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

discrete mass spectrum of z n spin systems perturbed by a thermal field the author calculates numerically the lowest masses in the discrete mass spectrum of the z n fateev zamolodchikov spin model 1985 perturbed by a thermal operator the mass ratios obtained are in agreement with those derived from the s matrix introduced by koberle and swieca 1979

recursive combination tests we present a method that extends the flexibility of adaptive designs to the number of interim analyses and to the choice of decision boundaries at each stage of the trial the design of the next stage can be determined using all of the information gathered so far additionally one can specify the next stage as the final stage or can plan a further interim analysis the method is based on a recursive application of the two stage combination tests for p values the crucial point is the appropriate definition of a p value function that combines p values from two separate stages to a single p value formally we start with a two stage combination test however the p value of the second stage can be replaced by the p value of a further combination test this applies if the experimenter decides in the first interim analysis to perform another interim analysis thereby extending the design to at least three stages obviously this can be also done in a recursive way in the following interim analyses the test

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

group sequential methods for clinical trials allowing early acceptance of ho and incorporating costs summary when interim accumulated results from a clinical trial clearly indicate that the null hypothesis should be accepted or rejected ethical and cost considerations may dictate terminating the trial and making the appropriate decision pocock 1977 has described a group sequential procedure for clinical trials that permits early termination only for rejecting the null hypothesis this paper extends pocock s procedure to allow early termination with acceptance of the null hypothesis theoretical and simulation results demonstrate that designs allowing early acceptance of the null hypothesis can have lower expected costs than designs that do not even when the alternative hypothesis is true

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

form factors of descendant operators free field construction and reflection relations the free field representation for form factors in the sinh gordon model and the sine gordon model in the breather sector are modified to describe the form factors of descendant operators which are obtained from the exponential ones e i by means of the action of the heisenberg algebra associated with the field x as a check of the validity of the construction we count the numbers of operators defined by the form factors at each level in each chiral sector another check is related to the so called reflection relations which identify in the breather sector the descendants of the exponential fields e i and e i 2 0 for generic values of we prove the operators defined by the obtained families of form factors to satisfy such reflection relations a generalization of the construction for form factors to the kink sector is also proposed

effects of assumption violations on type i error rate in group sequential monitoring we compare the degree to which the type i error probability can be inflated by assumption violations under the different sequential monitoring schemes for methods that assume equally spaced time intervals between looks at the data we examine the effects of unequal spacings for methods that do not specify the look times in advance we examine the degree of type 1 error inflation that can result when future look times are chosen based on data trends we also evaluate a bayesian method of monitoring from this non bayesian perspective of type i error inflation

a two stage sample size recalculation procedure for placebo and active controlled non inferiority trials many non inferiority trials of a test treatment versus an active control may also if ethical incorporate a placebo arm inclusion of a placebo arm enables a direct assessment of assay sensitivity it also allows construction of a non inferiority test that avoids the problematic specification of an absolute non inferiority margin and instead evaluates whether the test treatment preserves a pre specified proportion of the effect of the active control over placebo we describe a two stage procedure for sample size recalculation in such a setting that maintains the desired power more closely than a fixed sample approach when the magnitude of the effect of the active control differs from that anticipated we derive an allocation rule for randomization under which the procedure preserves the type i error rate and show that this coincides with that previously presented for optimal allocation of the sample size among the three treatment arms

piezoelectric structural acoustic problems symmetric variational formulations and finite element results this paper presents an original symmetric finite element formulation for piezoelectric structural acoustic coupled problems first an unsymmetric variational formulation in terms of structure displacement electric potential and fluid pressure field is proposed then through the introduction of an additional variable namely fluid displacement potential a symmetric finite element formulation is presented finally after a rigorous condensation procedure and using the fluid added mass and piezoelectric added stiffness concepts a reduced symmetric formulation is obtained some numerical examples concerning axisymmetric elastic piezoelectric structures filled with internal compressible fluid are presented in order to validate the proposed formulation

on the inefficiency of the adaptive design for monitoring clinical trials summary adaptive designs which allow the sample size to be modified based on sequentially computed observed treatment differences have been advocated recently for monitoring clinical trials although such methods have a great deal of appeal on the surface we show that such methods are inefficient and that one can improve uniformly on such adaptive designs using standard group sequential tests based on the sequentially computed likelihood ratio test statistic

