a likelihood ratio test for stationarity of rating transitions abstract we study the time stationarity of rating transitions modelled by a time continuous discrete state markov process and derive a likelihood ratio test for multiple markov processes from a multiplicative intensity model maximum likelihood parameter estimates can be written as martingale transform of the processes counting transitions between the rating states so that the profile partial likelihood ratio is asymptotically 2 distributed an application to an internal rating data set reveals highly significant instationarity

multilinear schur multipliers and schatten properties of operator taylor remainders abstract we establish sharp conditions on scalar functions and perturbations that guarantee schatten summability of n th order operator taylor remainders in the special case of dimension one our estimates of these remainders deliver well known classical estimates of scalar taylor remainders we prove that if a scalar function f is in the set c n and a perturbation is in the p th schatten class s p p n then the respective n th order operator taylor remainder is an element of s p n and has an estimate like the one in 16 we construct examples of f c n and perturbations in s n such that the n th order taylor remainder of the respective operator function is not in s 1 our construction relies in particular on novel dimension dependent estimates for schatten norms of multilinear schur multipliers from below that are of interest in their own right our results apply to both self adjoint and unitary operators

universality class of trails in two dimensions a trail is a walk on a lattice that may visit a site more than once but a bond at most once we have carried out transfer matrix studies of trails on the square lattice and of hybrid walks that interpolate between self avoiding walks and trails the results are in agreement with the same universal exponents as self avoiding walks however the finite size corrections are much larger than for self avoiding walks an explanation in terms of an irrelevant variable with scaling index is given

nonperturbative tricritical exponents of trails i exact enumeration on a triangular lattice as the fugacity of intersections in trails intersecting but non overlapping lattice walks is increased the configurations change from swollen ones with the scaling exponents of self avoiding walks to compact ones separating the two regimes is a potentially new tricritical point with no perturbative renormalisation fixed point associated with it supporting evidence for the existence of a tricritical point its likely location and exponents are computed for the first time from exact enumeration of all trails up to length of fifteen lattice constants on the triangular lattice the divergence of the specific heat indicates the location of the tricritical point generalised ratio and pade methods are used to extract the scaling exponents for the number of configurations and their end to end distance

statistical tests for multivariate bioequivalence although the u s food and drug administration fda 1992 recommends testing bioequivalence of individual pharmacokinetic parameters one at a time it seems reasonable and interesting to conduct a test simultaneously for all the parameters in this paper we discuss several ways to construct such tests it is shown that the confidence set approach leads to a test which can be uniformly improved by the intersection of schuirmann s two one sided tests procedure the latter test can further be improved upon noticeably by using the one dimensional unbiased test of brown hwang munk 1997 numerical calculations of powers are given to support this claim

nonparametric validation of similar distributions and assessment of goodness of fit summary in this paper the problem of assessing the similarity of two cumulative distribution functions f and g is considered an asymptotic test based on an x trimmed version of mallows distance r f g between f and g is suggested thus demonstrating the similarity of f and g within a preassigned r f g neighbourhood at a controlled type i error rate the test proposed is applied to the validation of goodness of fit and for the nonparametric assessment of bioequivalence it is shown that r f g can be interpreted as average and population equivalence our approach is illustrated by various examples

simultaneous confidence regions for multivariate bioequivalence demonstrating bioequivalence of several pharmacokinetic pk parameters such as auc and cmax that are calculated from the same biological sample measurements is in fact a multivariate problem even though this is neglected by most practitioners and regulatory bodies who typically settle for separate univariate analyses we believe however that a truly multivariate evaluation of all pk measures simultaneously is clearly more adequate in this paper we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation some of them work well for idealised scenarios but break down when faced with real data challenges such as unknown variance and correlation among the pk parameters we study the shapes of the confidence regions resulting from different methods discuss how marginal simultaneous confidence intervals for the individual pk measures can be derived and illustrate the application to data from a trial on ticlopidine hydrochloride an r package is available

self avoiding path walks on lattices a new universality class the trails problem self avoiding path walks is reconsidered by the conventional series expansion approach an exact enumeration on the square triangular and simple cubic lattices is done by computer up to 18 12 and 11 steps respectively the more self consistent and refined results between the connective constant and the corresponding critical exponent indicate the possibility of there being a different universality class from that of the self avoiding walk an average approach based on stolz s theorem is proposed which often appears to be smoother and better than the traditional one

specific heat and crossover exponents at the tricritical collapse of trails from the exact enumeration on a triangular lattice of trail configurations at the tricritical regime as the fugacity for intersections is increased the authors find phi t 0 68 8 for the crossover exponent and hence alpha t 0 5 2 for the specific heat exponent it indicates the collapse transition of trails to differ from that of polymer chains at the theta point in two dimensions

