non parametric analysis of covariance for confirmatory randomized clinical trials to evaluate dose response relationships in confirmatory randomized clinical trials that are designed to compare multiple doses of a test treatment with a control group and with one another there are often statistical issues regarding compound hypotheses and multiple comparisons which need to be considered in most cases the analysis plan needs a clear specification for the proposed order for conducting statistical tests or for managing the overall significance level which statistical methods will be used and whether adjustment for covariates will be performed there are several benefits of specifying non parametric analysis of covariance ancova for performing the primary confirmatory analyses only minimal assumptions are needed beyond randomization in the study design whereas regression model based methods have assumptions about model fit for which departures may require modifications that are incompatible with a fully prespecified analysis plan non parametric methods provide traditionally expected results of ancova namely a typically small adjustment to the estimate for a treatment comparison so as to account for random imbalance of covariates between treatment groups and variance reduction for this estimate when covariates are strongly correlated with the response of interest the application of non parametric ancova is illustrated for two randomized clinical trials the first has a 3 x 4 factorial response surface design for the comparison of 12 treatments that is combinations of three doses of one drug and four doses of a second drug for change in blood pressure and the second example addresses the comparison of three doses of test treatment and placebo for time to disease progression this clinical trial has comparisons among treatments made for a dichotomous criterion wilcoxon rank scores and averages of cumulative survival rates in each example the non parametric covariance method provides variance reduction relative to its unadjusted counterpart

a posteriori error estimators gradient recovery by averaging and superconvergence for the linear finite element solution to a linear elliptic model problem we derive an error estimator based upon appropriate gradient recovery by local averaging in contrast to popular variants like the zz estimator our estimator contains some additional terms that ensure reliability also on coarse meshes moreover the enhanced estimator is proved to be locally efficient and asymptotically exact whenever the recovered gradient is superconvergent we formulate an adaptive algorithm that is directed by this estimator and illustrate its aforementioned properties as well as their importance in numerical tests

a mixed variational formulation based on exact intrinsic equations for dynamics of moving beams abstract a nonlinear intrinsic formulation for the dynamics of initially curved and twisted beams in a moving frame is presented the equations are written in a compact matrix form without any approximations to the geometry of the deformed beam reference line or to the orientation of the intrinsic cross section frame in accordance with previously published work when effects of warping on the dynamics and local constraints on the cross sectional deformation are ignorable the in and out of plane st venant warping displacements which are fully coupled for nonhomogeneous anisotropic beams need only be included explicitly in the determination of a suitable elastic law a two dimensional problem and need not be considered explicitly in the one dimensional equations governing global deformation in this paper it is presupposed that such an elastic law is given as a one dimensional strain energy function thus the present equations which are based on only six generalized strain variables are valid for beams with closed cross sections and for which warping is unrestrained when simplified for various special cases they agree with similar intrinsic equations in the literature although the resulting equations are newtonian in structure closely resembling euler s dynamical equations for a rigid body the formulation adheres to a variational approach throughout thus providing a link between newtonian and energy based methods in particular the present development provides substantial insight into the relationships among variational formulations in which different displacement and rotational variables are used as well as between these formulations and newtonian ones for computational purposes a compact and complete mixed variational formulation is presented that is ideally suited for development of finite element analyses finally a specialized version of the intrinsic equations is developed in which shear deformations is suppressed

blind source separation in the time frequency domain based on multiple hypothesis testing this paper considers a time frequency t f based approach for blind separation of nonstationary signals in particular we propose a time frequency point selection algorithm based on multiple hypothesis testing which allows automatic selection of auto or cross source locations in the time frequency plane the selected t f points are then used via a joint diagonalization and off diagonalization algorithm to perform source separation the proposed algorithm is developed assuming deterministic signals with additive white complex gaussian noise a performance comparison of the proposed and existing approaches is provided

characterization of dose response relationships inferred by statistically significant trend tests summary a method is proposed for classifying various experimental outcomes associated with statistically significant trend tests according to a set of results of sequential testing within a family of closed under intersections one sided tests the intent of the procedure is to characterize the general shape of implied dose response relationships taking care neither to inflate the false positive type i error rate by overtesting nor to sacrifice power by overadjusting for mulitple comparisons

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

group sequential enrichment design incorporating subgroup selection an important component of clinical trials in drug development is the analysis of treatment efficacy in patient subgroups subpopulations because of concerns of multiplicity and of the small sample sizes often involved such analyses can present substantial statistical challenges and may lead to misleading conclusions as a confirmatory seamless phase ii iii design we propose an adaptive enrichment group sequential procedure whereby resources can be concentrated on subgroups most likely to respond to treatment stopping boundaries are defined through upper and lower spending functions the procedure is presented in terms of the efficient score enabling the analysis of normal binary or time to event data it addresses the dilution effect by eliminating populations at the first stage that appear likely to derive no therapeutic benefit it subsequently proceeds with the definitive assessment of treatment efficacy among the remaining pooled populations using a group sequential design the procedure provides strong protection of familywise type i error rate and we employ a bootstrap algorithm to obtain point and interval estimates that are adjusted for the selection bias we give examples to demonstrate how the design is used we make comparisons with adaptive two stage combination test procedures and with a group sequential test that does not account for the presence of subgroups numerical results show that the procedure has high power to detect subgroup specific effects and the use of multiple interim analysis points can lead to substantial sample size savings

