for the optimum distribution to the gain for the single-ramet, or non-clonal case) ranged from 1.00 to 1.20. Using clonal replicates in genetic tests usually results in increased cummulative genetic gain relative to non-clonal tests, without an increase in test effort.     

The evolution of spore size in Agarics: do big mushrooms have big spores?

As a first attempt to investigate evolutionary patterns of spore size in Agarics, I tested whether this trait was correlated to the size of the fruit-body (basidiocarp). Based on phylogenetically independent contrasts, it was shown that big mushroom species had on average 9% longer, 9% wider and 33% more voluminous spores (all with P < 0.05, one-tailed tests) than small congeneric species (a three-fold difference in cap diameter was used to discriminate big and small mushrooms). It is argued that larger spore size does not consistently confer higher fitness in fungi, owing to aerodynamic constraints. Surprisingly, the cap–spore correlation was strongly lineage-specific. Thus, spore volume correlated significantly with cap diameter in five of 16 large genera (four positive and one negative correlation). Positive cap–spore correlations are interpreted in terms of developmental constraints, mediated by hyphal swelling during cap expansion. The possible mechanisms which can account for the breakdown of this constraint in the majority of genera investigated are discussed.     

Optimal unified approach for rare-variant association testing with application to small-sample case-control whole-exome sequencing studies

We propose in this paper a unified approach for testing the association between rare variants and phenotypes in sequencing association studies. This approach maximizes power by adaptively using the data to optimally combine the burden test and the nonburden sequence kernel association test (SKAT). Burden tests are more powerful when most variants in a region are causal and the effects are in the same direction, whereas SKAT is more powerful when a large fraction of the variants in a region are noncausal or the effects of causal variants are in different directions. The proposed unified test maintains the power in both scenarios. We show that the unified test corresponds to the optimal test in an extended family of SKAT tests, which we refer to as SKAT-O. The second goal of this paper is to develop a small-sample adjustment procedure for the proposed methods for the correction of conservative type I error rates of SKAT family tests when the trait of interest is dichotomous and the sample size is small. Both small-sample-adjusted SKAT and the optimal unified test (SKAT-O) are computationally efficient and can easily be applied to genome-wide sequencing association studies. We evaluate the finite sample performance of the proposed methods using extensive simulation studies and illustrate their application using the acute-lung-injury exome-sequencing data of the National Heart, Lung, and Blood Institute Exome Sequencing Project.     

Assessing the goodness of fit of logistic regression models in large samples: A modification of the Hosmer-Lemeshow test

Evaluating the goodness of fit of logistic regression models is crucial to ensure the accuracy of the estimated probabilities. Unfortunately, such evaluation is problematic in large samples. Because the power of traditional goodness of fit tests increases with the sample size, practically irrelevant discrepancies between estimated and true probabilities are increasingly likely to cause the rejection of the hypothesis of perfect fit in larger and larger samples. This phenomenon has been widely documented for popular goodness of fit tests, such as the Hosmer-Lemeshow test. To address this limitation, we propose a modification of the Hosmer-Lemeshow approach. By standardizing the noncentrality parameter that characterizes the alternative distribution of the Hosmer-Lemeshow statistic, we introduce a parameter that measures the goodness of fit of a model but does not depend on the sample size. We provide the methodology to estimate this parameter and construct confidence intervals for it. Finally, we propose a formal statistical test to rigorously assess whether the fit of a model, albeit not perfect, is acceptable for practical purposes. The proposed method is compared in a simulation study with a competing modification of the Hosmer-Lemeshow test, based on repeated subsampling. We provide a step-by-step illustration of our method using a model for postneonatal mortality developed in a large cohort of more than 300 000 observations.