generation of coarse scale continuum flow models from detailed fracture characterizations 1 a procedure for developing coarse scale continuum models from detailed fracture descriptions is developed and applied the coarse models are in the form of a generalized dual porosity representation in which matrix rock and fractures exchange fluid locally while large scale flow occurs through the fracture network the methodology developed here introduces local subgrids to resolve dynamics within the matrix and provides appropriate coarse scale parameters describing fracture fracture matrix fracture and matrix matrix flow the geometry of the local subgrids as well as the required parameters for the coarse scale model are determined from local flow solutions using the underlying discrete fracture model the method is applied to two and three dimensional single phase and two phase flow problems and the accuracy of the coarse models is assessed relative to fully resolved discrete fracture simulations for the cases considered it is shown that the technique is capable of generating highly accurate coarse models with many fewer unknowns than the detailed characterizations and speedups of about a factor of 100 are achieved

increasing the sample size during clinical trials with t distributed test statistics without inflating the type i error rate in clinical trials with t distributed test statistics the required sample size depends on the unknown variance taking estimates from previous studies often leads to a misspecification of the true value of the variance hence re estimation of the variance based on the collected data and re calculation of the required sample size is attractive we present a flexible method for extensions of fixed sample or group sequential trials with t distributed test statistics the method can be applied at any time during the course of the trial and does not require the necessity to pre specify a sample size re calculation rule all available information can be used to determine the new sample size the advantage of our method when compared with other adaptive methods is maintenance of the efficient t test design when no extensions are actually made we show that the type i error rate is preserved

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

accurate multiscale finite element method for numerical simulation of two phase flow in fractured media using discrete fracture model numerical simulation in naturally fractured media is challenging because of the coexistence of porous media and fractures on multiple scales that need to be coupled we present a new approach to reservoir simulation that gives accurate resolution of both large scale and fine scale flow patterns multiscale methods are suitable for this type of modeling because it enables capturing the large scale behavior of the solution without solving all the small features dual porosity models in view of their strength and simplicity can be mainly used for sugar cube representation of fractured media in such a representation the transfer function between the fracture and the matrix block can be readily calculated for water wet media for a mixed wet system the evaluation of the transfer function becomes complicated due to the effect of gravity in this work we use a multiscale finite element method msfem for two phase flow in fractured media using the discrete fracture model by combining msfem with the discrete fracture model we aim towards a numerical scheme that facilitates fractured reservoir simulation without upscaling msfem uses a standard darcy model to approximate the pressure and saturation on a coarse grid whereas fine scale effects are captured through basis functions constructed by solving local flow problems using the discrete fracture model the accuracy and the robustness of msfem are shown through several examples in the first example we consider several small fractures in a matrix and then compare the results solved by the finite element method then we use the msfem in more complex models the results indicate that the msfem is a promising path toward direct simulation of highly resolution geomodels

winding of planar brownian curves the authors compute the joint probability for a closed brownian curve to wind n times around a prescribed point and to enclose a given algebraic area an estimate from below of the arithmetic area is obtained

a group sequential t test with updating of sample size if the maximum sample size for a group sequential t test is calculated on the basis of a prior estimate of the variance power at a fixed distance from the null hypothesis is not robust to misspecification of the variance we propose a new group sequential t test based on stein s 1945 two stage test in which we use internal estimates of the variance to update the maximum sample size and allow early stopping to reject the null hypothesis through a lan demets 1983 error spending function we evaluate our procedure s performance and show that it closely controls the type i and ii error rates

phase separation and coarsening in one dimensional driven diffusive systems local dynamics leading to long range hamiltonians a driven system of three species of particles diffusing on a ring is studied in detail the dynamics is local and conserves the three densities a simple argument suggesting that the model should phase separate and break the translational symmetry is given we show that for the special case where the three densities are equal the model obeys detailed balance and the steady state distribution is governed by a hamiltonian with asymmetric long range interactions this provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension the steady state of finite size systems is studied using a generalized matrix product ansatz the coarsening process leading to phase separation is studied numerically and in a mean field model the system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size the typical domain size is shown to grow logarithmically in time generalizations to a larger number of species are discussed

windings of the 2d free rouse chain we study the long time dynamical properties of a chain of harmonically bound brownian particles this chain is allowed to wander everywhere in the plane we show that the scaling variables for the occupation times tj areas aj and winding angles j j 1 n labels the particles take the same general form as in the usual brownian motion we also compute the asymptotic joint laws p tj p aj p j and discuss the correlations occurring in those distributions

statistical inference for self designing clinical trials with a one sided hypothesis in the process of monitoring clinical trials it seems appealing to use the interim findings to determine whether the sample size originally planned will provide adequate power when the alternative hypothesis is true and to adjust the sample size if necessary in the present paper we propose a flexible sequential monitoring method following the work of fisher 1998 in which the maximum sample size does not have to be specified in advance the final test statistic is constructed based on a weighted average of the sequentially collected data where the weight function at each stage is determined by the observed data prior to that stage such a weight function is used to maintain the integrity of the variance of the final test statistic so that the overall type i error rate is preserved moreover the weight function plays an implicit role in termination of a trial when a treatment difference exists finally the design allows the trial to be stopped early when the efficacy result is sufficiently negative simulation studies confirm the performance of the method

stable windings on hyperbolic surfaces let be a geometrically finite hyperbolic surface with infinite volume having at least one cusp we obtain the limit law under the patterson sullivan measure on t1 of the windings of the geodesics of around the cusps this limit law is stable with parameter 2 1 where is the hausdorff dimension of the limit set of the subgroup of mobius isometries associated with the normalization is t 1 2 1 for geodesics of length t our method relies on a precise comparison between geodesics and diffusion paths for which we need to approach the patterson sullivan measure mentioned above by measures that are regular along the stable leaves

the random walk winding number problem convergence to a diffusion process with excluded area the winding number of a random walk in the plane is the net angle through which the walker encircles the origin the author discusses the moments and asymptotic form of the winding number distribution for walks of constant step size l the author shows that the root mean square winding number theta rms grows logarithmically with the number of steps n as n to infinity in contrast with the n1 2 growth of the radial distribution the corresponding diffusion process however has infinite theta rms and does not provide a good approximation for the random walk distribution instead a diffusion process considered recently by rudnick and hu 1987 where the area surrounding the origin has been removed out to a radius r provides the correct asymptotic distribution the author finds that the optimum radius for convergence of the finite step and diffusion distributions is precisely r e 2l