on a generalized false discovery rate the concept of k fwer has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections for some flxed k 1 a less conservative notion the k fdr has been introduced very recently by sarkar 19 generalizing the false discovery rate of banjamini and hochberg 1 in this article we bring newer insight to the k fdr considering a mixture model involving independent p values before motivating the developments of some new procedures that control it we prove the k fdr control of the proposed methods under a slightly weaker condition than in the mixture model we provide numerical evidence of the proposed methods superior power performance over some kfwer and k fdr methods finally we apply our methods to a real data set

testing for unobserved heterogeneity in exponential and weibull duration models abstract we examine the use of the likelihood ratio lr statistic to test for unobserved heterogeneity in duration models based on mixtures of exponential or weibull distributions we consider both the uncensored and censored duration cases the asymptotic null distribution of the lr test statistic is not the standard chi square as the standard regularity conditions do not hold instead there is a nuisance parameter identified only under the alternative and a null parameter value on the boundary of the parameter space as in cho and white 2007a we accommodate these and provide methods delivering consistent asymptotic critical values we conduct a number of monte carlo simulations comparing the level and power of the lr test statistic to an information matrix im test due to chesher 1984 and lagrange multiplier lm tests of kiefer 1985 and sharma 1987 our simulations show that the lr test statistic generally outperforms the im and lm tests we also revisit the work of van den berg and ridder 1998 on unemployment durations and of ghysels et al 2004 on interarrival times between stock trades and as it turns out affirm their original informal inferences

guaranteed and robust discontinuous galerkin a posteriori error estimates for convection diffusion reaction problems we propose and study a posteriori error estimates for convection diffusion reaction problems with inhomogeneous and anisotropic diffusion approximated by weighted interior penalty discontinuous galerkin methods our twofold objective is to derive estimates without undetermined constants and to analyze carefully the robustness of the estimates in singularly perturbed regimes due to dominant convection or reaction we first derive locally computable estimates for the error measured in the energy semi norm these estimates are evaluated using h div w conforming diffusive and convective flux reconstructions thereby extending the previous work on pure diffusion problems the resulting estimates are semi robust in the sense that local lower error bounds can be derived using suitable cutoff functions of the local peclet and damkohler numbers fully robust estimates are obtained for the error measured in an augmented norm consisting of the energy semi norm a dual norm of the skew symmetric part of the differential operator and a suitable contribution of the interelement jumps of the discrete solution numerical experiments are presented to illustrate the theoretical results

a local a posteriori error estimator based on equilibrated fluxes we present and analyze a new a posteriori error estimator for lowest order conforming finite elements it is based on raviart thomas finite elements and can be obtained locally by a postprocessing technique involving for each vertex a local subproblem associated with a dual mesh under certain regularity assumptions on the right hand side we obtain an error estimator where the constant in the upper bound for the true error tends to one replacing the conforming finite element solution by a postprocessed one the error estimator is asymptotically exact the local equivalence between our estimator and the standard residual based error estimator is established numerical results illustrate the performance of the error estimator

large sample tests for binary outcomes in fixed dose combination drug studies several test statistics are developed for testing the hypothesis that the combination of two drugs at a fixed dose regimen is more effective than both of the single drugs used alone with respect to a dichotomous response variable the response probability logit and arcsine root scales are considered the power function and the significance level are derived for large samples for the sample size per group of 20 or greater the power and type i error rate can be accurately calculated using the large sample power function when the response probability ranges from 0 2 to 0 8 these tests have similar power behaviors in small samples the large sample power functions of two of the tests can severely underestimate the type i error rate while overestimation can occur with one other test the utilities of these tests are extended to unbalanced sample size cases generally speaking there is a loss of power with unequal sample size allocation but the loss is not severe

lower extremity control during turns initiated with and without hip external rotation the pirouette turn is often initiated in neutral and externally rotated hip positions by dancers this provides an opportunity to investigate how dancers satisfy the same mechanical objectives at the whole body level when using different leg kinematics the purpose of this study was to compare lower extremity control strategies during the turn initiation phase of pirouettes performed with and without hip external rotation skilled dancers n 5 performed pirouette turns with and without hip external rotation joint kinetics during turn initiation were determined for both legs using ground reaction forces grfs and segment kinematics hip muscle activations were monitored using electromyography using probability based statistical methods variables were compared across turn conditions as a group and within dancer despite differences in grfs and impulse generation between turn conditions at least 90 of each grf was aligned with the respective leg plane a majority of the net joint moments at the ankle knee and hip acted about an axis perpendicular to the leg plane however differences in shank alignment relative to the leg plane affected the distribution of the knee net joint moment when represented with respect to the shank versus the thigh during the initiation of both turns most participants used ankle plantar flexor moments knee extensor moments flexor and abductor moments at the push leg s hip and extensor and abductor moments at the turn leg s hip representation of joint kinetics using multiple reference systems assisted in understanding control priorities