an improved sequentially rejective bonferroni test procedure complexity these procedures can be used whenever the observed levels of significance are available for all individual tests it is shown that both the holm and shaffer procedures can be improved under the assumption of positive orthant dependence for the test statistics it is noted that this assumption is met in many important practical situations and recommended that in these cases the new procedure be used in place of its predecessors whenever the required observed significance levels are available the methodology is illustrated with a numerical example

critical exponents for square lattice trails with a fixed number of vertices of degree 4 we prove several previously conjectured results about the number of n edge trails and n edge embeddings of eulerian graphs each with a fixed number k of degree 4 vertices in the lattice 2 in particular under the assumption that the relevant critical exponents exist we prove that the difference between the critical exponent for closed trails eulerian graph embeddings and that for self avoiding circuits polygons is exactly k the number of degree 4 vertices similarly we prove that the difference between the critical exponent for either open trails or open eulerian graph embeddings and that for self avoiding walks is also k these results are proved by establishing upper and lower bounds for the number of n edge embeddings of closed open eulerian graphs with k vertices of degree 4 in terms of the number of n edge self avoiding polygons walks the lower bounds are proved using a kesten pattern theorem argument and the upper bounds are established by developing based on a detailed case analysis a method for removing vertices of degree 4 from an embedding by altering at most a constant independent of n number of vertices and edges of the embedding the work presented here extends and improves the arguments first given in the work of zhao and lookman 1993 j phys a math gen 26 1067 76

functions of noncommuting self adjoint operators under perturbation and estimates of triple operator integrals abstract we define functions of noncommuting self adjoint operators with the help of double operator integrals we are studying the problem to find conditions on a function f on r 2 for which the map a b f a b is lipschitz in the operator norm and in schatten von neumann norms s p it turns out that for functions f in the besov class b 1 1 r 2 the above map is lipschitz in the s p norm for p 1 2 however it is not lipschitz in the operator norm nor in the s p norm for p 2 the main tool is triple operator integrals to obtain the results we introduce new haagerup like tensor products of l spaces and obtain schatten von neumann norm estimates of triple operator integrals we also obtain similar results for functions of noncommuting unitary operators

the geometrical properties of planar lattice trails the authors investigate the winding angle and mean square end to end distance of lattice trails on a square lattice by both exact enumeration and monte carlo methods they find similar behaviour to that of self avoiding walks to the extent that the complete distribution is found to agree with the recent exact calculation of the winding angle distribution function for self avoiding walks by duplantier and saleur 1988 who found a gaussian distribution the exponent nu was found to be indistinguishable from 3 4

heisenberg relation for locally measurable operators abstract we show that heisenberg relation a b 1 does not hold in the algebra of locally measurable operators affiliated with an arbitrary infinite von neumann algebra in the case when the von neumann algebra is finite we prove that a b 1 provided that a is normal

asymptotic properties of lattice trails the trail problem a variant of the self avoiding walk in which excluded volume is associated with lattice bonds rather than sites is studied numerically in two and three dimensions monte carlo and exact series methods are used but the results obtained lack the consistency of similar results for self avoiding walks the evidence in support of the two models belonging to the same universality class is suggestive though not entirely convincing but slowly decaying corrections to scaling could account for apparent exponent differences

lattice trails i exact results considers the problem of lattice trails introduced by malakis 1975 1976 the author proves the existence of a finite connective constant and establishes a result for the growth of n step trails tn analogous to the best known result for self avoiding walks tn lambda n expt o n for the honeycomb d 2 and lave s lattice d 3 the author establishes a counting theorem from which one can deduce the exact value of the connective constant lambda for the honeycomb lattice lambda 2 2 square root 2 further it follows that the trail problem is in the same universality class as the self avoiding walk problem for those lattices an exact amplitude relation between trails and self avoiding walks and between dumb bells and trails and self avoiding walks is established the non existence of a counting theorem for arbitrary lattices is established an inequality for the triangular lattice connective constant is proved a high density expansion for lambda for the d dimensional hybercubic lattice is also obtained the author argues that contrary to recent suggestions the model is in the same universality class as the self avoiding walk model

