on the inappropriateness of an em algorithm based procedure for blinded sample size re estimation when planning a clinical trial the sample size calculation is commonly based on an a priori estimate of the variance of the outcome variable misspecification of the variance can have substantial impact on the power of the trial it is therefore attractive to update the planning assumptions during the ongoing trial using an internal estimate of the variance for this purpose an em algorithm based procedure for blinded variance estimation was proposed for normally distributed data various simulation studies suggest a number of appealing properties of this procedure in contrast we show that i the estimates provided by this procedure depend on the initialization ii the stopping rule used is inadequate to guarantee that the algorithm converges against the maximum likelihood estimator and iii the procedure corresponds to the special case of simple randomization which however in clinical trials is rarely applied further we show that maximum likelihood estimation leads to no reasonable results for blinded sample size re estimation due to bias and high variability the problem is illustrated by a clinical trial in asthma

numerical analysis of quasioptical multireflector antennas in 2 d with the method of discrete singularities e wave case numerical method for modeling the e polarized wave scattering by electrically large quasioptical two dimensional 2 d reflectors is presented reflectors are assumed zero thickness and perfectly electrically conducting efficient numerical solution is obtained from the coupled singular integral equations discretized using new quadrature formulas of interpolation type it has controlled accuracy and deals with small size matrices to simulate a small horn feeding the incident field is taken as a beam generated by a complex source point csp current presented numerical results validate empirical rule of 10 db edge illumination needed to provide the best electromagnetic performance of reflector

fast smoothing of mixed volume meshes based on the effective geometric element transformation method abstract the geometric element transformation method getme is an efficient geometry driven approach to mesh smoothing it is based on regularizing element transformations which if applied iteratively to a single element improve its regularity and with this its quality the smoothing method has already successfully been applied in the case of mixed surface meshes as well as all tetrahedral and all hexahedral meshes in this paper a getme based approach for smoothing mixed volume meshes is presented for this purpose dual element based regularizing transformations for tetrahedral hexahedral pyramidal and prismatic elements are introduced and analyzed furthermore it is shown that the general concept of getme smoothing also applies to mixed volume meshes requiring only minor modifications numerical results demonstrate that high quality meshes comparable to those obtained by a state of the art global optimization based approach can be achieved within significantly shorter runtimes

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

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

an improved double sampling procedure based on the variance summary sample size calculations for a continuous outcome require specification of the anticipated variance inaccurate specification can result in an underpowered or overpowered study for this reason adaptive methods whereby sample size is recalculated using the variance of a subsample have become increasingly popular the first proposal of this type stein 1945 annals of mathematical statistics16 243 258 used all of the data to estimate the mean difference but only the first stage data to estimate the variance stein s procedure is not commonly used because many people perceive it as ignoring relevant data this is especially problematic when the first stage sample size is small as would be the case if the anticipated total sample size were small a more naive approach uses in the denominator of the final test statistic the variance estimate based on all of the data applying the helmert transformation we show why this naive approach underestimates the true variance and how to construct an unbiased estimate that uses all of the data we prove that the type i error rate of our procedure cannot exceed

variance estimation in clinical studies with interim sample size reestimation summary we consider clinical studies with a sample size reestimation based on the unblinded variance estimation at some interim point of the study because the sample size is determined in such a flexible way the usual variance estimator at the end of the trial is biased we derive sharp bounds for this bias these bounds have a quite simple form and can help for the decision if this bias is negligible for the actual study or if a correction should be done an exact formula for the bias is also provided we discuss possibilities to get rid of this bias or at least to reduce the bias substantially for this purpose we propose a certain additive correction of the bias we see in an example that the significance level of the test can be controlled when this additive correction is used