stepup procedures controlling generalized fwer and generalized fdr in many applications of multiple hypothesis testing where more than one false rejection can be tolerated procedures controlling error rates measuring at least k false rejections instead of at least one for some fixed k 1 can potentially increase the ability of a procedure to detect false null hypotheses the k fwer a generalized version of the usual familywise error rate fwer is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed a further generalization of a result on the k fwer is provided in this article in addition an alternative and less conservative notion of error rate the k fdr is introduced in the same spirit as the k fwer by generalizing the usual false discovery rate fdr a k fwer procedure is constructed given any set of increasing constants by utilizing the kth order joint null distributions of the p values without assuming any specific form of dependence among all the p values procedures controlling the k fdr are also developed by using the kth order joint null distributions of the p values first assuming that the sets of null and nonnull p values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two mtp2 and then discarding that assumption about the overall dependence among the p values

evaluation of a combination drug with multiple doses in unbalanced factorial design clinical trials flexibilities for sample size allocation are often demanded for achieving multiple study objectives in combination drug trials the global tests of hung chi and lipicky are extended for analysis of unbalanced factorial design trials to test the hypothesis that at least one of the non zero dose combinations of two drugs is more effective than the respective component doses when the dose combinations have heterogeneous effect sizes an unbalanced design may induce greater power than the balanced design an adjusted p value approach is proposed for testing the individual dose combinations under the condition that the maximum type i error probability is protected

mixtures of multiple testing procedures for gatekeeping applications in clinical trials this paper proposes a general framework for constructing gatekeeping procedures for clinical trials with hierarchical objectives such problems frequently exhibit complex structures including multiple families of hypotheses and logical restrictions the proposed framework is based on combining multiple procedures across families it enables the construction of powerful and flexible gatekeeping procedures that account for general logical restrictions among the hypotheses of interest a clinical trial in patients with schizophrenia is used to illustrate the approach for parallel gatekeeping whereas another clinical trial in patients with hypertension is used to illustrate the approach for gatekeeping with general logical restrictions

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

strengthening some common multiple test procedures for discrete data this paper proposes modification of some commonly used multiple test procedures for testing problems that arise when the underlying distributions are discrete these procedures have been shown as conservative because the exact nominal levels are unattainable the amended procedures can achieve actual type i errors much closer to the nominal levels thus giving rise to more powerful tests

an adaptive confirmatory trial with interim treatment selection practical experiences and unbalanced randomization this article has been motivated by an ongoing international adaptive confirmatory trial at the interim analysis of this two stage trial none one or two active treatment regimens are selected for further study in the second stage a combination test approach is used in this practical setting with an extension of the theory to unbalanced randomization we show that a combination test with suitable weights can still preserve the overall type i error rate provided that the test statistic is chosen appropriately and the unpooled z test for proportions is not used the accuracy of stagewise p values is also discussed in a more general framework monte carlo simulations confirm the validity of the approach retained and evaluate the necessary sample size additional issues addressed during the design of the trial are also examined such as multiplicity due to testing hypotheses on key secondary endpoints a non inferiority comparison to an active treatment and covariate adjusted analyses for various types of outcome

testing for the existence of a desirable dose combination we consider the problem of studying several dose combinations of two drugs for a therapeutic endpoint in a multilevel factorial clinical trial two test statistics are constructed to test whether there exists at least one dose combination that is more effective than its component doses their distributions involve nuisance parameters quantifying the mean differences among the doses of the two component drugs it is shown that their power functions achieve maxima as all the nuisance parameters approach infinity in absolute value the significance levels of the two tests are derived and two alpha level tests are proposed tables are given to provide the alpha level critical values for these tests and to gain insights into their power performances

a posteriori error analysis for hybridizable discontinuous galerkin methods for second order elliptic problems we present a unified a posteriori error analysis for hybridizable discontinuous galerkin methods for second order elliptic partial differential equations the main feature of this analysis is that it reduces the task of establishing the reliability and efficiency of the estimator to the verification of three simple conditions this approach allows us not only to derive new estimates for hybridizable discontinuous galerkin methods but also to recover well known a posteriori error estimates for mixed methods and for the continuous galerkin method

equilibrated residual error estimator for edge elements reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem a cheap computation of such functions via equilibration is well known for scalar equations of second order we simplify and modify the equilibration such that it can be applied to the curl curl equation and edge elements the construction is more involved for edge elements since the equilibration has to be performed on subsets with different dimensions for this reason raviart thomas elements are extended in the spirit of distributions

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

closure procedures for monotone bi factorial dose response designs les essais en doses multiples ont deux buts i demontrer une amelioration de l efficacite pour une combinaison donnee de chacun des composants ii identifier un intervalle de doses efficaces et sures les auteurs s interessent aux deux aspects quoique avec un interet plus marque pour le second avec une procedure de cloture qui garantit un controle fort du risque global d erreur on etudie deux familles differentes d hypotheses nulles pour des dispositifs bi factoriels monotones par rapport a un ordre partiel l une est adaptee a la recherche d une ou plusieurs doses efficaces minimums l autre est suffisamment large pour permettre d identifier les doses efficaces les plus elevees on applique des tests du rapport de vraisemblance et des contrastes multiples appropries a un exemple d essai clinique tire de hung 2000 statistics in medicine 19 2079 2087 le code ecrit en langage r est disponible dans sa totalite sur internet

