An alternative foundation for the planning and evaluation of linkage analysis. II. Implications for multiple test adjustments

The 'multiple testing problem' currently bedevils the field of genetic epidemiology. Briefly stated, this problem arises with the performance of more than one statistical test and results in an increased probability of committing at least one Type I error. The accepted/conventional way of dealing with this problem is based on the classical Neyman-Pearson statistical paradigm and involves adjusting one's error probabilities. This adjustment is, however, problematic because in the process of doing that, one is also adjusting one's measure of evidence. Investigators have actually become wary of looking at their data, for fear of having to adjust the strength of the evidence they observed at a given locus on the genome every time they conduct an additional test. In a companion paper in this issue (Strug & Hodge I), we presented an alternative statistical paradigm, the 'evidential paradigm', to be used when planning and evaluating linkage studies. The evidential paradigm uses the lod score as the measure of evidence (as opposed to a p value), and provides new, alternatively defined error probabilities (alternative to Type I and Type II error rates). We showed how this paradigm separates or decouples the two concepts of error probabilities and strength of the evidence. In the current paper we apply the evidential paradigm to the multiple testing problem - specifically, multiple testing in the context of linkage analysis. We advocate using the lod score as the sole measure of the strength of evidence; we then derive the corresponding probabilities of being misled by the data under different multiple testing scenarios. We distinguish two situations: performing multiple tests of a single hypothesis, vs. performing a single test of multiple hypotheses. For the first situation the probability of being misled remains small regardless of the number of times one tests the single hypothesis, as we show. For the second situation, we provide a rigorous argument outlining how replication samples themselves (analyzed in conjunction with the original sample) constitute appropriate adjustments for conducting multiple hypothesis tests on a data set.     

Is it legitimate to characterize muscle strength using a limited number of measures?

The purpose of this systematic review was to examine the legitimacy of using a single measure or a small set of measures of strength to characterize an individual's overall strength. Briefly, the methods involved: (a) a search of electronic databases, article reference lists, and personal files to identify relevant literature; and (b) a summarizing of that literature. As a result of the searches, 25 relevant articles were identified. The articles reported correlation coefficients, Cronbach's alpha, and factor analysis. Together, these statistics suggest a tendency for different strength measures to be related. A close examination of the relationships, however, suggests that caution should be exercised in characterizing overall strength using a single measure such as grip strength. In conclusion, it may be legitimate to use one or several measures obtained from a single limb to characterize the strength of that limb but not the entire body. What this means practically is that the practitioner interested in characterizing strength of a limb can reduce test burden by testing a limited number of muscle actions of that limb.     

Combining dependent tests for linkage or association across multiple phenotypic traits

A robust statistical method to detect linkage or association between a genetic marker and a set of distinct phenotypic traits is to combine univariate trait-specific test statistics for a more powerful overall test. This procedure does not need complex modeling assumptions, can easily handle the problem with partially missing trait values, and is applicable to the case with a mixture of qualitative and quantitative traits. In this note, we propose a simple test procedure along this line, and show its advantages over the standard combination tests for linkage or association in the literature through a data set from Genetic Analysis Workshop 12 (GAW12) and an extensive simulation study.     

A simple measure of the coding efficiency of a neuronal population

We derive a simple measure for quantifying the average accuracy with which a neuronal population can represent a stimulus. This quantity, the basis set error, has three key properties: (1) it makes no assumptions about the form of the neuronal responses; (2) it depends only on their second order statistics, so although it is easy to compute, it does take noise correlations into account; (3) its magnitude has an intuitive interpretation in terms of the accuracy with which information can be extracted from the population using a simple method-"simple" meaning linear. We use the basis set error to characterize the efficacy of several types of population codes generated synthetically in a computer. In general, the basis set error typically ranks different encoding schemes in a way that is qualitatively similar to Shannon's mutual information, except when nonlinear readout methods are necessary. Because this measure is concerned with signals that can be read out easily (i.e., through linear operations), it provides a lower bound on coding accuracy relative to the computational capabilities that are accessible to a neuronal population.     