a finite volume scheme for two phase immiscible flow in porous media in this paper we prove the convergence of a numerical method for solving two phase immiscible incompressible flow in porous media the method combines an upwind time implicit finite volume scheme for the saturation equation hyperbolic parabolic type and a centered finite volume scheme for the chavent global pressure equation elliptic type the capillary pressure is not neglected and we study the case when the diffusion term in the saturation equation is weakly degenerated estimates on the approximate solution are proven then by using compactness theorems we obtain a limit when the size of the discretization goes to zero and we prove that this limit is the unique weak solution of the problem that we study

winding angle distribution for planar random walk polymer ring entangled with an obstacle and all that spitzer edwards prager frisch model revisited using a general green function formulation we re derive both i spitzer and his followers results for the winding angle distribution of the planar brownian motion and ii edwards prager frisch results on the statistical mechanics of a ring polymer entangled with a straight bar in the statistical mechanics part we consider both cases of quenched and annealed topology among new results we compute exactly the expectation value of the surface area of the locus of points such that each of them has linking number n with a given closed random walk trajectory ring polymer we also consider the generalizations of the problem for the finite diameter disc like obstacle and winding within a cavity

comparison of fully implicit and impes formulations for simulation of water injection in fractured and unfractured media in this work we compare the fully implicit fi and implicit pressure explicit saturation impes formulations for the simulation of water injection in fractured media the system of partial differential equations is discretized within the discrete fracture framework using a control volume method a unique feature of the methodology is that there is no need for the computation of matrix fracture transfer terms the non linear system of equations resulting from the fi formulation is solved with state of the art newton and tensor methods direct and krylov iterative methods are employed to solve the system resulting from the newton linearization the performance of the fi and impes formulations is compared with numerical testing results show that the contrast between matrix and fracture properties affects the performance of both impes and fi formulations and that the tensor method outperforms all the newton solvers for the near singular jacobian matrix copyright 2006 john wiley sons ltd

nonparametric estimation of a delay distribution based on left censored and right truncated data this paper proposes a nonparametric method for estimating a delay distribution based on left censored and right truncated data a variance covariance estimator is provided the method is applied to the australian aids data in which some data are left censored and some data are not left censored this situation arises with aids case reporting data in australia because reporting delays were recorded only from november 1990 rather than from the beginning of the epidemic there it is shown that inclusion of the left censored data as opposed to analyzing only the uncensored data improves the precision of the estimate

re estimating the sample size of an on going blinded trial based on the method of randomization block sums we extend a method we had previously described statist med 2005 to estimate the within group variance of a continuous endpoint without breaking the blind in a randomized clinical trial specifically we a explain how the method may be used for a wider set of designs than we had previously indicated b obtain a within group covariate adjusted blinded variance estimator c illustrate use of the method for sample size re estimation and d describe a procedure to determine whether or not the blinded variance estimator works well not just on average but for the data set at hand the proposed method is simple to use and makes no additional assumptions than is made for unblinded analysis simulations show that for realistic sample sizes there is virtually no inflation in the type i error rate when weighing the burden imposed by interim unblinded re estimation with the loss in precision with blinded re estimation it may be advantageous for some trials to use the blinded method

sharp crossover and anomalously large correlation length in driven systems models of one dimensional driven diffusive systems sometimes exhibit an abrupt increase in the correlation length to an anomalously large but finite value as the parameters of the model are varied this behaviour may be misinterpreted as a genuine phase transition a simple mechanism for this sharp increase is presented the mechanism is introduced within the framework of a recently suggested correspondence between driven diffusive systems and zero range processes it is shown that when the dynamics of the model is such that small domains are suppressed in the steady state distribution anomalously large correlation lengths may build up the mechanism is examined in detail in two models

the winding angle distribution of an ordinary random walk the winding angle about a selected point of a random walk quantifies what is perhaps the simplest manifestation of entanglement a phenomenon of great importance in the study of polymers the distribution of winding angles is studied here for ordinary or non self avoiding walks new results highlight the crucial influence of the exclusion of a finite region about the selected point on the winding angle distribution the results of this analysis are compared with simulations of random walks on a lattice the agreement between the two is very good there are however small and as yet unexplained discrepancies

an approach to the conditional error rate principle with nuisance parameters summary in the presence of nuisance parameters the conditional error rate principle is difficult to apply because of the dependency of the conditional error function of the preplanned test on nuisance parameters to use the conditional error rate principle with nuisance parameters we propose to search among tests that guarantee overall error control for the test that maximizes a weighted combination of the conditional error rates over possible values of the nuisance parameters we show that the optimization problem that defines such a test can be solved efficiently by existing algorithms

controlling test size while gaining the benefits of an internal pilot design summary to compensate for a power analysis based on a poor estimate of variance internal pilot designs use some fraction of the planned observations to reestimate error variance and modify the final sample size ignoring the randomness of the final sample size may bias the final variance estimate and inflate test size we propose and evaluate three different tests that control test size for an internal pilot in a general linear univariate model with fixed predictors and gaussian errors test 1 uses the first sample plus those observations guaranteed to be collected in the second sample for the final variance estimate test 2 depends mostly on the second sample for the final variance estimate test 3 uses the unadjusted variance estimate and modifies the critical value to bound test size we also examine three sample size modification rules only test 2 can control conditional test size align with a modification rule and provide simple power calculations we recommend it if the minimum second incremental sample is at least moderate perhaps 20 otherwise the bounding test appears to have the highest power in small samples reanalyzing published data highlights some advantages and disadvantages of the various tests

power calculations for general linear multivariate models including repeated measures applications abstract recently developed methods for power analysis expand the options available for study design we demonstrate how easily the methods can be applied by 1 reviewing their formulation and 2 describing their application in the preparation of a particular grant proposal the focus is a complex but ubiquitous setting repeated measures in a longitudinal study describing the development of the research proposal allows demonstrating the steps needed to conduct an effective power analysis discussion of the example also highlights issues that typically must be considered in designing a study first we discuss the motivation for using detailed power calculations focusing on multivariate methods in particular second we survey available methods for the general linear multivariate model glmm with gaussian errors and recommend those based on f approximations the treatment includes coverage of the multivariate and univariate approaches to repeated measures manova anova multivariate regression and