comparison of weighted kappa coefficients of multiple binary diagnostic tests done on the same subjects sensitivity and specificity are classic parameters to assess and compare the performance of binary diagnostic tests versus a gold standard in a population another useful parameter to assess and compare the performance of binary tests is the weighted kappa coefficient which is defined as a measure of the beyond chance agreement between the diagnostic test and the gold standard in this study we deduce the maximum likelihood estimators of the weighted kappa coefficients of multiple binary tests and we propose an asymptotic method to compare the weighted kappa coefficients of multiple binary tests with regard to the same gold standard when all of the diagnostic tests are applied to the same sample of patients we have carried out simulation experiments to study the type i error and the power of the method that we propose when we compared three binary tests we have applied the results obtained to the diagnosis of coronary disease

a posteriori error estimates for a discontinuous galerkin method applied to elliptic problems log number r74 abstract a posteriori error estimates for locally mass conservative methods for subsurface flow are presented these methods are based on discontinuous approximation spaces and referred to as discontinuous galerkin methods in the case where penalty terms are added to the bilinear form one obtains the nonsymmetric interior penalty galerkin methods in a previous work we proved optimal rates of convergence of the methods applied to elliptic problems here h adaptivity is investigated for flow problems in 2d we derive global explicit estimators of the error in the l 2 norm and we numerically investigate an implicit indicator of the error in the energy norm model problems with discontinuous coefficients are considered

on weighted hochberg procedures summary we consider different ways of constructing weighted hochberg type step up multiple test procedures including closed procedures based on weighted simes tests and their conservative step up short cuts and step up counterparts of two weighted holm procedures it is shown that the step up counterparts have some serious pitfalls such as lack of familywise error rate control and lack of monotonicity in rejection decisions in terms of p values therefore an exact closed procedure appears to be the best alternative its only drawback being lack of simple stepwise structure a conservative step up short cut to the closed procedure may be used instead but with accompanying loss of power simulations are used to study the familywise error rate and power properties of the competing procedures for independent and correlated p values although many of the results of this paper are negative they are useful in highlighting the need for caution when procedures with similar pitfalls may be used

asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes part 1 a smooth problem and globally quasi uniform meshes a class of a posteriori estimators is studied for the error in the maximum norm of the gradient on single elements when the finite element method is used to approximate solutions of second order elliptic problems the meshes are unstructured and in particular it is not assumed that there are any known superconvergent points the estimators are based on averaging operators which are approximate gradients recovered gradients which are then compared to the actual gradient of the approximation on each element conditions are given under which they are asympotically exact or equivalent estimators on each single element of the underlying meshes asymptotic exactness is accomplished by letting the approximate gradient operator average over domains that are large in a controlled fashion to be detailed below compared to the size of the elements

familywise robustness criteria for multiple comparison procedures a criticism of multiple comparison procedures is that the family of inferences over which an error rate is controlled is often arbitrarily selected yet the conclusion may depend heavily on the choice of the family such ambiguity is most likely in large exploratory studies requiring numerous simultaneous inferences in ambiguous situations it is desirable that results of multiple comparison procedures depend little on the chosen family to assess this we propose several familywise robustness criteria to evaluate such procedures and we find some of their properties theoretically and by simulation procedures that control the false discovery rate seem to be familywise robust

a general multistage procedure for k out of n gatekeeping we generalize a multistage procedure for parallel gatekeeping to what we refer to as k out of n gatekeeping in which at least k out of n hypotheses 1 k n in a gatekeeper family must be rejected in order to test the hypotheses in the following family this gatekeeping restriction arises in certain types of clinical trials for example in rheumatoid arthritis trials it is required that efficacy be shown on at least three of the four primary endpoints we provide a unified theory of multistage procedures for arbitrary k with k 1 corresponding to parallel gatekeeping and k n to serial gatekeeping the theory provides an insight into the construction of truncated separable multistage procedures using the closure method explicit formulae for calculating the adjusted p values are given the proposed procedure is simpler to apply for this particular problem using a stepwise algorithm than the mixture procedure and the graphical procedure with memory using entangled graphs

comparison of several testing strategies for combination drug efficacy trials based on the closure principle the author discusses three multiple testing procedures for identifying the minimum efficacious doses in a balanced factorial combination drug trial all of these procedures utilize the closed testing principle and hence strongly control the overall error rate and satisfy the coherence property that is if a hypothesis is retained then any hypothesis implied by it is also retained while coherence is an essential requirement for any multiple testing procedure consonance is a highly desirable characteristic in the considered settings if a testing procedure is consonant then it always provides a set of all minimum efficacious combinations as a result otherwise it may lead to ambiguity although the coherence property is satisfied for any closed testing procedure and thus does not depend on the test used for an individual hypothesis whether the considered procedures satisfy the consonance property depends entirely on the nature of the test statistic the author identifies the consonant and non consonant procedures among the presented procedures and discusses possible drawbacks of non consonant procedures with respect to combination drug efficacy trials additional properties of these procedures are assessed by simulations