assessment of individual and population bioequivalence using the probability that bioavailabilities are similar in this paper a new method for the assessment of both individual and population bioequivalence is proposed that is derived from the approach of schall and luus 1993 statistics in medicine 12 1109 1124 the method considers the probability that the bioavailability of the test product is close to the bioavailability of the reference product against the probability that the bioavailability of the reference product is close to itself when administered on different occasions the method can accommodate unequal variances of the bioavailabilities of the test and reference formulations as well as formulation by subject interaction it is thus as general and comprehensive as the methods proposed by sheiner 1992 statistics in medicine 11 1777 1778 and schall and luus 1993 but the resulting bioequivalence criteria are simple and easy to interpret

scaling of self avoiding walks and self avoiding trails in three dimensions motivated by recent claims of a proof that the length scale exponent for the end to end distance scaling of self avoiding walks is precisely 7 12 0 5833 we present results of large scale simulations of self avoiding walks and self avoiding trails with repulsive contact interactions on the simple cubic lattice we find no evidence to support this claim our estimate 0 5874 2 is in accord with the best previous results from simulations

four dimensional polymer collapse ii interacting self avoiding trails we have simulated four dimensional interacting self avoiding trails isat on the hypercubic lattice with standard interactions at a wide range of temperatures up to length 4096 and at some temperatures up to length 16384 the results con3rm the earlier prediction using data from a non standard model at a single temperature of a collapse phase transition occurring at 3nite temperature moreover they are in accordwith the phenomenological theory originally proposed by lifshitz grosberg andkhokhlov in three d andrecently given new impetus by its use in the description of simulational results for four dimensional interacting self avoiding walks isaw in fact we argue that the available data is consistent with the conclusion that the collapse transitions of isat andisaw lie in the same universality class in contrad iction with long standing predictions we deduce that there exists a pseudo 3rst order transition for isat in four dimensions at 3nite lengths while the thermodynamic limit is described by the standard polymer mean 3eld theory giving a second order transition in contradiction to the prediction that the upper critical dimension for isat is du 4 c 2001 elsevier science b v all rights reserved

on the universality classes of growing self avoiding walks and trails it is shown that within a two parameter 3 3 cell to bond position space renormalisation group theory growing self avoiding walks and growing self avoiding trails on the square lattice are in the same universality class

the best constants for operator lipschitz functions on schatten classes suppose that f is a lipschitz function on r with kfklip 1 let a be a bounded self adjoint operator on a hilbert space h let p 1 and suppose that x b h is an operator such that the commutator a x is contained in the schatten class sp it is proved by the last two authors that then also f a x sp and there exists a constant cp independent of x and f such that k f a x kp cpk a x kp the main result of this paper is to give a sharp estimate for cp in terms of p namely we show that cp p 2 p 1 in particular this gives the best estimates for operator lipschitz inequalities we treat this result in a more general setting this involves commutators of n self adjoint operators a1 an for which we prove the analogous result the case described here in the abstract follows as a special case

confidence intervals associated with tests for bioequivalence summary previously the connection between bioequivalence tests and their associated confidence intervals was not well understood in fact the oc level two one sided tests approach was thought to be associated with a 1 20c confidence interval in this paper we build up connections which allow us to construct 1 oc confidence intervals from cx level tests and vice versa when applied to the cc level two one sided tests the resultant 1 oc confidence intervals are properly contained in westlake s 1 oc symmetric interval 1976 our approach is readily generalized to different settings including the nonparametric setting the ratio parameter setting and the repeated confidence interval setting

bayesian modeling of multivariate average bioequivalence bioequivalence trials are usually conducted to compare two or more formulations of a drug simultaneous assessment of bioequivalence on multiple endpoints is called multivariate bioequivalence despite the fact that some tests for multivariate bioequivalence are suggested current practice usually involves univariate bioequivalence assessments ignoring the correlations between the endpoints such as auc and cmax in this paper we develop a semiparametric bayesian test for bioequivalence under multiple endpoints specifically we show how the correlation between the endpoints can be incorporated in the analysis and how this correlation affects the inference resulting estimates and posterior probabilities borrow strength from one another where the amount and the direction of the strength borrowed are determined by the prior correlations the method developed is illustrated using a real data set copyright 2007 john wiley sons ltd

sample sizes for bioequivalence studies in recent years a number of decision rules based on sound statistical principles have been proposed for deciding if a test formulation is bioequivalent to a reference formulation the decision rule based on confidence intervals has been accepted by regulatory agencies at least by the food and drug administration of the united states a useful property of this decision rule is that the regulatory agency need not require a certain sample size since the level of protection against wrongly deciding bioequivalence is set by the choice of the alpha level used to compute the confidence intervals the manufacturer claiming bioequivalence is concerned about sample size for sample size determines the probability of falsely deciding non bioequivalence when the test formulation does indeed have an acceptable relative bioavailability curves of probability of rejecting bioequivalence have been computed for error coefficient of variation of 10 20 and 30 per cent for relative bioavailability from 70 to 130 per cent and for protection levels of 90 and 95 per cent these curves can be used for choosing the sample size for a bioequivalence study