increasing the sample size when the unblinded interim result is promising increasing the sample size based on unblinded interim result may inflate the type i error rate and appropriate statistical adjustments may be needed to control the type i error rate at the nominal level we briefly review the existing approaches which allow early stopping due to futility or change the test statistic by using different weights or adjust the critical value for final test or enforce rules for sample size recalculation the implication of early stopping due to futility and a simple modification to the weighted z statistic approach are discussed in this paper we show that increasing the sample size when the unblinded interim result is promising will not inflate the type i error rate and therefore no statistical adjustment is necessary the unblinded interim result is considered promising if the conditional power is greater than 50 per cent or equivalently the sample size increment needed to achieve a desired power does not exceed an upper bound the actual sample size increment may be determined by important factors such as budget size of the eligible patient population and competition in the market the 50 per cent conditional power approach is extended to a group sequential trial with one interim analysis where a decision may be made at the interim analysis to stop the trial early due to a convincing treatment benefit or to increase the sample size if the interim result is not as good as expected the type i error rate will not be inflated if the sample size may be increased only when the conditional power is greater than 50 per cent if there are two or more interim analyses in a group sequential trial our simulation study shows that the type i error rate is also well controlled

group sequential tests for delayed responses with discussion summary group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect a lack of an effect or concerns about patient safety in many studies the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond we formulate a new form of group sequential test which gives a proper treatment of these pipeline subjects these tests can be applied even when the continued accrual of data after the decision to stop the trial is unexpected we illustrate our methods through a series of examples we define error spending versions of these new designs which handle unpredictable group sizes and provide an information monitoring framework that can accommodate nuisance parameters such as an unknown response variance by studying optimal versions of our new designs we show how the benefits of lower expected sample size that are normally achieved by a group sequential test are reduced when there is a delay in response the loss of efficiency for larger delays can be ameliorated by incorporating data on a correlated short term end point fitting a joint model for the two end points but still making inferences on the original longer term end point we derive p values and confidence intervals on termination of our new tests

3d hybrid mesh generation for reservoir simulation a great challenge for flow simulators of new generation is to gain more accuracy at well proximity within complex geological structures for this purpose a new approach based on hybrid mesh modelling was proposed in 2d by balaven et al proceedings of the 7th international conference on numerical grid generation in computational field simulations whistler canada 2000 407 416 in this hybrid mesh the reservoir is described by a structured quadrilateral mesh and drainage areas around wells are represented by radial circular meshes in order to generate a global conforming mesh unstructured transition meshes constituted by convex polygonal elements satisfying finite volume properties are used to connect these two structured meshes the hybrid mesh allows us to take full advantage of the simplicity and practical aspects of structured meshes while complexity inherent to unstructured meshes is introduced only where strictly needed this paper presents the 3d extension of the generation of such a hybrid mesh eccomas jyvaskyla finland 2004 the proposed method uses 3d power diagrams to generate the transition mesh due to the round off errors this mesh is modified in order to ensure the conformity with the structured meshes in addition some criteria are introduced to measure the mesh quality as well as an optimization procedure to remove or to expand small edges of the transition mesh under finite volume properties constraints numerical results are given to show the efficiency of the approach copyright 2005 john wiley sons ltd

optimal delaunay point insertion summary an efficient algorithm for delaunay triangulation of a given set of points in d dimensions is presented various steps of the point insertion algorithm are reviewed and many acceleration procedures are implemented to speed up the triangulation process new features include the search for a neighbouring point by a layering scheme locating the containing simplex by a random walk formulas of important geometrical quantities of a new simplex based on those of an old one a novel approach in establishing the adjacency relationship using connection matrices the resulting scheme seems to be one of the fastest triangulation algorithms known which enables us to generate tetrahedra in r3 with a linear generation rate of 15 ooo tetrahedra per second for randomly generated points on an hp 735 workstation

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

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

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

connections between permutation and t tests relevance to adaptive methods a permutation test assigns a p value by conditioning on the data and treating the different possible treatment assignments as random the fact that the conditional type i error rate given the data is controlled at level ensures validity of the test even if certain adaptations are made we show the connection between permutation and t tests and use this connection to explain why certain adaptations are valid in a t test setting as well we illustrate this with an example of blinded sample size re calculation

quadrature rules for weakly singular strongly singular and hypersingular integrals in boundary integral equation methods we present n point gauss gegenbauer quadrature rules for weakly singular strongly singular and hypersingular integrals that arise in integral equation formulations of potential problems in domains with edges and corners the rules are tailored to weight functions with algebraic endpoint singularities related to the geometrical singularities of the domain each rule has two different expressions involving legendre functions and hypergeometric functions respectively numerical examples amply demonstrate the accuracy and stability of the proposed algorithms application to the solution of a singular integral equation is exemplified