improving the reliability of causal discovery from small data sets using argumentation we address the problem of improving the reliability of independence based causal discovery algorithms that results from the execution of statistical independence tests on small data sets which typically have low reliability we model the problem as a knowledge base containing a set of independence facts that are related through pearl s well known axioms statistical tests on finite data sets may result in errors in these tests and inconsistencies in the knowledge base we resolve these inconsistencies through the use of an instance of the class of defeasible logics called argumentation augmented with a preference function that is used to reason about and possibly correct errors in these tests this results in a more robust conditional independence test called an argumentative independence test our experimental evaluation shows clear positive improvements in the accuracy of argumentative over purely statistical tests we also demonstrate significant improvements on the accuracy of causal structure discovery from the outcomes of independence tests both on sampled data from randomly generated causal models and on real world data sets

a comparison of two modified bonferroni procedures summary it is shown that hommel s 1988 modified bonferroni procedure is at least as powerful as hochberg s 1988 procedure and in general more powerful

multiple testing for a combination drug with two study endpoints a combination drug product with two or more active compounds may be superior to each of its components with higher dose levels and therefore is preferred in terms of efficacy cost and safety to study a combination drug researchers often conduct trials by using a factorial design with combinations of dose levels of each drug component by applying some bootstrap methods we construct multiple testing procedures to simultaneously identify combinations superior to each drug component with any dose level these multiple testing procedures are more powerful than holm s step down procedure that is known to be very conservative when there is only one study endpoint applying the bootstrap is straightforward in many studies however there are two or more study endpoints and it is not simple to apply the bootstrap we apply one version of the bootstrap and then use an upper bound to control the familywise error defined as the probability of rejecting at least one true null hypothesis properties of the bootstrap multiple testing procedures are discussed and examined in some simulation studies

bayesian nonparametric variable selection as an exploratory tool for discovering differentially expressed genes high throughput scientific studies involving no clear a priori hypothesis are common for example a large scale genomic study of a disease may examine thousands of genes without hypothesizing that any specific gene is responsible for the disease in these studies the objective is to explore a large number of possible factors e g genes in order to identify a small number that will be considered in follow up studies that tend to be more thorough and on smaller scales a simple hierarchical linear regression model with random coefficients is assumed for case control data that correspond to each gene the specific model used will be seen to be related to a standard bayesian variable selection model relatively large regression coefficients correspond to potential differences in responses for cases versus controls and thus to genes that might matter for large scale studies and using a dirichlet process mixture model for the regression coefficients we are able to find clusters of regression effects of genes with increasing potential effect or relevance in relation to the outcome of interest one cluster will always correspond to genes whose coefficients are in a neighborhood that is relatively close to zero and will be deemed least relevant other clusters will correspond to increasing magnitudes of the random latent regression coefficients using simulated data we demonstrate that our approach could be quite effective in finding relevant genes compared with several alternative methods we apply our model to two large scale studies the first study involves transcriptome analysis of infection by human cytomegalovirus the second study s objective is to identify differentially expressed genes between two types of leukemia copyright 2012 john wiley sons ltd

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

a bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data with applications to analysis of quality of life outcomes in clinical trials this article is concerned about the test for the difference in the distributions of multigroup proportional data which is motivated by the problem of comparing the distributions of quality of life qol outcomes among different treatment groups in clinical trials the proportional data such as qol outcomes assessed by answers to questions on a questionnaire are bounded in a closed interval such as 0 1 with continuous observations in 0 1 and in addition excess observations taking the boundary values 0 and or 1 common statistical procedures used in practice such as t and rank based tests may not be very powerful since they ignore the specific feature of the proportional data in this article we propose a three component mixture model for the proportional data and a density ratio model for the distributions of continuous observations in 0 1 a semiparametric test statistic for the homogeneity of distributions of multigroup proportional data is derived based on the empirical likelihood ratio principle and shown to be asymptotically distributed as a chi squared random variable under null hypothesis a nonparametric bootstrap procedure is proposed to further improve the performance of the semiparametric test simulation studies are performed to evaluate the empirical type i error and power of the proposed test procedure and compare it with likelihood ratio tests lrts under parametric distribution assumptions rank based kruskal wallis test and wald type test the proposed test procedure is also applied to the analysis of qol outcomes from a clinical trial on colorectal cancer that motivated our study

on the constants in hp finite element trace inverse inequalities we derive inverse trace inequalities for hp finite elements utilizing orthogonal polynomials we show how to derive explicit expressions for the constants when considering triangular and tetrahedral elements we also discuss how to generalize this technique to the general d simplex

asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes part ii the piecewise linear case we extend results from part i about estimating gradient errors elementwise a posteriori given there for quadratic and higher elements to the piecewise linear case the key to our new result is to consider certain technical estimates for differences in the error e x 1 e x 2 rather than for e x itself we also give a posteriori estimators for second derivatives on each element

short note an explicit expression for the penalty parameter of the interior penalty method we derive an explicit expression for the penalty parameter of the interior penalty method for elliptic problems the expression yields a coercive bilinear form and is valid for general meshes comprising of geometrically nonconforming simplical elements

a posteriori error estimator based on gradient recovery by averaging for discontinuous galerkin methods we consider some anisotropic and piecewise constant diffusion problems in domains of r 2 approximated by a discontinuous galerkin method with polynomials of any fixed degree we propose an a posteriori error estimator based on gradient recovery by averaging it is shown that this estimator gives rise to an upper bound where the constant is one up to some additional terms that guarantee reliability the lower bound is also established moreover these additional terms are negligible when the recovered gradient is superconvergent the reliability and efficiency of the proposed estimator is confirmed by some numerical tests