optimum allocation of treatments for welch s test in equivalence assessment as an extension of welch s test to equivalence trials in a matched pair design we determine the sample sizes n1 and n2 that maximize the power at given alternatives for a given total sample size n n1 n2 although the optimal allocation is obtained asymptotically when the ratio of the standard deviations in both treatment groups equals the ratio of the sample sizes numerical investigations show that this result does not hold for sample sizes where n or 25 for convenience we provide tables containing the optimal combinations for the bioequivalence problem as well as for the problem of testing a clinically relevant difference results indicate that for small sample sizes the optimum allocations of the treatments differ significantly in both testing problems although they are asymptotically identical in addition we provide simple approximate equations that can be used for the determination of the required sample sizes to control a preassigned probability of type ii error

validation of linear regression models a new test is proposed in order to verify that a regression function say g has a prescribed linear parametric form this procedure is based on the large sample behavior of an empirical l 2 distance between g and the subspace u spanned by the regression functions to be verified the asymptotic distribution of the test statistic is shown to be normal with parameters depending only on the variance of the observations and the l 2 distance between the regression function g and the model space u based on this result a test is proposed for the hypothesis that g is not in a preassigned l 2 neighborhood of u whichallows the verification of the model u at a controlled type i error rate the suggested procedure is very easy to apply because of its asymptotic normal law and the simple form of the test statistic in particular it does not require nonparametric estimators of the regression function and hence the test does not depend on the subjective choice of smoothing parameters

sample size determination for proving equivalence based on the ratio of two means for normally distributed data equivalence trials aim to demonstrate that two treatments do not differ by more than a prespecified clinically irrelevant amount we consider the problem when equivalence is defined in terms of the ratio of population means and the original untransformed data are normally distributed application of the intersection union principle to the test proposed by sasabuchi results in a two one sided tests procedure of size we give the associated 100 1 2 per cent confidence interval and derive the exact methods for calculation of power and sample sizes for the parallel group design and the two period cross over we present tables and figures of required sample sizes and achieved power copyright 1999 john wiley sons ltd

comparison of different methods for decision making in bioequivalence assessment if the regulatory requirements are symmetrical the use of symmetrical confidence intervals as a decision rule for bioequivalence assessment leads as shown by simulations to better level properties and an inferior power compared to a rule based on shortest confidence intervals a choice between these two approaches will have to depend on a loss function for asymmetric regulatory requirements symmetrical confidence intervals should not be used however a decision can still be based on posterior probabilities pr theta epsilon r1 r2 x or shortest confidence intervals for purposes of inference presentation and interpretation of results we think that the use of symmetrical confidence intervals alone can be misleading and we therefore recommend that the posterior probabilities and densities or at least the shortest confidence intervals be given

the subject by formulation interaction as a criterion of interchangeability of drugs summary the primary purpose of a bioequivalence study is often to meet the regulatory requirement of similar average bioavailabilities this is usually done by estimating the mean difference between formulations in a crossover design however a small difference as well as a rather narrow confidence interval might be obtained also if the subjects respond differently to the formulations i e if there is a nonnegligible subject by formulation interaction hence it can be argued that this interaction should be part of the criterion of interchangeability to be able to study this interaction the ordinary simple crossover design is not appropriate instead a design where each formulation is administered at least twice to each subject is desirable such a design is obtained by repeating a simple crossover layout to evaluate the impact of the subject by formulation interaction the ratio of the variance components of the interaction and the error is estimated this approach is illustrated by an example two different formulations of a drug are considered bioequivalent if their average bioavailabilities are similar the assessment of this similarity is usually based on an interval estimate of the mean difference between the formulations however this focus on means is an insufficient criterion since a small difference as well as a rather narrow confidence interval might be obtained also if the formulation differences show a considerable variation among subjects the impact on drug interchangeability of this so called subject byformulation interaction is discussed for example by hwang et al 1978 in order to estimate this interaction they suggest a design where each formulation is administered at least twice to each subject in this paper we briefly discuss how to design and analyze a bioequivalence study in order to evaluate the impact of the subject by formulation interaction as a measure of the magnitude of the interaction we propose the ratio of the variance components of the interaction and the error the ideas of the paper are illustrated with data from a comparative study of two generic formulations of furosemide