Simple cultural test for relative cellulolytic activity of fungi

A simple method is described for determining the relative cellulolytic activity of fungi. Opaque columns of an agar medium containing a partially crystalline cellulose preparation were inoculated with the fungi. Depth of the clear zone that developed beneath the growing cultures provided a visual measure of cellulolytic activity on a continuous, cumulative basis. Depth of clearing (DC) was determined for 25 species of fungi differing widely in cellulolytic activity, and compared by correlation analysis with results of three other methods for measuring cellulolytic activity. Relatively high coefficients of correlation (greater than 0.6) were obtained between DC and weight loss of cotton sliver, loss in tensile strength of cotton duck, and carboxymethyl cellulase activity in culture filtrates. In comparison with conventional assay procedures, the clearing method offered several advantages: (i) results were at least as well correlated with the capacity to utilize native cellulose as a substrate; (ii) the method measured activity of growing cultures rather than culture filtrates, thus involving less risk of losses due to product inhibition, binding, or denaturation of enzymes; (iii) repeated measurements were made on the same experimental set up, so that errors due to arbitrarily selected times of harvest were avoided conveniently; and (iv) the method required less working time and very simple equipment, making it convenient for large-scale screening tests.     

Novel metrics for evaluating the functional coherence of protein groups via protein semantic network

We present the metrics for assessing overall functional coherence of a group of proteins based on associated biomedical literature. A probabilistic topic model is applied to extract biologic concepts from a corpus of protein-related biomedical literature. Bipartite protein semantic networks are constructed, so that the functional coherence of a protein group can be evaluated with metrics that measure the closeness and strength of connectivity of the proteins in the network.     

The D' measure of overall gametic disequilibrium between pairs of multiallelic loci

Abstract The D ' coefficient is one of the most commonly used measures of the extent of gametic disequilibrium between multiallelic loci. It has been suggested that the range of the D ' measure of overall disequilibrium between pairs of multiallelic loci depends on allele frequencies, except under some very restricted conditions. Nevertheless, the problem of dependence of the range of D ' has not been characterized under a wide set of possible polymorphisms. Evaluation of the utility of D ' as a measure of the strength of overall disequilibrium between all possible pairs of alleles at two multiallelic loci requires better knowledge of its range than is currently available. In this work, the conditions of polymorphism under which the range of D ' is frequency independent are given. It is found that the range of D ' is more often independent of allelic frequencies than is commonly thought. Furthermore, the range of D ' undergoes only small fluctuations as a function of the polymorphisms at the loci. Numerical cases and microsatellite data from humans are used for illustration. These observations indicate that the D ' coefficient is a useful tool for the estimation and comparison of the extent of overall disequilibrium across pairs of multiallelic loci.     

Measuring intrarater association between correlated ordinal ratings

Variability between raters' ordinal scores is commonly observed in imaging tests, leading to uncertainty in the diagnostic process. In breast cancer screening, a radiologist visually interprets mammograms and MRIs, while skin diseases, Alzheimer's disease, and psychiatric conditions are graded based on clinical judgment. Consequently, studies are often conducted in clinical settings to investigate whether a new training tool can improve the interpretive performance of raters. In such studies, a large group of experts each classify a set of patients' test results on two separate occasions, before and after some form of training with the goal of assessing the impact of training on experts' paired ratings. However, due to the correlated nature of the ordinal ratings, few statistical approaches are available to measure association between raters' paired scores. Existing measures are restricted to assessing association at just one time point for a single screening test. We propose here a novel paired kappa to provide a summary measure of association between many raters' paired ordinal assessments of patients' test results before versus after rater training. Intrarater association also provides valuable insight into the consistency of ratings when raters view a patient's test results on two occasions with no intervention undertaken between viewings. In contrast to existing correlated measures, the proposed kappa is a measure that provides an overall evaluation of the association among multiple raters' scores from two time points and is robust to the underlying disease prevalence. We implement our proposed approach in two recent breast-imaging studies and conduct extensive simulation studies to evaluate properties and performance of our summary measure of association.     

Novel antibody-based strategies for the rapid diagnosis of mitochondrial disease and dysfunction

We are developing rapid immunoassays to measure the protein levels, enzymatic activities and post-translational modifications of mitochondrial proteins. These assays can be arrayed in multi-analyte panels for biomarker discovery and they can also be used individually at point of care where the level or activity of a small number proteins or even a single protein is highly informative. For example, we have characterized OXPHOS deficits associated with lipoatrophy, an adverse metabolic side-effect of anti-retroviral therapy, and have shown that OXPHOS deficits observed in vitro are also exhibited not only in clinically affected tissue (peripheral fat) but also in more easily accessible tissue (peripheral blood mononucleated cells). Similarly, we have shown that a small set of assays can be used to identify almost all patients with genetic deficits in OXPHOS complexes I or IV, the most common cause of inherited mitochondrial disease. Finally, we recently reported that Friedreich's Ataxia (FA) patients and carriers can be identified on the basis of a simple dipstick test to measure levels of a single protein, frataxin, an iron regulatory protein whose disrupted expression is the proximal cause of neurodegeneration in FA. Because each of these tests can be performed in an extremely simple, rapid dipstick format using non-invasive samples such as cheek swabs and fingerprick blood, they have potential for use as point of care diagnostics for mitochondrial disease and as front-line screening tools to help guide drug therapies and minimize adverse off-target drug effects.     