dynamical windings of random walks and exclusion models part i thermodynamic limit in bbb z2 we consider a system consisting of a planar random walk on a square lattice subjected to stochastic elementary local deformations both numerical and theoretical results are reported depending on the deformation transition rates and specifically on a parameter which breaks the symmetry between the left and right orientation the winding distribution of the walk is modified and the system can be in three different phases folded stretched and glassy an explicit mapping is found leading to consider the system as a coupling of two exclusion processes particles of the first one move in a landscape defined by particles of the second one and vice versa this can be viewed as an inhomogeneous exclusion process for all closed or periodic initial sample paths a convenient scaling permits to show a convergence in law or almost surely on a modified probability space to a continuous curve the equation of which is given by a system of two non linear stochastic differential equations the deterministic part of this system is explicitly analyzed via elliptic functions in a similar way by using a formal fluid limit approach the dynamics of the system is shown to be equivalent to a system of two coupled burgers equations

asymptotic laws of planar brownian motion on presente des resultats recents sur la distribution asymptotique des nombres de passages et d enroulements

brownian charges around loops let x t n be a poisson sequence of independent brownian motions in d d 3 let be a compact oriented submanifold of d of dimensiond 2 and volume l let t be the sum of the windings of x s n 0 s t around then t t converges in law towards a cauchy variable of parameter l 2 a similar result is valid when the winding is replaced by the integral of a harmonic 1 form in d

beyond multiple continuum modeling for the simulation of complex flow mechanisms in multiscale shale porous media abstract simulation of mass transfer in shale porous media continues to challenge the hydrocarbon recovery industry due the involved complex porous media transport mechanisms and complicated porous structures in this paper we present a new multiscale approach to improve the simulation of gas flow in shale porous media based on a coupled triple continuum and discrete fracture model gas transport in shale formations entails porous media flow through matrix which contains organic and inorganic matters and fractures the fractures consist of small scale natural fractures and large scale artificial fractures from hydraulic fracturing in the triple continuum model kerogen matrix inorganic matrix and natural fractures are modeled as three superimposed continua the hydraulic fractures are handled by discrete fracture model using a framework via the multiscale mixed finite element method our methodology couples the triple continuum model and discrete fracture model in a rigorous and systematic approach the method can capture the small scale features of gas flow through multiscale basis functions calculated based on the triple continuum background we go beyond multiple continuum modeling by enabling explicit discrete fracture representation in our multiscale framework as a result our approach could avoid some oversimplified assumptions made in conventional triple continuum models and enjoy explicit fracture treatment with high computational efficiency numerical aspects of the new approach are detailed with examples demonstrating its efficiency and accuracy for simulating gas flow in shale porous media with multiscale porous features

blinded sample size re estimation in three arm trials with gold standard design in this article we study blinded sample size re estimation in the gold standard design with internal pilot study for normally distributed outcomes the gold standard design is a three arm clinical trial design that includes an active and a placebo control in addition to an experimental treatment we focus on the absolute margin approach to hypothesis testing in three arm trials at which the non inferiority of the experimental treatment and the assay sensitivity are assessed by pairwise comparisons we compare several blinded sample size re estimation procedures in a simulation study assessing operating characteristics including power and type i error we find that sample size re estimation based on the popular one sample variance estimator results in overpowered trials moreover sample size re estimation based on unbiased variance estimators such as the xing ganju variance estimator results in underpowered trials as it is expected because an overestimation of the variance and thus the sample size is in general required for the re estimation procedure to eventually meet the target power to overcome this problem we propose an inflation factor for the sample size re estimation with the xing ganju variance estimator and show that this approach results in adequately powered trials because of favorable features of the xing ganju variance estimator such as unbiasedness and a distribution independent of the group means the inflation factor does not depend on the nuisance parameter and therefore can be calculated prior to a trial moreover we prove that the sample size re estimation based on the xing ganju variance estimator does not bias the effect estimate copyright 2017 john wiley sons ltd

sensitivity of spin glass order to temperature changes by a loop expansion around parisi s mean field theory for an ising spin glass it is shown that the overlap of the magnetization patterns belonging to two different temperatures t and t vanishes to any order si t si t 0 while the correlation overlap sisj t sisj t calculated to first loop order and for technical reasons for dimensions d 8 only is found to decay exponentially with a characteristic length approximately t t 1

power calculation for overall hypothesis testing with high dimensional commensurate outcomes the complexity of system biology means that any metabolic genetic or proteomic pathway typically includes so many components e g molecules that statistical methods specialized for overall testing of high dimensional and commensurate outcomes are required while many overall tests have been proposed very few have power and sample size methods we develop accurate power and sample size methods and software to facilitate study planning for high dimensional pathway analysis with an account of any complex correlation structure between high dimensional outcomes the new methods allow power calculation even when the sample size is less than the number of variables we derive the exact finite sample and approximate non null distributions of the univariate approach to repeated measures test statistic as well as power equivalent scenarios useful to generalize our numerical evaluations extensive simulations of group comparisons support the accuracy of the approximations even when the ratio of number of variables to sample size is large we derive a minimum set of constants and parameters sufficient and practical for power calculation using the new methods and specifying the minimum set to determine power for a study of metabolic consequences of vitamin b6 deficiency helps illustrate the practical value of the new results free software implementing the power and sample size methods applies to a wide range of designs including one group pre intervention and post intervention comparisons multiple parallel group comparisons with one way or factorial designs and the adjustment and evaluation of covariate effects

optimal conditional error functions for the control of conditional power ethical considerations and the competitive environment of clinical trials usually require that any given trial have sufficient power to detect a treatment advance if at an interim analysis the available data are used to decide whether the trial is promising enough to be continued investigators and sponsors often wish to have a high conditional power which is the probability to reject the null hypothesis given the interim data and the alternative of interest under this requirement a design with interim sample size recalculation which keeps the overall and conditional power at a prespecified value and preserves the overall type i error rate is a reasonable alternative to a classical group sequential design in which the conditional power is often too small in this article two stage designs with control of overall and conditional power are constructed that minimize the expected sample size either for a simple point alternative or for a random mixture of alternatives given by a prior density for the efficacy parameter the presented optimality result applies to trials with and without an interim hypothesis test in addition one can account for constraints such as a minimal sample size for the second stage the optimal designs will be illustrated with an example and will be compared to the frequently considered method of using the conditional type i error level of a group sequential design