modelling and numerical solution of elastoacoustic vibrations with interface damping a finite element method is applied to compute the vibrations of an elastoacoustic system subject to an external harmonic excitation the effect of a thin layer of noise damping material between the fluid and the solid is taken into account by relaxing the interface kinematic condition of perfect contact we consider the non linear eigenvalue problem arising from the free vibration problem for the damped system for the case of a fluid in a rectangular rigid cavity with one absorbing wall we deduce the dispersion equation which allows computing analytically its eigenvalues and eigenmodes and compare the numerical solution with them finally we apply the finite element method to assess the effect of introducing a real viscoelastic material to damp the elastoacoustic vibrations of a coupled system copyright 1999 john wiley sons ltd

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

finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics a quadratic eigenvalue problem arising in the determination of the vibration modes of an acoustic fluid contained in a cavity with absorbing walls is considered the problem is shown to be equivalent to the spectral problem for a noncompact operator and a thorough spectral characterization is given a numerical discretization based on raviart thomas finite elements is analyzed the method is proved to be free of spurious modes and to converge with optimal order implementation issues and numerical experiments confirming the theoretical results are reported

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

free field representation for massive integrable models a new approach to massive integrable models is considered it allows one to find symmetry algebras which define the spaces of local operators and to get general integral representations for form factors in thesu 2 thirring and sine gordon models

quantum groups and generalized statistics in integrable models the paper deals with the integrable massive models of quantum field theory it is shown that generalized statistics of physical particles is closely connected with the invariance under quantum groups this invariance provides the possibility to construct quasi local operators parafermions possessing generalized statistics which interpolates the physical particles for the particular examples of sg rsg models and scaling 3 state potts model the parafermions are described completely all their matrix elements in the space of states are presented

adaptive and nonadaptive group sequential tests summary methods have been proposed for redesigning a clinical trial at an interim stage in order to increase power in order to preserve the type i error rate methods for unplanned design change have to be defined in terms of nonsufficient statistics and this calls into question their efficiency and the credibility of conclusions reached we evaluate schemes for adaptive redesign extending the theoretical arguments for use of sufficient statistics of tsiatis mehta 2003 and assessing the possible benefits of preplanned adaptive designs by numerical computation of optimal tests these optimal adaptive designs are concrete examples of optimal sequentially planned sequential tests proposed by schmitz 1993 we conclude that the flexibility of unplanned adaptive designs comes at a price and we recommend that the appropriate power for a study should be determined as thoroughly as possible at the outset then standard error spending tests possibly with unevenly spaced analyses provide efficient designs but it is still possible to fall back on flexible methods for redesign should study objective change unexpectedly once the trial is under way

vibration and transient response of structural acoustic interior coupled systems with dissipative interface this work concerns the variational formulation and the numerical computation of vibroacoustic interior problems with interface damping the coupled system consists of an elastic structure described by a displacement field containing an inviscid compressible and barotropic fluid described by a pressure field gravity effects being neglected within the context of noise reduction techniques we propose to investigate the effect of introducing a thin layer of damping material at the fluid structure interface the originality of this work lies in the introduction of an additional unknown field at the fluid structure interface namely the normal fluid displacement field with this new scalar unknown various interface damping models can be introduced in the variational formulation moreover the associated finite element matrix system can be written in a symmetric form and directly solved in frequency and time domains

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

efficient adaptive designs with mid course sample size adjustment in clinical trials adaptive designs have been proposed for clinical trials in which the nuisance parameters or alternative of interest are unknown or likely to be misspecified before the trial although most previous works on adaptive designs and mid course sample size re estimation have focused on two stage or group sequential designs in the normal case we consider here a new approach that involves at most three stages and is developed in the general framework of multiparameter exponential families this approach not only maintains the prescribed type i error probability but also provides a simple but asymptotically efficient sequential test whose finite sample performance measured in terms of the expected sample size and power functions is shown to be comparable to the optimal sequential design determined by dynamic programming in the simplified normal mean case with known variance and prespecified alternative and superior to the existing two stage designs and also to adaptive group sequential designs when the alternative or nuisance parameters are unknown or misspecified

a new finite element formulation for internal acoustic problems with dissipative walls this work concerns the variational formulation and the numerical computation of internal acoustic problems with absorbing walls the originality of the proposed approach compared to other existing methods is the introduction of the normal fluid displacement field on the damped walls this additional variable allows to transpose formulations in frequency domain to time domain when the fluid is described by a scalar field pressure or fluid displacement potential with this new scalar unknown various absorbing wall models can be introduced in the variational formulation moreover the associated finite element matrix system in symmetric form can be solved in frequency and time domain