fieller s confidence intervals for the ratio of two means in the assessment of average bioequivalence from crossover data the two period crossover design is the most commonly used study design for bioequivalence of one test formulation to be assessed in comparison to one reference formulation consequently in this paper all derivation is based on this particular design it is assumed that for the underlying statistical model the usual assumptions of normality and additivity are satisfied on the original scale of measurement and that it is wanted to base the assessment of average bioavailability on the ratio of the unknown population means for the test and reference formulation the purpose of this paper is to illustrate that it is reasonable to assume a uniform covariance structure for the two period crossover design because the demand of equal variability in bioavailabilities in addition to equal average bioavailabilities for the reference and test formulation makes the assumption of uniform covariance structure very realistic and also because the properties of a decision rule based upon a fieller s confidence interval under a uniform covariance structure are competitive with those of the corresponding rule based on a general covariance structure

lattice trails ii numerical results for pt i see ibid vol 18 p 567 1985 a numerical study of the properties of lattice trails on the honeycomb square triangular and simple cubic lattices is made critical points are estimated for all lattices and upper and lower bounds established extensive series have been obtained and series analysis of both trail generating functions and mean square end to end distance series are not inconsistent with the conclusion that the problem is in the same universality class as the self avoiding walk problem a pseudo star triangle transformation is defined and the analyticity properties of that function coupled with previous exact results clearly supports that conclusion for the triangular lattice as well as providing excellent unbiased critical point estimates the author also shows that the connective constant for d or 2 dimensional hypercubic trails is strictly greater than the corresponding quantity for saws

semiparametric bayesian modeling of multivariate average bioequivalence bioequivalence trials are usually conducted to compare two or more formulations of a drug simultaneous assessment of bioequivalence on multiple endpoints is called multivariate bioequivalence despite the fact that some tests for multivariate bioequivalence are suggested current practice usually involves univariate bioequivalence assessments ignoring the correlations between the endpoints such as auc and cmax in this paper we develop a semiparametric bayesian test for bioequivalence under multiple endpoints specifically we show how the correlation between the endpoints can be incorporated in the analysis and how this correlation affects the inference resulting estimates and posterior probabilities borrow strength from one another where the amount and direction of the strength borrowed are deter department of mathematics and statistics georgia state university atlanta ga 30303 3083 usa email pghosh mathstat gsu edu department of epidemiology and biostatistics memorial sloan kettering cancer center 1275 york avenue new york ny 10021

an improvement of commonly used tests in bioequivalence assessment if equivalence of two treatments has to be proved by an experiment with normally distributed observations and fixed sample size there are two usual methods on the one hand there is the double t test and on the other hand a test procedure suggested by anderson hauck which is uniformly more powerful than the first one but only capable of keeping asymptotically to the nominal level based on these two methods a new test is presented which is uniformly more powerful than the double t test and also keeps the preassigned level

self avoiding walks neighbour avoiding walks and trails on semiregular lattices we study self avoiding and neighbour avoiding walks and lattice trails on two semiregular lattices the lattice and the lattice for the lattice we find the exact connective constant for both self avoiding walks neighbour avoiding walks and trails for the lattice we generate long series which permit the accurate estimation of the connective constant for self avoiding walks and trails

a unifying approach for confidence intervals and testing of equivalence and difference summary general families of null hypotheses are defined which refer to problems of testing equivalence and difference between treatments corresponding confidence intervals have been proposed in the literature in a different context the unifying approach demonstrates how waiving of particular one sided tests in the parameter space relates to the construction of the corresponding confidence interval

on bayesian methods for bioequivalence bayesian methods are presented for assessing bioequivalence for studies in which a new formulation and a standard are administered simultaneously and for latin square designs which compare two or more new formulations to a standard two examples illustrate the application of the methods

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

1 α equivariant confidence rules for convex alternatives are α 2 level tests with applications to the multivariate assessment of bioequivalence abstract in general a 1 confidence region c x for a parameter yields a test at level a for h h versus k c h whenever we reject if c x h we show under certain equivariance properties of c x that for the case of convex alternatives c h the level of the resulting test is in fact 2 this extends recent findings for hyperrectangular alternatives as they occur in the multivariate bioequivalence problem furthermore we apply the suggested test to ellipsoid type alternatives instead of hyperrectangulars in the multivariate bioequivalence problem and to a problem occurring in neurophysiology finally we compare our test numerically with existing methods

step down multiple tests for comparing treatments with a control in unbalanced one way layouts we show how a well known multiple step down significance testing procedure for comparing treatments with a control in balanced one way layouts can be applied in unbalanced layouts unequal sample sizes for the treatments the method we describe has the advantage that it provides p values for each treatment versus control comparison that take account of the multiple step down testing nature of the procedure these joint p values can be used with any value of alpha the fixed type i family wise error rate bound that may be specified by the investigator to determine the p values it is necessary to compute a multivariate student t integral for which a computer program is available this procedure is more powerful than the step down bonferroni procedure of holm and the single step procedure of dunnett an example from the pharmaceutical literature is used to illustrate the procedure