adjusting power for a baseline covariate in linear models the analysis of covariance provides a common approach to adjusting for a baseline covariate in medical research with gaussian errors adding random covariates does not change either the theory or the computations of general linear model data analysis however adding random covariates does change the theory and computation of power analysis many data analysts fail to fully account for this complication in planning a study we present our results in five parts i a review of published results helps document the importance of the problem and the limitations of available methods ii a taxonomy for general linear multivariate models and hypotheses allows identifying a particular problem iii we describe how random covariates introduce the need to consider quantiles and conditional values of power iv we provide new exact and approximate methods for power analysis of a range of multivariate models with a gaussian baseline covariate for both small and large samples the new results apply to the hotelling lawley test and the four tests in the univariate approach to repeated measures unadjusted huynh feldt geisser greenhouse box the techniques allow rapid calculation and an interactive graphical approach to sample size choice v calculating power for a clinical trial of a treatment for increasing bone density illustrates the new methods we particularly recommend using quantile power with a new satterthwaite style approximation

a locally conservative enriched galerkin approximation and efficient solver for elliptic and parabolic problems we present and analyze an enriched galerkin finite element method eg to solve elliptic and parabolic equations with jump coefficients eg is formulated by enriching the conforming continuous galerkin finite element method cg with piecewise constant functions which can be considered as a penalty stabilization the method is shown to be locally and globally conservative while keeping fewer degrees of freedom in comparison with discontinuous galerkin finite element methods dg moreover we present and analyze a fast effective eg solver whose cost is roughly that of cg and which can handle an arbitrary order of approximations a number of numerical tests in two and three dimensions are presented to confirm our theoretical results as well as to demonstrate the advantages of eg when coupled with transport

global hypothesis testing for high dimensional repeated measures outcomes high throughput technology in metabolomics genomics and proteomics gives rise to high dimension low sample size data when the number of metabolites genes or proteins exceeds the sample size for a limited class of designs the classic univariate approach for gaussian repeated measures can provide a reasonable global hypothesis test we derive new tests that not only accurately allow more variables than subjects but also give valid analyses for data with complex between subject and within subject designs our derivations capitalize on the dual of the error covariance matrix which is nonsingular when the number of variables exceeds the sample size to ensure correct statistical inference and enhance computational efficiency simulation studies demonstrate that the new tests accurately control type i error rate and have reasonable power even with a handful of subjects and a thousand outcome variables we apply the new methods to the study of metabolic consequences of vitamin b6 deficiency free software implementing the new methods applies to a wide range of designs including one group pre intervention and post intervention comparisons multiple parallel group comparisons with one way or factorial designs and the adjustment and evaluation of covariate effects copyright 2011 john wiley sons ltd

physics based preconditioners for flow in fractured porous media discrete fracture models are an attractive alternative to upscaled models for flow in fractured media as they provide a more accurate representation of the flow characteristics a major challenge in discrete fracture simulation is to overcome the large computational cost associated with resolving the individual fractures in large scale simulations in this work two characteristics of the fractured porous media are utilized to construct efficient preconditioners for the discretized flow equations first the preconditioners are tailored to the fracture geometry and presumed flow properties so that the dominant features are well represented there this assures good scalability of the preconditioners in terms of problem size and permeability contrast for fracture dominated problems numerical examples show that such geometric preconditioners are comparable or preferable when compared to state of the art algebraic multigrid preconditioners the robustness of the physics based preconditioner for less favorable fracture conditions is further demonstrated by a systematic degradation of the fracture hierarchy second the preconditioners are physics preserving in the sense that conservative fluxes can be computed even for an inexact pressure solutions this facilitates a scheme where accuracy in the linear solver can be traded for efficiency by terminating the iterative solvers based on error estimates and without sacrificing basic physical modeling principles with the combination of these two properties a novel preconditioner is obtained which bridges the gap between multiscale approximations and iterative linear solvers

planning and revising the sample size for a trial the sample size for a trial depends on the type i and type ii error rates and on the minimum relevant clinical difference all of which are known and on the anticipated but unknown value of a measure of variation for the key response this measure is the overall response rate when the key response is binomially distributed or the residual variance in each treatment group when the key response is continuous and normally distributed since the true value of the measure is unknown it must be guessed or estimated from previous trials we describe approaches to determine an appropriate value for it both before the trial begins and after it has begun for use in calculating the final sample size these approaches differ from previously described internal pilot methods in not requiring unblinding of the treatment assignments in the trial they preserve the power and do not affect the type i error rate materially the approaches can be applied to longitudinal studies where the rate of change over time is the response of interest and to group sequential trials

locally conservative galerkin and finite volume methods for two phase flow in porous media in this paper we propose a locally conservative galerkin lcg finite element method for two phase flow simulations in heterogeneous porous media the main idea of the method is to use the property of local conservation at steady state conditions in order to define a numerical flux at element boundaries it provides a way to apply standard galerkin finite element method in two phase flow simulations in porous media the lcg method has all the advantages of the standard finite element method while explicitly conserving fluxes over each element all the examples presented show that the formulation employed is accurate and robust while using less cpu time than finite volume method

on the use of a pilot sample for sample size determination to compute the sample size needed to achieve the planned power for a t test one needs an estimate of the population standard deviation sigma if one uses the sample standard deviation from a small pilot study as an estimate of sigma it is quite likely that the actual power for the planned study will be less than the planned power monte carlo simulations indicate that using a 100 1 gamma per cent upper one sided confidence limit on sigma will provide a sample size sufficient to achieve the planned power in at least 100 1 gamma per cent of such trials

finite element techniques for modeling groundwater flow in fractured aquifers a mathematical description of groundwater flow in fractured aquifers is presented four alternative conceptual models are considered the first three are based on the dual porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks and the fourth is based on the discrete fracture approach two numerical solution techniques are presented for solving the governing equations associated with the dual porosity flow models in the first technique the galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks in the second the galerkin finite element approximation is used in conjunction with a one dimensional finite difference approximation to handle flow in the fractures and matrix blocks respectively both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model to verify the proposed numerical techniques and compare various conceptual models four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed each simulation corresponded to one of the four conceptual models for the three simulated cases where analytical solutions are available the numerical and the analytical solutions were compared it was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations greater accuracy was achieved by the combined finite element convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture matrix interface could not be accommodated by the linear finite difference approximation finally the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models