free vibration and lateral buckling of a cantilever slender beam with an edge crack experimental and numerical studies the effects of crack ratios and positions on the fundamental frequencies and buckling loads of slender cantilever euler beams with a single edge crack are investigated both experimentally and numerically using the finite element method based on energy approach the governing matrix equations are derived from the standard and cracked beam elements combined with the local flexibility concept the experiments are conducted using specimens having edge cracks of different depths at different positions to validate the numerical results obtained the numerical results are shown to be in good agreement with the experimental results for the considered crack ratios

traditional multiplicity adjustment methods in clinical trials this tutorial discusses important statistical problems arising in clinical trials with multiple clinical objectives based on different clinical variables evaluation of several doses or regiments of a new treatment analysis of multiple patient subgroups etc simultaneous assessment of several objectives in a single trial gives rise to multiplicity if unaddressed problems of multiplicity can undermine integrity of statistical inferences the tutorial reviews key concepts in multiple hypothesis testing and introduces main classes of methods for addressing multiplicity in a clinical trial setting general guidelines for the development of relevant and efficient multiple testing procedures are presented on the basis of application specific clinical and statistical information case studies with common multiplicity problems are used to motivate and illustrate the statistical methods presented in the tutorial and software implementation of the multiplicity adjustment methods is discussed copyright 2013 john wiley sons ltd

a posteriori error indicators for maxwell s equations abstract in this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for maxwell s equations in the presence of a bounded inhomogeneous and anisotropic scatterer problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue we briefly recall existence and uniqueness theory associated with this problem then we show how a posteriori error indicators can be derived using an adjoint equation approach the error indicators use both the jump in normal and tangential components of the field across faces in the mesh

improved approximations via rayleigh s quotient two methods for obtaining excellent results based on one term approximations via rayleigh s quotient are described along with their applications a combination of these methods can be used to obtain accurate resutls for a wide class of problems as well after a few iterations depending on the starting function the stodola vianello method sometimes leads to overly complicated formulae so that symbolic manipulation software may become bogged down

a linear non gaussian acyclic model for causal discovery in recent years several methods have been proposed for the discovery of causal structure from non experimental data such methods make various assumptions on the data generating process to facilitate its identification from purely observational data continuing this line of research we show how to discover the complete causal structure of continuous valued data under the assumptions that a the data generating process is linear b there are no unobserved confounders and c disturbance variables have non gaussian distributions of non zero variances the solution relies on the use of the statistical method known as independent component analysis and does not require any pre specified time ordering of the variables we provide a complete matlab package for performing this lingam analysis short for linear non gaussian acyclic model and demonstrate the effectiveness of the method using artificially generated data and real world data

multiplicity adjustment for multiple endpoints in clinical trials with multiple doses of an active treatment frequently multiple doses of an active treatment and multiple endpoints are simultaneously considered in the designs of clinical trials for these trials traditional multiplicity adjustment procedures such as bonferroni hochberg and hommel procedures can be applied when treating the comparisons of different doses to the control on all endpoints at the same level however these approaches will not take into account the possible dose response relationship on each endpoint and therefore are less specific and may have lower power to gain power in this paper we consider the problem as a two dimensional multiplicity problem one dimension concerns the multiple doses and the other dimension concerns the multiple endpoints we propose procedures which consider the dose order to form the closure of the procedures and control the family wise type i error rate in a strong sense for this two dimensional problem numerical examples show that procedures proposed in this paper in general have higher power than the commonly used procedures e g the regular hochberg procedure especially for comparing the higher dose to the control

identifying chromosomal fragile sites from a hierarchical clustering point of view summary identification of fragile sites is a way to investigate the genetic abnormalities that are the hallmark of cancer and play an important role in carcinogenesis manifestation of nonrandom breakage at a chromosome band is an essential criterion for determination of the fragility of the band in this article a new detection procedure is proposed this new procedure takes the relationship of one site with the others into consideration and can be applied to tests of the randomness of breakpoints under either the proportional probability model ppm or the equiprobability model epm the procedure can form a grouping structure that classifies all sites into several clusters it is applied to identification of fragile sites for a real data set for chinese patients with colorectal carcinoma for illustration of the proposed method

testing multivariate economic restrictions using quantiles the example of slutsky negative semidefiniteness abstract this paper is concerned with testing a core economic restriction negative semidefiniteness of the slutsky matrix we consider a system of nonseparable structural equations with infinite dimensional unobservables and employ quantile regression methods because they allow us to utilize the entire distribution of the data difficulties arise because the restriction involves several equations while the quantile is a univariate concept we establish that we may use quantiles of linear combinations of the dependent variable develop a new empirical process based test that applies kernel quantile estimators and investigate its finite and large sample behavior finally we apply all concepts to canadian microdata

energy norm a posteriori error estimation for discontinuous galerkin methods in this paper we present a residual based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous galerkin approximations of elliptic problems the theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed we also present some illustrating numerical examples