universal amplitudes ratio at the collapse transition of polymers in two dimensions first values of the universal ratio of the mean square radius of gyration and the mean square end to end distance for 2d linear polymers at their collapse transition are calculated by the scanning simulation method two models are considered i self avoiding walks saws with nearest neighbour attractions for which this ratio is found to be 0 179 or 0 003 at the theta point ii self intersecting trails at their tricritical point for which the value 0 166 or 0 002 is obtained this provides yet another indication that these models may belong to different tricritical universality classes the authors have also computed this ratio for trails at the high temperature limit with non interacting intersections and found 0 141 or 0 001 in excellent agreement with earlier estimates of this ratio for saws in their swollen phase

non perturbative tricritical exponents of trails ii exact enumerations on square and simple cubic lattices for pt i see ibid vol 21 p 773 1988 the authors present exact enumerations of trails self intersecting but non overlapping lattice walks tabulated according to their length l number of intersection i and end to end distance for the square lattice up to l 21 i 7 and for the simple cubic lattice up to l 15 i 5 they introduce a fugacity for intersection to explore the transition to a collapsed phase through a novel tricritical point which is unaccessible by the renormalisation group approach the existence of tricritical points in both lattices is manifested by the divergence of the specific heat the values of the tricritical couplings and exponents are extracted by a dlogpade analysis they find for the three dimensional lattice nu t approximately 0 48 and gamma t approximately 0 43 nu t approximately 0 52 and gamma t approximately 1 25 for the square lattice

a statistical assessment of clinical equivalence an observed confidence distribution is proposed as a measure of strength of evidence for practically equivalent efficacies of two treatments the concept is independent of prior opinions about relevant sizes of a difference in efficacy it also avoids retrospective power calculations for trials with missed recruitment goals and allows combination of the confidence from independent experiments

an unbiased test for the bioequivalence problem it is shown that the standard two one sided tests procedure for bioequivalence is a biased test better tests exist in this paper an unbiased level test and other tests which are uniformly more powerful than the two one sided tests procedure are constructed its power can be noticeably larger than that of the level two one sided tests procedure

deviance estimates of sample size for equivalence tests in vaccine trials this paper proposes a sample size procedure for both equivalence and conventional tests for the comparison of two binomial proportions based on the signed square root of the deviance when the comparison is based on the odds ratio i describe an alternate close conditional exact method that gives results that support those given by the deviance method i summarize the advantages of the deviance based method and also show that in general equivalence situations the sample size estimate depends upon the measure of comparison selected odds ratio risk ratio or risk difference

bmo estimates for non commutative vector valued lipschitz functions abstract we construct markov semi groups t and associated bmo spaces on a finite von neumann algebra m and obtain results for perturbations of commutators and non commutative lipschitz estimates in particular we prove that for any a m self adjoint and f r r lipschitz there is a markov semi group t such that for x m f a x bmo m t c a b s f a x we obtain an analogue of this result for more general von neumann valued functions f r n n by imposing hormander mikhlin type assumptions on f in establishing these result we show that markov dilations of markov semi groups have certain automatic continuity properties we also show that markov semi groups of double operator integrals admit standard and reversed markov dilations

bayesian inference for ratios of coefficients in a linear model a variety of statistical problems e g slope ratio and parallel line bioassay calibration bioequivalence can be viewed as questions of inference on the ratio of two coefflcients in a suitably constructed linear model this paper develops a bayesian approach for the general formulation of the problem using a class of priors which involve the unknown ratio explicitly the posterior distribution of the ratio is obtained analytically and its properties are investigated especially the sensitivity to the choice of the prior examples are given of applications to slope ratio bioassay comparison of the mean effects of two drugs and a bioequivalence problem

higher order s2 differentiability and application to koplienko trace formula abstract let a be a selfadjoint operator in a separable hilbert space k a selfadjoint hilbert schmidt operator and f c n r we establish that t f a t k f a is n times continuously differentiable on r in the hilbert schmidt norm provided either a is bounded or the derivatives f i i 1 n are bounded this substantially extends the results of 3 on higher order differentiability of in the hilbert schmidt norm for f in a certain wiener class as an application of the second order s 2 differentiability we extend the koplienko trace formula from the besov class b 1 2 r 20 to functions f for which the divided difference f 2 admits a certain hilbert space factorization