on the joint residence time of n independent two dimensional brownian motions we study the behaviour of several joint residence times of n independent brownian particles in a disc of radius r in two dimensions we consider i the time tn t spent by all n particles simultaneously in the disc within the time interval 0 t ii the time t m n t which at least m out of n particles spend together in the disc within the time interval 0 t and iii the time m n t which exactly m out of n particles spend together in the disc within the time interval 0 t we obtain very simple exact expressions for the expectations of these three residence times in the limit t

evaluation of experiments with adaptive interim analyses summary a general method for statistical testing in experiments with an adaptive interim analysis is proposed the method is based on the observed error probabilities from the disjoint subsamples before and after the interim analysis formally an intersection of individual null hypotheses is tested by combining the twop values into a global test statistic stopping rules for fisher s product criterion in terms of critical limits for the p value in the first subsample are introduced including early stopping in the case of missing effects the control of qualitative treatment stage interactions is considered a generalization to three stages is outlined the loss of power when using the product criterion instead of the optimal classical test on the whole sample is calculated for the test of the mean of a normal distribution depending on increasing proportions of the first subsample in relation to the total sample size an upper bound on the loss of power due to early stopping is derived a general example is presented and rules for assessing the sample size in the second stage of the trial are given the problems of interpretation and precautions to be taken for applications are discussed finally the sources of bias for estimation in such designs are described

adaptive design and estimation in randomized clinical trials with correlated observations summary clinical trial designs involving correlated data often arise in biomedical research the intracluster correlation needs to be taken into account to ensure the validity of sample size and power calculations in contrast to the fixed sample designs we propose a flexible trial design with adaptive monitoring and inference procedures the total sample size is not predetermined but adaptively reestimated using observed data via a systematic mechanism the final inference is based on a weighted average of the block wise test statistics using generalized estimating equations where the weight for each block depends on cumulated data from the ongoing trial when there are no significant treatment effects the devised stopping rule allows for early termination of the trial and acceptance of the null hypothesis the proposed design updates information regarding both the effect size and within cluster correlation based on the cumulated data in order to achieve a desired power estimation of the parameter of interest and its confidence interval are proposed we conduct simulation studies to examine the operating characteristics and illustrate the proposed method with an example

blinded sample size reassessment in non inferiority and equivalence trials even in situations where the design and conduct of clinical trials is highly standardized there may be a considerable between study variation in the observed variability of the primary outcome variable as a consequence performing a study in a fixed sample size design implies a considerable risk of resulting in a too high or too low sample size this difficulty can be alleviated by applying a design with internal pilot study after a provisional sample size calculation in the planning stage a portion of the planned sample is recruited and the sample size is recalculated on the basis of the observed variability to comply with the requirement of some regulatory guidelines only blinded data should be used for the reassessment procedure furthermore the effect on the type i error rate should be quantified the current literature presents analytical results on the actual level in the t test situation only for superiority trials in these situations blinded sample size recalculation does not lead to an inflation of the type i error rate we extended the methodology to non inferiority and equivalence trials with normally distributed outcome variable and hypotheses formulated in terms of the ratio and difference of means surprisingly in contrast to the case of testing superiority we observed actual type i error rates above the nominal level the extent of inflation depends on the required sample size the sample size of the internal pilot study and the standardized equivalence or non inferiority margin it turned out that the elevation of the significance level is negligible for most practical situations nevertheless the consequences of sample size reassessment have to be discussed case by case and regulatory concerns with respect to the actual size of the procedure cannot generally be refuted by referring to the fact that only blinded data were used

a locally conservative multiscale finite element method for multiphase flow simulation through heterogeneous and fractured porous media abstract a multiscale locally conservative galerkin mslcg method is proposed to accurately simulate multiphase flow in heterogeneous and fractured porous media mslcg employs a coarse partition of the fine grids and multiscale basis function for mapping the fine scale information to the coarse scale unknowns different from standard multiscale finite element method msfem the main improvement of our mslcg is to use the property of local conservation at steady state conditions to define a numerical flux at element boundaries mslcg provides a way to extend standard msfem to handle challenging multiphase flow problems in heterogeneous and fractured porous media mslcg preserves all the advantages of the standard msfem while it provides explicitly conservative fluxes through each element we present a number of representative numerical examples to demonstrate that our method is efficient and accurate for simulating multiphase flow through heterogeneous and fractured porous media

a topological problem in polymer physics configurational and mechanical properties of a random walk enclosing a constant are the authors show how a random walk in a plane constrained to enclose a given area can be used to approximately represent the properties of an entangled polymer molecule the statistical mechanical properties of the loop are calculated exactly and the distribution function for the enclosed areas is found for the case of a random walk with free ends joined by a straight line segment the distribution function is given by the cauchy distribution this implies that the area has statistical fractal properties but does not have a mean for a genuinely closed random walk a mean exists but the distribution of areas is not fractal the spatial and mechanical properties of the constrained configurations have also been calculated analytically if the unrestricted coil can be regarded as an entropic spring of zero natural length then the area constrained configurations behave qualitatively like springs with a finite natural length the deformation behaviour also shows both softening and hardening dependent on the area imposed

a method for determining the size of internal pilot studies the assessment of sample size in clinical trials comparing population means requires a variance estimate of the main efficacy variable when this variance estimate has a low precision it may be appropriate to use the data from the first patients entered in the trial internal pilot study to estimate the sample size we suggest a method for determining the size of internal pilot studies which aims at ensuring that this size is as large as possible but not larger than the optimal size of the planned study advantages and limitations of the method are discussed

penalized normal likelihood and ridge regularization of correlation and covariance matrices high dimensionality causes problems in various areas of statistics a particular situation that rarely has been considered is the testing of hypotheses about multivariate regression models in which