The ratio and allometric scaling of speed, power, and strength in elite male rugby union players

This study compared the effectiveness of ratio and allometric scaling for normalizing speed, power, and strength in elite male rugby union players. Thirty rugby players (body mass [BM] 107.1 ± 10.1 kg, body height [BH] 187.8 ± 7.1 cm) were assessed for sprinting speed, peak power during countermovement jumps and squat jumps, and horizontal jumping distance. One-repetition maximum strength was assessed during a bench press, chin-up, and back squat. Performance was normalized using ratio and allometric scaling (Y/X), where Y is the performance, X, the body size variable (i.e., BM or BH), and b is the power exponent. An exponent of 1.0 was used during ratio scaling. Allometric scaling was applied using proposed exponents and derived exponents for each data set. The BM and BH variables were significantly related, or close to, performance during the speed, power and/or strength tests (p < 0.001-0.066). Ratio scaling and allometric scaling using proposed exponents were effective in normalizing performance (i.e., no significant correlations) for some of these tests. Allometric scaling with derived exponents normalized performance across all the tests undertaken, thereby removing the confounding effects of BM and BH. In terms of practical applications, allometric scaling with derived exponents may be used to normalize performance between larger rugby forwards and smaller rugby backs, and could provide additional information on rugby players of similar body size. Ratio scaling may provide the best predictive measure of performance (i.e., strongest correlations).     

Estimates of the average strength of natural selection are not inflated by sampling error or publication bias

Kingsolver et al.'s review of phenotypic selection gradients from natural populations provided a glimpse of the form and strength of selection in nature and how selection on different organisms and traits varies. Because this review's underlying database could be a key tool for answering fundamental questions concerning natural selection, it has spawned discussion of potential biases inherent in the review process. Here, we explicitly test for two commonly discussed sources of bias: sampling error and publication bias. We model the relationship between variance among selection gradients and sample size that sampling error produces by subsampling large empirical data sets containing measurements of traits and fitness. We find that this relationship was not mimicked by the review data set and therefore conclude that sampling error does not bias estimations of the average strength of selection. Using graphical tests, we find evidence for bias against publishing weak estimates of selection only among very small studies (N<38). However, this evidence is counteracted by excess weak estimates in larger studies. Thus, estimates of average strength of selection from the review are less biased than is often assumed. Devising and conducting straightforward tests for different biases allows concern to be focused on the most troublesome factors.     

Intrinsic versus extrinsic influences in the development of neuronal maps

Accumulating evidence suggests that the plasticity of extrinsic thalamocortical inputs in cortical layer IV may be guided or instructed by earlier plasticity events in the intrinsic, horizontal connections within the extragranular cortical layers. We analyse a rate-based model of the plasticity of a set of extrinsic afferents in the presence of a pre-existing (and fixed) plexus of intrinsic, overall excitatory horizontal connections between a set of target neurons. We determine conditions under which afferent synaptic pattern formation respects this pre-existing lateral structure. We find three broad regimes under which extrinsic afferent plasticity may violate this structure: the initial pattern of extrinsic afferent innervation of the target cells is far from balanced; the gain of the extrinsic afferents greatly exceeds the overall scale of the strength of lateral excitation; the target cell horizontal coupling matrix is sparse. If none of these conditions is satisfied, then extrinsic afferent plasticity respects the pre-existing lateral connectivity, so that afferent synaptic pattern formation conforms to the pattern of lateral excitation.     