enumeration of self avoiding trails on a square lattice using a transfer matrix technique the authors describe a new algebraic technique utilizing transfer matrices for enumerating self avoiding trails on the square lattice they have enumerated trails to 31 steps and find increased evidence that trails are in the self avoiding walk universality class assuming that trails behave like a lambda nn1132 they find lambda 2 72062 or 0 000006 and a 1 272 or 0 002

functions of perturbed n tuples of commuting self adjoint operators let a1 an and b1 bn be n tuples of commuting self adjoint operators on hilbert space for functions f on rn satisfying certain conditions we obtain sharp estimates of the operator norms or norms in operator ideals of f a1 an f b1 bn in terms of the corresponding norms of aj bj 1 j n we obtain analogs of earlier results on estimates for functions of perturbed self adjoint and normal operators it turns out that for n 3 the methods that were used for self adjoint and normal operators do not work we propose a new method that works for arbitrary n we also get sharp estimates for quasicommutators f a1 an r rf b1 bn in terms of norms of ajr rbj 1 j n for a bounded linear operator r

a multivariate test for population bioequivalence in this article we propose a multivariate generalization of the criteria for testing univariate population bioequivalence recently a number of approaches for testing multivariate equivalence have appeared in the literature most of them consider a multivariate equivalence region which implies simultaneous comparison of means in each dimension in contrast our proposal combines a comparison of means and a comparison of variances into a single aggregate criterion using the trace of the covariance matrix as a scalar measure of the total variability we use a confidence interval approach to multivariate population bioequivalence testing similar to the univariate case two versions of the modified large sample confidence interval for the linearized multivariate criterion are constructed in a simulation study we evaluate the empirical coverage of these confidence intervals and rejection rates of the corresponding tests in finite samples the proposed methodology is illustrated with an example of testing equivalence of the spray pattern of nasal sprays

a semi parametric bayesian approach to average bioequivalence bioequivalence assessment is an issue of great interest development of statistical methods for assessing bioequivalence is an important area of research for statisticians bioequivalence is usually determined based on the normal distribution we relax this assumption and develop a semi parametric mixed model for bioequivalence data the proposed method is quite flexible and practically meaningful our proposed method is based on a mixture normal distribution and a non parametric bayesian approach using a dirichlet process mixture prior a numerical example illustrates the use of our procedure

a monte carlo study of lattice trails the authors use the recently developed monte carlo algorithm of berretti and sokal j stat phys vol 40 p 483 1985 to study the critical behaviour of lattice trails on the square and triangular lattices they find support for the earlier belief that this problem is in the same universality class as self avoiding walks accepting this they obtain the most precise estimates to date of the connective constants it is argued that this problem is particularly well suited to study by monte carlo methods rather than by series analysis

maximum likelihood estimation of variance components for a multivariate mixed model with equal design matrices an algorithm is described for estimating variance and covariance components by restricted maximum likelihood for a multivariate mixed two way classification with equal design matrices the procedure involves a transformation to canonical scale effectively reducing a q variate analysis to q corresponding univariate analyses a small numerical example is given as well as a large scale practical application

the statistics of collapsing square lattice trails with a fixed number of vertices of degree 4 a trail on the square lattice with a fixed number k of vertices of degree 4 is called a k trail we model polymer collapse using k trails by incorporating an interaction energy which is proportional to the number of nearest neighbour contact edges of the trail it is known that the number of square lattice n edge closed open k trails can be bounded above and below to o nk by the number of n step self avoiding circuits walks this along with pattern theorems for self interacting self avoiding circuits and walks are used herein to establish upper and lower bounds to o nk for the collapsing free energy of k trails in terms of self avoiding circuits or walks as appropriate we also use pattern theorems to obtain bounds on the limiting nearest neighbour contact density for collapsing k trails finally we investigate k trails with a fixed density of nearest neighbour contacts and show that their limiting entropy per monomer is independent of k