simple procedures for blinded sample size adjustment that do not affect the type i error rate for normally distributed data determination of the appropriate sample size requires a knowledge of the variance because of the uncertainty in the planning phase two stage procedures are attractive where the variance is reestimated from a subsample and the sample size is adjusted if necessary from a regulatory viewpoint preserving blindness and maintaining the ability to calculate or control the type i error rate are essential recently a number of proposals have been made for sample size adjustment procedures in the t test situation unfortunately none of these methods satisfy both these requirements we show through analytical computations that the type i error rate of the t test is not affected if simple blind variance estimators are used for sample size recalculation furthermore the results for the expected power of the procedures demonstrate that the methods are effective in ensuring the desired power even under initial misspecification of the variance a method is discussed that can be applied in a more general setting and that assumes analysis with a permutation test this procedure maintains the significance level for any design situation and arbitrary blind sample size recalculation strategy

issues in designing flexible trials we outline the general framework of adaptive combination tests and discuss their relationship to flexible group sequential designs an important field of applications is sample size reassessment we discuss reassessment rules based on conditional power arguments using either the observed or the prefixed effect size these rules tend to lead to large expected sample sizes for small actual effects however the application of a maximal bound for the second stage sample size leads to more favourable properties additionally we consider an optimized reassessment rule in terms of expected sample sizes since the adaptive design does not use the classical test statistics for some types of sample size reassessments the adaptive test may reject the null hypothesis while the classical one sample test does not we characterize sample size reassessment rules where such inconsistencies are avoided finally the extension of flexibility to the number of stages is explored in the first interim analysis a second interim analysis is only planned if the chance to achieve a decision there is high this leads to savings in the average number of interim analysis performed without paying a noticeable price in terms of expected sample size

estimation in flexible two stage designs adaptive test designs for clinical trials allow for a wide range of data driven design adaptations using all information gathered until an interim analysis the basic principle is to use a test statistics which is invariant with respect to the design adaptations under the null hypothesis this allows for a control of the type i error rate for the primary hypothesis even for adaptations not specified a priori in the study protocol estimation is usually another important part of a clinical trial however is more difficult in adaptive designs in this research paper we give an overview of point and interval estimates for flexible designs and compare methods for typical sample size rules we also make some proposals for confidence intervals which have nominal coverage probability also after an unforeseen design adaptation and which contain the maximum likelihood estimate and the usual unadjusted confidence interval

notes on the two dimensional fractional brownian motion we study the two dimensional fractional brownian motion with hurst parameter h 1 2 in particular we show using stochastic calculus that this process admits a skew product decomposition and deduce from this representation some asymptotic properties of the motion

properties of internal pilots with the univariate approach to repeated measures uncertainty surrounding the error covariance matrix often presents the biggest barrier to achieving accurate power analysis in the univariate approach to repeated measures analysis of variance unirep a poor choice gives either an overpowered study which wastes resources or an underpowered study with little chance of success internal pilot designs were introduced to resolve such uncertainty about error variance for t tests in earlier papers we extended the use of internal pilots to any univariate linear model with fixed predictors and independent gaussian errors here we further extend our exact and approximate results to unirep analysis for a fixed treatment effect the inaccuracy in a power calculation depends only on the ratio of the true variance to the value used for planning the greater complexity of repeated measures requires generalizing misspecification of error variance to the misspecification of the eigenvalues of the error covariance we recommend approximating the misspecification in terms of the first and second moments of the eigenvalues for both fixed sample and internal pilot designs we also describe an unadjusted approach for internal pilots with repeated measures simulations illustrate the fact that both positive and negative properties in the univariate setting extend to repeated measures analysis in particular internal pilots allow maintaining power or reducing expected sample size when the covariance matrix used for planning differs from the true value however an unadjusted approach can inflate test size at least with small to moderate sample sizes hence new adjusted methods must be developed for small samples at this time we caution against using an internal pilot design with repeated measures without first conducting simulations to document the amount of test size inflation possible for the conditions of interest

modification of sample size in group sequential clinical trials in group sequential clinical trials sample size reestimation can be a complicated issue when it allows for change of sample size to be influenced by an observed sample path our simulation studies show that increasing sample size based on an interim estimate of the treatment difference can substantially inflate the probability of type i error in most practical situations a new group sequential test procedure is developed by modifying the weights used in the traditional repeated significance two sample mean test the new test has the type i error probability preserved at the target level and can provide a substantial gain in power with the increase of sample size generalization of the new procedure is discussed

the winding of stationary gaussian processes this paper studies the winding of a continuously differentiable gaussian stationary process f mathbb r rightarrow mathbb c in the interval 0 t we give formulae for the mean and the variance of this random variable the variance is shown to always grow at least linearly with t and conditions for it to be asymptotically linear or quadratic are given moreover we show that if the covariance function together with its second derivative are in l 2 mathbb r then the winding obeys a central limit theorem these results correspond to similar results for zeroes of real valued stationary gaussian functions by malevich cuzick slud and others

an adaptive method for establishing a dose response relationship a multistage sampling method is proposed in dose response trials where dose adaptions can be performed in the preplanned adaptive interim analyses the overall test for proving a dose response relationship is performed by fisher s product criterion for the p values from the separate tests of a dose effect in the disjoint samples at the different stages based on these p values decision boundaries for early stopping with the rejection of the global null hypothesis of no existing dose response relationship are introduced the power of the adaptive two stage procedure using a particular adaptation rule is compared with the power of the test for a linear trend under analysis of variance assumptions in extensive simulations the bias in estimation is also quantified this procedure could be used for establishing a dose response relationship without including a placebo treatment

asymptotic winding angle distributions for planar brownian motion with drift we study the asymptotic winding angle distribution of a two dimensional brownian curve around a given point the influence of boundaries and or drifts on this distribution is addressed in particular we show that for some special drifts the limiting distribution is given in terms of levy laws

control volume method for numerical simulation of two phase immiscible flow in two and three dimensional discrete fractured media 1 we provide a numerical procedure for the simulation of two phase immiscible and incompressible flow in two and three dimensional discrete fractured media the concept of cross flow equilibrium is used to reduce the fracture dimension from n to n 1 in the calculation of flow in the fractures this concept which is often referred to as the discrete fracture model has a significant effect on the reduction of computational time the spatial discretization is performed with the control volume method this method is locally conservative and allows the use of unstructured grids to represent complex geometries such as discrete fracture configurations the relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes which is consistent with the physics of fluid flow the system of partial differential equations is decoupled and solved using the implicit pressure explicit saturation impes approach the algorithm has been successfully tested in two and three dimensional numerical simulations of wetting phase fluid injection such as water in discrete fractured media saturated by a nonwetting phase such as nonaqueous phase liquid or oil with mild to high nonlinearity in relative permeability and capillary pressure to the best of our knowledge results for simulations of two phase immiscible and incompressible flow in three dimensional discrete fractured media including capillary and gravity effects are the first to appear in the literature