Identifying genetic marker sets associated with phenotypes via an efficient adaptive score test

In recent years, genome-wide association studies (GWAS) and gene-expression profiling have generated a large number of valuable datasets for assessing how genetic variations are related to disease outcomes. With such datasets, it is often of interest to assess the overall effect of a set of genetic markers, assembled based on biological knowledge. Genetic marker-set analyses have been advocated as more reliable and powerful approaches compared with the traditional marginal approaches (Curtis and others, 2005. Pathways to the analysis of microarray data. TRENDS in Biotechnology 23, 429-435; Efroni and others, 2007. Identification of key processes underlying cancer phenotypes using biologic pathway analysis. PLoS One 2, 425). Procedures for testing the overall effect of a marker-set have been actively studied in recent years. For example, score tests derived under an Empirical Bayes (EB) framework (Liu and others, 2007. Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models. Biometrics 63, 1079-1088; Liu and others, 2008. Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed models. BMC bioinformatics 9, 292-2; Wu and others, 2010. Powerful SNP-set analysis for case-control genome-wide association studies. American Journal of Human Genetics 86, 929) have been proposed as powerful alternatives to the standard Rao score test (Rao, 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 50-57). The advantages of these EB-based tests are most apparent when the markers are correlated, due to the reduction in the degrees of freedom. In this paper, we propose an adaptive score test which up- or down-weights the contributions from each member of the marker-set based on the Z-scores of their effects. Such an adaptive procedure gains power over the existing procedures when the signal is sparse and the correlation among the markers is weak. By combining evidence from both the EB-based score test and the adaptive test, we further construct an omnibus test that attains good power in most settings. The null distributions of the proposed test statistics can be approximated well either via simple perturbation procedures or via distributional approximations. Through extensive simulation studies, we demonstrate that the proposed procedures perform well in finite samples. We apply the tests to a breast cancer genetic study to assess the overall effect of the FGFR2 gene on breast cancer risk.     

Persistence increases with diversity and connectance in trophic metacommunities

Background

We are interested in understanding if metacommunity dynamics contribute to the persistence of complex spatial food webs subject to colonization-extinction dynamics. We study persistence as a measure of stability of communities within discrete patches, and ask how do species diversity, connectance, and topology influence it in spatially structured food webs.

Methodology/Principal Findings

We answer this question first by identifying two general mechanisms linking topology of simple food web modules and persistence at the regional scale. We then assess the robustness of these mechanisms to more complex food webs with simulations based on randomly created and empirical webs found in the literature. We find that linkage proximity to primary producers and food web diversity generate a positive relationship between complexity and persistence in spatial food webs. The comparison between empirical and randomly created food webs reveal that the most important element for food web persistence under spatial colonization-extinction dynamics is the degree distribution: the number of prey species per consumer is more important than their identity.

Conclusions/Significance

With a simple set of rules governing patch colonization and extinction, we have predicted that diversity and connectance promote persistence at the regional scale. The strength of our approach is that it reconciles the effect of complexity on stability at the local and the regional scale. Even if complex food webs are locally prone to extinction, we have shown their complexity could also promote their persistence through regional dynamics. The framework we presented here offers a novel and simple approach to understand the complexity of spatial food webs.     

Information loss with transform methods in system identification: a new set of transforms with high information content

Linear transform methods like moments, modulating functions, and Laplace transforms are widely used for parameter estimation in system identification problems because they can reduce a large set of overdetermined equations to a small set of linear and nonlinear equations, which often have a very simple form and a unique solution. However, the effects of noise in the data are neglected in deriving these equations. We show (in terms of Fisher's information measure, the generalized variance, and simulations) that these methods can lead to very large errors in the estimates. We develop a new set of transforms based on the idea of maximizing their Fisher information content. The robustness of these new transforms, in contrast to the others, is illustrated by simulations of nanosecond flourescence decay and multicomponent exponential decay.     

An application of fuzzy set ordination to determine tree habitat suitability of sites from a regional data set

Abstract. Fuzzy set ordination is employed to evaluate sites on the basis of their suitability for particular tree species. The technique orders sites along an axis defined by the presences and absences of a given species of interest. A rationale is given in terms of noise reduction; in many situations the overall vegetation of a site will reflect habitat conditions better than the presence, absence, or quantitative performance of any single species. A data set of tree presence/absence covering a large part of the southeastern United States was analyzed and habitat suitability scores were calculated for each species. Monte-Carlo tests were used to measure the statistical power of the data set with regard to habitat preferences; 38 of the 49 species have cumulative frequency distributions showing significant departures from random expectation. Most statistically significant habitat preferences seem to be related to geographic range limits located within the study area, but some species found throughout the area also show significant departures from random expectation. The method may find applications in autecological studies of species, selection of representative site conditions for simulation modeling, and the solution of certain technical problems in ordination.     