hochberg s step up method cutting corners off holm s step down method holm s method and hochberg s method for multiple testing can be viewed as step down and step up versions of the bonferroni test we show that both are special cases of partition testing the difference is that while holm s method tests each partition hypothesis using the largest order statistic setting a critical value based on the bonferroni inequality hochberg s method tests each partition hypothesis using all the order statistics setting a series of critical values based on simes inequality geometrically hochberg s step up method cuts corners off the acceptance regions of holm s step down method by making assumptions on the joint distribution of the test statistics as can be expected partition testing making use of the joint distribution of the test statistics is more powerful than partition testing using probabilistic inequalities thus if the joint distribution of the test statistics is available through modelling for example we recommend partition step down testing setting exact critical values based on the joint distribution

estimation of the number of true null hypotheses in multivariate analysis of neuroimaging data abstract the repeated testing of a null univariate hypothesis in each of many sites either regions of interest or voxels is a common approach to the statistical analysis of brain functional images procedures such as the bonferroni are available to maintain the type i error of the set of tests at a specified level an initial assumption of these methods is a global null hypothesis i e the statistics computed on each site are assumed to be generated by null distributions this framework may be too conservative when a significant proportion of the sites is affected by the experimental manipulation this report presents the development of a rigorous statistical procedure for use with a previously reported graphical method the p plot for estimation of the number of true null hypotheses in the set this estimate can then be used to sharpen existing multiple comparison procedures performance of the p plot method in the multiple comparison problem is investigated in simulation studies and in the analysis of autoradiographic data

testing whether an identified treatment is best summary we consider the problem of testing whether an identified treatment is better than each of k treatments suppose there are univariate test statistics si that contrast the identified treatment with treatment i for i 1 2 k the min test is defined to be the a level procedure that rejects the null hypothesis that the identified treatment is not best when for all i si rejects the one sided hypothesis at the a level that the identified treatment is not better than the ith treatment in the normal case where si are t statistics the min test is the likelihood ratio test for distributions satisfying mild regularity conditions if attention is restricted to test statistics that are monotone nondecreasing functions of si then regardless of their covariance structure the min test is an optimal a level test tables of the sample size needed to achieve power 5 8 90 and 95 are given for the min test when the si are student s t and wilcoxon

a comparative evaluation of wavelet based methods for hypothesis testing of brain activation maps wavelet based methods for hypothesis testing are described and their potential for activation mapping of human functional magnetic resonance imaging fmri data is investigated in this approach we emphasise convergence between methods of wavelet thresholding or shrinkage and the problem of hypothesis testing in both classical and bayesian contexts specifically our interest will be focused on the trade off between type i probability error control and power dissipation estimated by the area under the roc curve we describe a technique for controlling the false discovery rate at an arbitrary level of error in testing multiple wavelet coefficients generated by a 2d discrete wavelet transform dwt of spatial maps of fmri time series statistics we also describe and apply change point detection with recursive hypothesis testing methods that can be used to define a threshold unique to each level and orientation of the 2d dwt and bayesian methods incorporating a formal model for the anticipated sparseness of wavelet coefficients representing the signal or true image the sensitivity and type i error control of these algorithms are comparatively evaluated by analysis of null images acquired with the subject at rest and an experimental data set acquired from five normal volunteers during an event related finger movement task we show that all three wavelet based algorithms have good type i error control the fdr method being most conservative and generate plausible brain activation maps the bayesian method being most powerful we also generalise the formal connection between wavelet based methods for simultaneous multiresolution denoising hypothesis testing and methods based on monoresolution gaussian smoothing followed by statistical testing of brain activation maps

a posteriori error estimation for discontinuous galerkin finite element approximation it is shown that the interelement discontinuities in a discontinuous galerkin finite element approximation are subordinate to the error measured in the broken h 1 seminorm one consequence is that the dg norm of the error is equivalent to the broken energy seminorm computable a posteriori error bounds are obtained for the error measured in both the dg norm and the broken energy seminorm and are shown to be efficient in the sense that they also provide lower bounds up to a constant and higher order data oscillation terms the estimators are completely free of unknown constants and provide guaranteed numerical bounds for the error

asymptotic theory for static behavior of elastic anisotropic i beams abstract end effects for prismatic anisotropic beams with thin walled open cross sections are analyzed by the variational asymptotic method the decay rates for disturbances at the ends of prismatic beams are evaluated and the most influential end disturbances are incorporated into a refined beam theory thus the foundations of vlasovs theory as well as restrictions on its applicability are obtained from the variational asymptotic point of view vlasovs theory is proved to be asymptotically correct for isotropic i beams the asymptotically correct generalization of vlasovs theory for static behavior of anisotropic beams is presented in light of this development various published generalizations of vlasovs theory for thin walled anisotropic beams are discussed comparisons with a numerical 3 d analysis are provided showing that the present approach gives the closest agreement of all published theories the procedure can be applied to any thin walled beam with open cross sections