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

numerical analysis of eigenproblem for cavities by a particular integral method with a low frequency approximation of surface admittance in this paper a three dimensional boundary element method for the eigenanalysis of complex shaped cavity is presented a particular integral method is proposed with general absorbing boundary conditions well suited for determination of the lower modes in this approach a polynomial approximation of surface admittance is used with a recent class of compactly supported radial basis function two common absorbent models are employed in order to demonstrate the relevance of high order approximation of the admittance resulting eigenproblems of several orders linear to cubic are thus performed on basic geometries and a car interior results show significant improvements for the computed damped eigenfrequencies and the associated modal reverberation time while using an approximation polynomial matching the surface admittance variation order

reduced models for fluid structure interaction problems several so called reduced order formulations are reviewed for linear vibration analysis of bounded fluid structure systems for low modal density situations compressibility effects in the fluid for interior structural acoustic problems and free surface gravity effects for hydroelastic sloshing interaction problems in the case of incompressible liquids are examined reduced order models leading to symmetric matrix systems are then described using the static well posed behaviour of the irrotational fluid in this respect the fluid structure boundary value local equations expressed in terms of fluid scalar field variables for the fluid and displacement variables for the structure are regularized for zero frequency limit copyright 2004 john wiley sons ltd

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

type i error in sample size re estimations based on observed treatment difference sample size re estimation based on an observed difference can ensure an adequate power and potentially save a large amount of time and resources in clinical trials one of the concerns for such an approach is that it may inflate the type i error however such a possible inflation has not been mathematically quantified in this paper the mathematical mechanism of this inflation is explored for two sample normal tests a conditional type i error function based on normal data is derived this function not only provides the quantification but also gives mathematical mechanisms of possible inflation in the type i error due to the sample size re estimation theoretically based on their decision rules certain upper and lower bounds people can calculate this function and exactly visualize the changes in type i error computer simulations are performed to ensure the results if there are no bounds for the adjustment the inflation is evident if proper adjusting rules are used the inflation can be well controlled in some cases the type i error can even be reduced the trade off is to give up some unrealistic power we investigated several scenarios in which the mechanisms to change the type i error are different our simulations show that similar results may apply to other distributions copyright 2001 john wiley sons ltd

free field construction for the abf models in regime ii the wakimoto construction for the quantum affine algebra u q widehat mathfrak s mathfrak l 2 admits a reduction to the q deformed parafermion algebras we interpret the latter theory as a free field realization of the andrews baxter forrester models in regime ii we give multi particle form factors of some local operators on the lattice and compute their scaling limit where the models are described by a massive field theory with mathbb z k symmetric minimal scattering matrices

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

efficient group sequential designs when there are several effect sizes under consideration we consider the construction of efficient group sequential designs where the goal is a low expected sample size not only at the null hypothesis and the alternative taken to be the minimal clinically meaningful effect size but also at more optimistic anticipated effect sizes pre specified type i error rate and power requirements can be achieved both by standard group sequential tests and by more recently proposed adaptive procedures we investigate four nested classes of designs a group sequential tests with equal group sizes and stopping boundaries determined by a monomial error spending function the rho family b as a but the initial group size is allowed to be different from the others c group sequential tests with arbitrary group sizes and arbitrary boundaries fixed in advance d adaptive tests as c but at each analysis future group sizes and critical values are updated depending on the current value of the test statistic by examining the performance of optimal procedures within each class we conclude that class b provides simple and efficient designs with efficiency close to that of the more complex designs of classes c and d we provide tables and figures illustrating the performances of optimal designs within each class and defining the optimal procedures of classes a and b

correlation functions of disorder fields and parafermionic currents in zn ising models we study the correlation functions of parafermionic currents and disorder fields in the zn symmetric conformal field theory perturbed by the first thermal operator following the ideas of al zamolodchikov zamolodchikov 1991 nucl phys b 348 619 zamolodchikov 1990 nucl phys b 342 695 and zamolodchikov 1995 int j mod phys a 10 1125 we develop for the correlation functions the conformal perturbation theory at small scales and the form factors spectral decomposition at large ones for all n there is an agreement between the data at the intermediate distances we consider the problems arising in the description of the space of scaling fields in perturbed models such as null vector relations equations of motion and a consistent treatment of fields related by a resonance condition