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

stochastic dynamics of discrete curves and multi type exclusion processes this study deals with continuous limits of interacting one dimensional diffusive systems arising from stochastic distortions of discrete curves with various kinds of coding representations these systems are essentially of a reaction diffusion nature in the non reversible case the invariant measure has in general a non gibbs form the corresponding steady state regime is analyzed in detail by using a tagged particle together with a state graph cycle expansion of the probability currents as a consequence the constants appearing in lotka volterra equations which describe the fluid limits of stationary states can be traced back directly at the discrete level to tagged particle cycles coefficients current fluctuations are also studied and the lagrangian is obtained via an iterative scheme the related hamilton jacobi equation which leads to the large deviation functional is investigated and solved in the reversible case just for the sake of checking

estimating the sample size for a t test using an internal pilot if the sample size for a t test is calculated on the basis of a prior estimate of the variance then the power of the test at the treatment difference of interest is not robust to misspecification of the variance we propose a t test for a two treatment comparison based on stein s two stage test which involves the use of an internal pilot to estimate variance and thus the final sample size required we evaluate our procedure s performance and show that it controls the type i and ii error rates more closely than existing methods for the same problem we also propose a rule for choosing the size of the internal pilot and show that this is reasonable in terms of the efficiency of the procedure

a comparison of adaptive allocation rules for group sequential binary response clinical trials in clinical trials to compare two or more treatments with dichotomous responses group sequential designs may reduce the total number of patients involved in the trial and response adaptive designs may result in fewer patients being assigned to the inferior treatments in this paper we combine group sequential and response adaptive designs extending recent work on sample size re estimation in trials to compare two treatments with normally distributed responses to analogous binary response trials we consider the use of two parameters of interest in the group sequential design the log odds ratio and the simple difference between the probabilities of success in terms of the adaptive sampling rules we study two urn models the drop the loser rule and the randomized polya urn rule and compare their properties with those of two sequential maximum likelihood estimation rules which minimize the expected number of treatment failures we investigate two ways in which adaptive urn designs can be used in conjunction with group sequential designs the first method updates the urn at each interim analysis and the second method continually updates the urn after each patient response assuming immediate patient responses our simulation results show that the group sequential design which uses the drop the loser rule applied fully sequentially is the most effective method for reducing the expected number of treatment failures and the average sample number whilst still maintaining the nominal error rates over a range of success probabilities

phase transition in the abc model recent studies have shown that one dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules the mathrm abc model which comprises three particle species that diffuse asymmetrically around a ring shows anomalous coarsening into a phase separated steady state in the limiting case in which the dynamics is symmetric and the parameter q describing the asymmetry tends to one no phase separation occurs and the steady state of the system is disordered in the present work we consider the weak asymmetry regime q mathrm exp ensuremath ensuremath beta n where n is the system size and study how the disordered state is approached in the case of equal densities we find that the system exhibits a second order phase transition at some nonzero ensuremath beta c the value of ensuremath beta c 2 ensuremath pi sqrt 3 and the optimal profiles can be obtained by writing the exact large deviation functional for nonequal densities we write down mean field equations and analyze some of their predictions

interim analysis and sample size reassessment this article deals with sample size reassessment for adaptive two stage designs based on conditional power arguments utilizing the variability observed at the first stage fisher s product test for the p values from the disjoint samples at the two stages is considered in detail for the comparison of the means of two normal populations we show that stopping rules allowing for the early acceptance of the null hypothesis that are optimal with respect to the average sample size may lead to a severe decrease of the overall power if the sample size is a priori underestimated this problem can be overcome by choosing designs with low probabilities of early acceptance or by midtrial adaptations of the early acceptance boundary using the variability observed in the first stage this modified procedure is negligibly anticonservative and preserves the power

multicomponent fluid flow by discontinuous galerkin and mixed methods in unfractured and fractured media 1 a discrete fracture model for the flow of compressible multicomponent fluids in homogeneous heterogeneous and fractured media is presented in single phase in the numerical model we combine the mixed finite element mfe and the discontinuous galerkin dg methods we use the cross flow equilibrium concept to approximate the fractured matrix mass transfer the discrete fracture model is numerically superior to the single porosity model and overcomes limitations of the dual porosity models including the use of a shape factor the mfe method provides a direct and accurate approximation for the velocity field which is crucial for the convective terms in the flow equations the dg method associated with a slope limiter is used to approximate the species balance equations this method can capture the sharp moving fronts the calculation of the fracture fracture flux across three and higher intersecting fracture branches is a challenge in this work we provide an accurate approximation of these fluxes by using the mfe formulation numerical examples in unfractured and fractured media illustrate the efficiency and robustness of the proposed numerical model

internal pilot studies ii comparison of various procedures the two stage design involves sample size recalculation using an interim variance estimate stein proposed the design in 1945 biostatisticians recently have shown renewed interest in it wittes and brittain proposed a modification aimed at greater efficiency gould and shih proposed a similar procedure but with a different interim variance estimate based on blinded data we compare the power of stein s original test an idealized version of the wittes brittain test and a theoretical optimal test which can be approximated in practice we also compare two procedures that control the conditional type i error rate given the actual final sample size gould and shih s procedure and a newly proposed second segment procedure the comparison among the first three procedures indicates that the stein test is unexpectedly the test of choice under the original design alternative whereas the approximate optimal and wittes brittain procedures appear to have superior power for detecting smaller treatment differences as between the latter two procedures the second segment procedure is more powerful when many observations are likely to be taken after the interim resizing whereas otherwise the gould shih procedure is superior

adaptive sample size calculations in group sequential trials a method for group sequential trials that is based on the inverse normal method for combining the results of the separate stages is proposed without exaggerating the type i error rate this method enables data driven sample size reassessments during the course of the study it uses the stopping boundaries of the classical group sequential tests furthermore exact test procedures may be derived for a wide range of applications the procedure is compared with the classical designs in terms of power and expected sample size