type ii generalized family wise error rate formulas with application to sample size determination multiple endpoints are increasingly used in clinical trials the significance of some of these clinical trials is established if at least r null hypotheses are rejected among m that are simultaneously tested the usual approach in multiple hypothesis testing is to control the family wise error rate which is defined as the probability that at least one type i error is made more recently the q generalized family wise error rate has been introduced to control the probability of making at least q false rejections for procedures controlling this global type i error rate we define a type ii r generalized family wise error rate which is directly related to the r power defined as the probability of rejecting at least r false null hypotheses we obtain very general power formulas that can be used to compute the sample size for single step and step wise procedures these are implemented in our r package rpowersamplesize available on the cran making them directly available to end users complexities of the formulas are presented to gain insight into computation time issues comparison with monte carlo strategy is also presented we compute sample sizes for two clinical trials involving multiple endpoints one designed to investigate the effectiveness of a drug against acute heart failure and the other for the immunogenicity of a vaccine strategy against pneumococcus copyright 2016 john wiley sons ltd

a group sequential holm procedure with multiple primary endpoints we propose a group sequential holm procedure when there are multiple primary endpoints this method addresses multiplicities arising from multiple primary endpoints and from multiple analyses in a group sequential design it has been shown to be a closed testing procedure and preserves the familywise error rate in the strong sense when multiple endpoints are the only concern without an interim analysis the method simplifies to the weighted holm procedure the proposed method is more powerful than the parallel group sequential method and avoids the need to anticipate the testing order as in the fixed sequence testing scheme

tests for precision and accuracy of multiple measuring devices we propose a multivariate linear model for analyzing measurement device data that follow grubbs s model the multivariate model generates the well known regression multiple correlation test for equality of device variances it also yields a new simultaneous test for equality of variances and biases the multivariate model readily permits testing of interesting subhypotheses involving the variances and biases we examine the power of these tests for onedimensional hypotheses compare them to tests proposed by grubbs and propose generalizations of grubbs s tests we also consider extensions of grubbs s model that allow similar regression and simultaneous tests to be performed

lateral torsional buckling of cantilevered elastically coupled composite strip and i beams the lateral torsional buckling of composite strip and i beams is considered the geometrically exact governing equations are simplified by consistently regarding certain configuration parameters as small the assumption that these parameters are indeed small is equivalent to the assumption that the square of the maximum prebuckling cross sectional rotation due to bending is small compared to unity the analysis takes into account various refinements of previously published results including the vlasov eaect elastic coupling the oaset of the load from the centroid and of course prebuckling deflections the analysis is thereby reduced to a single fourth order diaerential equation and boundary conditions all of which are derivable from a corresponding energy expression from the form of matched asymptotic expansions of the buckling mode when small parameters are ignored altogether a single comparison function is found which gives the correct buckling load to within 1 for a wide range of the warping rigidity using this comparison function a formula for the buckling load as a function of the small parameters of the problem is found and validated with certain exceptions regarding the load oaset parameter the formula provides results which agree quite well with the numerical solution of the exact equations as long as all the small parameters remain small however the load oaset parameter always appears in the governing equations as multiplied by a ratio of stianesses which can become large especially for composite i beams for this case a special treatment is required 2001 elsevier science ltd all rights reserved

one sided significance tests for generalized linear models under dichotomous response summary dichotomous response models are common in many experimental settings often concomitant explanatory variables are recorded and a generalized linear model such as a logit model is fit in some cases interest in specific model parameters is directed only at one sided departures from some null effect in these cases procedures can be developed for testing the null effect against a one sided alternative these include bonferroni type adjustments of univariate wald tests and likelihood ratio tests that employ inequality constrained multivariate theory this paper examines such tests of significance monte carlo evaluations are undertaken to examine the small sample properties of the various procedures the procedures are seen to perform fairly well generally achieving their nominal sizes at total sample sizes near 100 experimental units extensions to the problem of one sided tests against a control or standard are also considered

energy norm a posteriori error estimation for mixed discontinuous galerkin approximations of the maxwell operator in this paper we develop the a posteriori error estimation of mixed discontinuous galerkin finite element approximations of the maxwell operator in particular by employing suitable helmholtz decompositions of the error together with the conservation properties of the underlying method computable upper bounds on the error measured in terms of a natural mesh dependent energy norm are derived numerical experiments testing the performance of our a posteriori error bounds for problems with both smooth and singular analytical solutions are presented

a novel approach to statistical comparison of meta heuristic stochastic optimization algorithms using deep statistics abstract in this paper a novel approach for making a statistical comparison of meta heuristic stochastic optimization algorithms over multiple single objective problems is introduced where a new ranking scheme is proposed to obtain data for multiple problems the main contribution of this approach is that the ranking scheme is based on the whole distribution instead of using only one statistic to describe the distribution such as average or median averages are sensitive to outliers i e the poor runs of the stochastic optimization algorithms and consequently medians are sometimes used however using the common approach with either averages or medians the results can be affected by the ranking scheme that is used by some standard statistical tests this happens when the differences between the averages or medians are in some neighborhood and the algorithms obtain different ranks though they should be ranked equally given the small differences that exist between them the experimental results obtained on black box benchmarking 2015 show that our approach gives more robust results compared to the common approach in cases when the results are affected by outliers or by a misleading ranking scheme

testing for elevated disease rates using smoothed estimates a method of testing for elevated disease rates using smoothed estimates is introduced for counts aggregated to a specific administrative level a test statistic is developed based on an approximation to the smoothed estimate from a penalized multinomial likelihood and an approximate critical value is derived empirical investigation reveals that smoothing can increase the ability to detect elevated rates the methods are applied to data on gastric cancer in nova scotia canada