are flexible designs sound flexible designs allow large modifications of a design during an experiment in particular the sample size can be modified in response to interim data or external information a standard flexible methodology combines such design modifications with a weighted test which guarantees the type i error level however this inference violates basic inference principles in an example with independent n mu 1 observations the test rejects the null hypothesis of mu or 0 while the average of the observations is negative we conclude that flexible design in its most general form with the corresponding weighted test is not valid several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests

a differential equation for a four point correlation function in liouville field theory and elliptic four point conformal blocks liouville field theory on a sphere is considered we explicitly derive a differential equation for four point correlation functions with one degenerate field we also introduce and study a class of four point conformal blocks which can be calculated exactly and represented by finite dimensional integrals of elliptic theta functions for an arbitrary intermediate dimension we also study the bootstrap equations for these conformal blocks and derive integral representations for corresponding four point correlation functions a relation between the one point correlation function of a primary field on a torus and a special four point correlation function on a sphere is proposed

null vectors in integrable field theory the form factor bootstrap approach allows to construct the space of local fields in the massive restricted sine gordon model this space has to be isomorphic to that of the corresponding minimal model of conformal field theory we describe the subspaces which correspond to the verma modules of primary fields in terms of the commutative algebra of local integrals of motion and of a fermion neveu schwarz or ramond depending on the particular primary field the description of null vectors relies on the relation between form factors and deformed hyper elliptic integrals the null vectors correspond to the deformed exact forms and to the deformed riemann bilinear identity in the operator language the null vectors are created by the action of two operators linear in the fermion and quadratic in the fermion we show that by factorizing out the null vectors one gets the space of operators with the correct character in the classical limit using the operators and we obtain a new very compact description of the kdv hierarchy we also discuss a beautiful relation with the method of whitham

sequential monitoring of clinical trials the role of information and brownian motion sequential monitoring has been a topic of major interest in clinical trials methodology over the past two decades this paper presents a unified conceptual framework for sequential monitoring that covers a wide variety of monitoring procedures in a wide variety of clinical trial settings the central elements of this framework consist of a suitable concept of statistical information and a scheme for using this concept as a basis for summarizing the accumulating results of a trial in a standardized form through a stochastic process that can be shown to approximate classical brownian motion the ideas are developed in a simple step by step fashion and illustrated by several practical examples

monitoring clinical trials with a conditional probability stopping rule conditional probability procedures offer a flexible means of performing sequential analysis of clinical trials since these procedures are not based on repeated significance tests the number and schedule of the interim analyses is less important than with group sequential procedures their main disadvantage is that the magnitude of their effect on the significance level is difficult to assess this paper describes a conditional probability procedure which attempts to maintain the overall significance level by balancing the probabilities of false early rejection and false early acceptance monte carlo sampling results suggest that this procedure can achieve a large reduction in expected sample size without greatly affecting either the significance level or power of the trial

exact confidence bounds following adaptive group sequential tests summary we provide a method for obtaining confidence intervals point estimates and p values for the primary effect size parameter at the end of a two arm group sequential clinical trial in which adaptive changes have been implemented along the way the method is based on applying the adaptive hypothesis testing procedure of muller and schafer 2001 to a sequence of dual tests derived from the stage wise adjusted confidence interval of tsiatis rosner and mehta 1984 in the non adaptive setting this confidence interval is known to provide exact coverage in the adaptive setting exact coverage is guaranteed provided the adaptation takes place at the penultimate stage in general however all that can be claimed theoretically is that the coverage is guaranteed to be conservative nevertheless extensive simulation experiments supported by an empirical characterization of the conditional error function demonstrate convincingly that for all practical purposes the coverage is exact and the point estimate is median unbiased no procedure has previously been available for producing confidence intervals and point estimates with these desirable properties in an adaptive group sequential setting the methodology is illustrated by an application to a clinical trial of deep brain stimulation for parkinson s disease

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

asymptotic efficiency of three stage hypothesis tests multi stage hypothesis tests are studied as competitors of sequential tests a class of three stage tests for the one dimensional exponential family is shown to be asymptotically efficient whereas two stage tests are not moreover in order to be asymptotically optimal three stage tests must mimic the behavior of sequential tests similar results are obtained for the problem of testing two simple hypotheses