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

exponentially converging nystro spl uml m s methods for systems of singular integral equations with applications to open closed strip or slot loaded 2 d structures this paper concerns the fast highly accurate and exponentially convergent solution of three sets of integral equations pertaining to two dimensional generalized microstrip or microslot structures the analysis relies on nystroumlm s method with due regard to all singular integrals and slowly converging series that appear in the kernels the sophisticated treatment and efficient computation of such series and integrals is of paramount importance entailing the use of advanced techniques as a result of our specialized treatment the discretization procedures developed herein a fully account for both the singular nature of the kernels and the singularities of the solution at the edges b obviate the need for taking inner products with testing functions c appear to converge exponentially versus matrix size and d enable expressing all matrix elements via single finite sums detailed numerical examples and case studies illustrate the simplicity flexibility and remarkable efficiency of the algorithms

scattering and absorption of waves by flat material strips analyzed using generalized boundary conditions and nystrom type algorithm the scattering of the h and e polarized plane waves by a thin flat homogeneous magneto dielectric strip is considered assuming the strip to be thinner than the wavelength we shrink its cross section to the median line where the generalized boundary conditions are imposed the numerical solution is built on two singular integral equations discretized using nystrom type numerical algorithm the obtained results demonstrate fast convergence and good agreement with data known for the limiting values of the strip parameters this opens a way to the accurate numerical analysis of various striplike configurations simulating natural objects and electromagnetic circuit components both in traditional microwave applications and nanophotonics

exponentially converging nystrom methods in scattering from infinite curved smooth strips part 1 tm case low order subdomain basis methods of moments provide little help when highly accurate electromagnetic computations are required high order modeling on the other hand can fill the need for enhanced accuracy but at the expense of greater implementation cost to supplement such methods this paper presents nystrom techniques both easily implemented and highly accurate relevant to te scattering by arbitrarily shaped smooth infinite curved strips the analysis takes full account of both the singular nature of the kernels and the singularities of the solution at the edges as a result the proposed solutions are exponentially converging in addition by eliminating inner product integrals closed form analytical expressions are obtained for all matrix elements thus our algorithms have very low implementation and computational cost detailed numerical examples and case studies amply demonstrate the efficiency stability and extremely high accuracy of the algorithms these algorithms apply uniformly from electrically small to electrically large conducting screens with only slight modifications the present analysis can be also used to obtain exponentially converging galerkin solutions

power diagrams properties algorithms and applications the power pow x s of a point x with respect to a sphere s in euclidean d space e d is given by d 2 x z r 2 where d denotes the euclidean distance function and z and r are the center and the radius of s the power diagram of a finite set s of spheres in e d is a cell complex that associates each s in s with the convex domain x in e d operatorname pow x s operatorname pow x t text for all t in s s the close relationship to convex hulls and arrangements of hyperplanes is investigated and exploited efficient algorithms that compute the power diagram and its order k modifications are obtained among the applications of these results are algorithms for detecting k sets for union and intersection problems for cones and paraboloids and for constructing weighted voronoi diagrams and voronoi diagrams for spheres upper space bounds for these geometric problems are derived

voronoi diagram in the laguerre geometry and its applications we extend the concept of voronoi diagram in the ordinary euclidean geometry for n points to the one in the laguerre geometry for n circles in the plane where the distance between a circle and a point is defined by the length of the tangent line and show that there is an o n log n algorithm for this extended case the voronoi diagram in the laguerre geometry may be applied to solving effectively a number of geometrical problems such as those of determining whether or not a point belongs to the union of n circles of finding the connected components of n circles and of finding the contour of the union of n circles as in the case with ordinary voronoi diagrams the algorithms proposed here for those problems are optimal to within a constant factor some extensions of the problem and the algorithm from different viewpoints are also suggested

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