sample size recalculation using conditional power the sample size required to achieve a given power at a prespecified absolute difference in mean response may depend on one or more nuisance parameters which are usually unknown proposed methods for using an internal pilot to recalculate the sample size using estimates of these parameters have been well studied most of these methods ignore the fact that data on the parameter of interest from within this internal pilot will contribute towards the value of the final test statistic we propose a method which involves recalculating the target sample size by computing the number of further observations required to maintain the probability of rejecting the null hypothesis at the end of the study under the prespecified absolute difference in mean response conditional on the data observed so far we do this within the framework of a two group error spending sequential test modified so as to prevent inflation of the type i error rate

statistical tests with accurate size and power for balanced linear mixed models the convenience of linear mixed models for gaussian data has led to their widespread use unfortunately standard mixed model tests often have greatly inflated test size in small samples many applications with correlated outcomes in medical imaging and other fields have simple properties which do not require the generality of a mixed model alternately stating the special cases as a general linear multivariate model allows analysing them with either the univariate or multivariate approach to repeated measures unirep multirep even in small samples an appropriate unirep or multirep test always controls test size and has a good power approximation in sharp contrast to mixed model tests hence mixed model tests should never be used when one of the unirep tests uncorrected huynh feldt geisser greenhouse box conservative or multirep tests wilks hotelling lawley roy s pillai bartlett apply convenient methods give exact power for the uncorrected and box conservative tests simulations demonstrate that new power approximations for all four unirep tests eliminate most inaccuracy in existing methods in turn free software implements the approximations to give a better choice of sample size two repeated measures power analyses illustrate the methods the examples highlight the advantages of examining the entire response surface of power as a function of sample size mean differences and variability

approximate power for repeated measures anova lacking sphericity abstract violation of sphericity of covariance across repeated measures inflates type i error rates in univariate repeated measures analysis of variance hence the use of geisser greenhouse or huynh feldt is now common to provide improved type i error rate with nonsphericity no method has been available to compute power a convenient method is suggested for approximating power and test size under nonsphericity new approximations are suggested for a a weighted sum of independent noncentral 2 s b the trace of a noncentral wishart or pseudo wishart matrix c the expected values of and and d the noncentral test statistic whether corrected or uncorrected the new approximations are extensions of the work of box 1954a b and satterthwaite 1941 the method performed well when evaluated against published and new simulations

the reassessment of trial perspectives from interim data a critical view if an interim analysis is performed during a trial it is tempting to determine the conditional power to reach a rejection in the trial given the observed results in the interim analysis since the true effect size is unknown the conditional power may be calculated by using the effect size which the study has been powered for in the planning phase or by using an interim estimate of the true size or a combination of both in either case the conditional power is a random variable and its density is investigated depending on the analysis time and the true effect size under the null hypothesis in early interim analyses after a small proportion of sample units the conditional power typically will be close to the overall power when the effect size from the planning stage is used for calculation in this case the majority of observations must still be made and the small first stage sample in general will be dominated by the hypothetical second stage chance based on the wrong parameter value it is shown that the conditional power in moderately underpowered studies can have a distribution symmetric around 0 5 when using the interim estimate for calculating the conditional power the density in general will be u shaped the impact of using conditional power to reassess the sample size using flexible two stage combination tests is shown for a specific example in terms of overall power and average sample size as compared to the corresponding group sequential design for small true effect sizes mid trial sample size recalculation based on an interim estimate may lead to an overly large price to be paid in average sample size in relation to the gain in overall power finally the problem is discussed in terms of estimating the true conditional power

a two sample test for high dimensional data with applications to gene set testing we proposed a two sample test for means of high dimensional data when the data dimension is much larger than the sample size the classical hotelling s t 2 test does not work for this large p small n situation the proposed test does not require explicit conditions on the relationship between the data dimension and sample size this offers much flexibility in analyzing high dimensional data an application of the proposed test is in testing significance for sets of genes which we demonstrate in an empirical study on a leukemia data set

exact test size and power of a gaussian error linear model for an internal pilot study wittes and brittain recommended using an internal pilot study to adjust sample size the approach involves five steps in testing a general linear hypothesis for a general linear univariate model with gaussian errors first specify the design hypothesis desired test size power a smallest clinically meaningful effect and a speculated error variance second conduct a power analysis to choose provisionally a planned sample size third collect a specified proportion of the planned sample as the internal pilot sample and estimate the variance but do not test the hypothesis fourth update the power analysis with the variance estimate to adjust the total sample size fifth finish the study and test the hypothesis with all data we describe methods for computing exact test size and power under this scenario our analytic results agree with simulations of wittes and brittain furthermore our exact results apply to any general linear univariate model with fixed predictors which is much more general than the two sample t test considered by wittes and brittain in addition our results allow for examination of the impact on test size of internal pilot studies for more complicated designs in the framework of the general linear model we examine the impact of i small samples ii allowing the planned sample size to decrease iii the choice of internal pilot sample size and iv the maximum allowable size of the second sample all affect test size power and expected total sample size we present a number of examples including one that uses an internal pilot study in a three group analysis of variance

designed extension of studies based on conditional power we propose a flexible method of extending a study based on conditional power the possibility for extension when the p value at the planned end is small but not statistically significant is built in to the design of the study the significance of the treatment difference at the planned end is used to determine the number of additional observations needed and the critical value necessary for use after accruing those additional observations it may therefore be thought of as a two stage procedure even though the observed treatment difference at stage 1 is used to make decisions the type i error rate is protected

internal pilot studies i type i error rate of the naive t test when sample size is recalculated using unblinded interim data use of the usual t test at the end of a study may lead to an elevated type i error rate this paper describes a numerical quadrature investigation to calculate the true probability of rejection as a function of the time of the recalculation the magnitude of the detectable treatment effect and the ratio of the guessed to the true variance we consider both restricted designs those that require final sample size at least as large as the originally calculated size and unrestricted designs those that permit smaller final sample sizes than originally calculated our results indicate that the bias in the type i error rate is often negligible especially in restricted designs some sets of parameters however induce non trivial bias in the unrestricted design

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100