A smooth test of goodness-of-fit for growth curves and monotonic nonlinear regression models

We propose a goodness-of-fit test for growth curves based on an adaptation of the data-driven smooth test paradigm. It is simple to apply and can assess the fit of a model to a set of growth experiences. A simulation study shows that for small samples, the test holds its level. Moreover, its power is found to be generally greater than existing tests. The article concludes by revisiting the long-standing problem of validating a model for the growth of human stature.     

GSA-PCA: gene set generation by principal component analysis of the Laplacian matrix of a metabolic network

ABSTRACT: BACKGROUND: Gene Set Analysis (GSA) has proven to be a useful approach to microarray analysis. However, most of the method development for GSA has focused on the statistical tests to be used rather than on the generation of sets that will be tested. Existing methods of set generation are often overly simplistic. The creation of sets from individual pathways (in isolation) is a poor reflection of the complexity of the underlying metabolic network. We have developed a novel approach to set generation via the use of Principal Component Analysis of the Laplacian matrix of a metabolic network. We have analysed a relatively simple data set to show the difference in results between our method and the current state of the art pathway-based sets. RESULTS: The sets generated with this method are semi-exhaustive and capture much of the topological complexity of the metabolic network. This semi-exhaustive nature of this method has also allowed us to design a hypergeometric enrichment test to determine which genes are likely responsible for set significance. We show that our method finds significant aspects of biology that would be missed (i.e. false negatives) and addresses the false positive rates found with the use of simple pathway-based sets. CONCLUSIONS: The set generation step for GSA is often neglected but is a crucial part of the analysis as it defines the full context for the analysis. As such, set generation methods should be robust and yield as complete a representation of the extant biological knowledge as possible. The method reported here achieves this goal and is demonstrably superior to previous set analysis methods.     

Improving profile HMM discrimination by adapting transition probabilities

Profile hidden Markov models (HMMs) are used to model protein families and for detecting evolutionary relationships between proteins. Such a profile HMM is typically constructed from a multiple alignment of a set of related sequences. Transition probability parameters in an HMM are used to model insertions and deletions in the alignment. We show here that taking into account unrelated sequences when estimating the transition probability parameters helps to construct more discriminative models for the global/local alignment mode. After normal HMM training, a simple heuristic is employed that adjusts the transition probabilities between match and delete states according to observed transitions in the training set relative to the unrelated (noise) set. The method is called adaptive transition probabilities (ATP) and is based on the HMMER package implementation. It was benchmarked in two remote homology tests based on the Pfam and the SCOP classifications. Compared to the HMMER default procedure, the rate of misclassification was reduced significantly in both tests and across all levels of error rate.     

Development of biomotor characteristics and athletic abilities of sprint and throw in boys aged six to eight years

The aim of this research was to examine the influences of specially programmed physical education lessons on biomotor development in boys, as well as the influence of those changes on relations between the set of morphological and motor variables and athletic variables for the assessment of sprint and throw abilities. For this purpose, an overall sample of 325 primary school first grade pupils from the city of Split area, aged 6-8 years, was divided into control group of subjects (N=140) attending regular physical education lessons and experimental group attending specially programmed lessons based on athletics, sports gymnastics and games elements as well as on general preparatory exercises. The relations between the predictor set of variables composed of 4 morphological measurements and 6 motor tests with the criteria of sprint and ball throwing were established by the regression correlation analysis at the beginning and at the end of the academic year Both groups of subjects achieved positive quantitative resultant shift between the two points of measurements, whereas this shift was more significant in the experimental group in relation to the control group, especially in motor abilities coordination of flexibility, movement frequency and of explosive, repetitive and static strength. The number of significant predictors for criteria variables of sprint and ball throwing increased in the final measurement in relation to the first one in both groups of subjects. While in the control group the best results predictor in sprint were the motor abilities of explosive strength and trunk strength, the best results predictor in sprint in the experimental group were coordination, trunk strength, flexibility and explosive strength. As far as the morphological characteristics are concerned muscle mass has a positive and body mass a negative effect on the sprint result. The best results predictor in ball throwing are explosive strength and trunk strength which, in the experimental group of pupils are additionally followed by coordination development as well as the overall body mass development. By comparison of these and the earlier obtained results, a new work model for the disciplines of sprint and throws within the athletic sport school, has been proposed.