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

the growing self avoiding trail the author introduces a new random walk which can be used as a model for the theta polymer the walk belongs to a different universality class from the usual saw extensive monte carlo calculations have been performed to calculate the exponents gamma and nu the author finds in two dimensions nu 0 535 and gamma 1 025 and in three dimensions nu 0 50 and gamma 1 0 this result strongly suggests that the upper critical dimension is equal to three

p value adjustments for multiple tests in multivariate binomial models abstract data from rodent carcinogenicity preclinical and clinical studies involving new drugs may be modeled as having come from multivariate binomial distributions in two year rodent carcinogenicity studies there are typically 20 50 tissues examined for occurrence of any of several possible lesions for a particular treatment group the number of occurrences of a particular lesion at a particular tissue may be modeled as binomial and the vector of such frequencies may be considered multivariate binomial with unspecified dependence structure the same model may also apply to clinical side effects data in this case the marginal frequencies may represent occurrences of events ranging from headaches to ingrown toenails frequently the goal of such studies is to isolate site specific significant differences between treatment and control groups for example in rodent carcinogenicity analyses it is generally not sufficient to claim that a new compound causes an increase in tumors at some unspecified si

equivalence and interval testing for lehmann s alternative abstract equivalence and interval tests for lehmann s alternative that extend the well known savage test for one sided hypotheses are proposed the proposed tests are shown to be unbiased with a strictly unimodal power function provided the sample sizes in both treatment groups are equal by means of a numerical investigation of the bias in the case of unequal sample sizes that are not too far apart the suggested tests still turn out to provide practicable solutions because the computational effort to perform the suggested tests is considerable tables containing the critical values are displayed to perform these tests easily a numerical analysis of the power function of the interval test establishes this procedure as a powerful tool for detection of a significantly relevant difference in the small sample case in contrast to the case of interval testing the fact arises that the performance of a powerful equivalence study under lehmann s alternative requires an extensive amount of data because the p

bounds on connective constants for self avoiding walks new lower bounds on the connective constant of the square and simple cubic lattice self avoiding walks are obtained by enumerating a particular subset of self avoiding walks and using a result of kesten the author finds mu sq 2 5680 and mu sc 4 352

a proposal for interpreting and reporting negative studies an issue of continuing interest is the interpretation and reporting of negative studies namely studies that do not find statistically significant differences the most common approach is the design power method which determines irrespective of the observed difference what differences the study could have been expected to detect we propose an alternative approach the application of equivalence testing methods where we define equivalence to mean that the actual difference lies within some specified limits this approach in contrast to the design power approach provides a way of quantifying with p values what was actually determined from the study instead of saying what the study may or may not have accomplished with some degree of certainty power for example a possible outcome of the equivalence testing approach is the conclusion at the 5 per cent level that two means or proportions do not differ by more than some specified amount the equivalence testing approach applies to any study design we illustrate the method with a cancer clinical trial and an epidemiologic case control study in addition for those studies in which one cannot specify limits a priori we propose the use of equivalence curves to summarize and present the study results

critical exponents for simple non uniform polymer networks the authors study a number of non uniform specified topologies and show rigorously that for certain topologies with cut edges the critical exponent gamma t is in agreement with a conjecture given by gaunt et al 1984 and that the exponent nu t nu the exponent for self avoiding walks the authors also find that the scaling relations gamma t gamma t1 and gamma t gamma t11 are the same as for self avoiding walks previously conjectured only for uniform networks by assigning an interaction energy to a nearest neighbour contact they prove that the collapse transition for these topologies is the same as that for self avoiding walks

on two dimensional self avoiding random walks following nienhuis 1982 exact evaluation of the connective constant of the honeycomb lattice self avoiding walk model and the exact exponent values he has conjectured the author has re examined the available data on all three regular two dimensional lattices in the case of the triangular lattice the author has additionally corrected and extended the extant series the author finds support for nienhuis value gamma 111 32 for all three lattices and further finds that alpha 1 2 for all three lattices as given by nienhuis result nu 3 4 and the hyperscaling relation d nu 2 alpha the author is unable to find any consistent evidence of a correction to scaling exponent delta 1 1 cannot be ruled out

existence of four dimensional polymer collapse i kinetic growth trails abstract we present the results of simulations of kinetic growth trails kgt bond avoiding walks in four dimensions we use a mapping from a kinetic growth model to a static model of self interacting trails isat at a particular temperature to argue that this temperature is precisely the collapse temperature of four dimensional interacting trails to do this we show that the kinetic growth trails behave neither like static non interacting trails which should behave as excluded volume dominated four dimensional polymers that is self avoiding walks or collapsed four dimensional polymers but rather show an intermediate behaviour this is the first indication of collapse in any four dimensional lattice polymer model and so may be helpful in deciding which of the competing models of polymers is a good model in lower dimensions we have calculated various exponents of the kgt model and identified them with certain critical exponents of the static isat problem

the calculation of probabilities in rejecting bioequivalence methods are given for deriving the lower and upper bounds of the probabilities for rejecting bioequivalence except when two formulations are nearly equal the lower and upper bounds become very close and thus give an exact probability the methods can be used in two or higher way crossover or parallel groups designs one can also determine the sample size from the equations the results are compared with the probabilities obtained by simulation