a return mapping algorithm for isotropic elastoplasticity a return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces constructed from all three invariants of the stress tensor based on the first order backward euler difference formula bdf the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter the stresses are recovered afterwards the solution concept is applied to a pressure independent yield function expressed in terms of the second and third invariant of the stress tensor the numerical performance of the method is demonstrated with two examples

statistical inference for correlated data in ophthalmologic studies in ophthalmologic studies each subject usually contributes important information for each of two eyes and the values from the two eyes are generally highly correlated previous studies showed that test procedures for binary paired data that ignore the presence of intraclass correlation could lead to inflated significance levels furthermore it is possible that asymptotic versions of these procedures that take the intraclass correlation into account could also produce unacceptably high type i error rates when the sample size is small or the data structure is sparse we propose two alternatives for these situations namely the exact unconditional and approximate unconditional procedures according to our simulation results the exact procedures usually produce extremely conservative empirical type i error rates that is the corresponding type i error rates could greatly underestimate the pre assigned nominal level e g empirical type i error rate nominal type i error rate 0 8 on the other hand the approximate unconditional procedures usually yield empirical type i error rates close to the pre chosen nominal level we illustrate our methodologies with a data set from a retinal detachment study copyright 2005 john wiley sons ltd

exact integration of constitutive equations in elasto plasticity a unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity assuming the total strain rate direction to be constant this unified approach includes all previous exact integration procedures as special cases and in addition some new closed form solutions are derived for combined kinematic and isotropic hardening special emphasis is laid on combined kinematic and isotropic hardening for von mises material and on isotropic hardening for mohr coulomb and tresca materials

confidence interval construction for proportion difference in small sample paired studies paired dichotomous data may arise in clinical trials such as pre post test comparison studies and equivalence trials reporting parameter estimates e g odds ratio rate difference and rate ratio along with their associated confidence interval estimates becomes a necessity in many medical journals various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions nevertheless the performance of these asymptotic methods may have poor coverage properties in small samples in this article we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small sample paired data specifically we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test the exact unconditional confidence interval guarantees the coverage probability and it is recommended if strict control of coverage probability is required however the exact method tends to be overly conservative and computationally demanding our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small sample designs and yet they are relatively easy to implement computationally we illustrate the methods using real examples from a pain management study and a cancer study

simultaneous comparison of sensitivity and specificity of two tests in the paired design a straightforward graphical approach often the performances of two binary diagnostic or screening tests are compared by applying them to the same set of subjects some of whom are affected some unaffected the mcnemar test and corresponding interval estimation methods may be used to compare the sensitivity of the two tests but this disregards both any observed difference in specificity and its imprecision due to sampling variation the suggested approach is to display point and interval estimates for a weighted mean of the differences in sensitivity and specificity between the two tests the mixing parameter which is allowed to range from 0 to 1 represents the prevalence in the population to which application is envisaged together with the relative seriousness of false positives and false negatives the confidence interval for is obtained by a simple extension of a closed form method for the paired difference of proportions which has favourable coverage properties and is based on the wilson single proportion score method a plot of against is readily obtained using a minitab macro copyright 2001 john wiley sons ltd

integration schemes for von mises plasticity models based on exponential maps numerical investigations and theoretical considerations summary we consider three different exponential map algorithms for associative von mises plasticity with linear isotropic and kinematic hardening the first scheme is based on a different formulation of the time continuous plasticity model which automatically grants the yield consistency of the method in the numerical solution the second one is the quadratically accurate but non yield consistent method already proposed in auricchio and beirao da veiga int j numer meth engng 2003 56 1375 1396 the third method is an improved version of the second one in which the yield consistency condition is enforced a posteriori we also compare the performance of the three methods with the classical radial return map algorithm we develop extensive numerical tests which clearly show the main advantages and disadvantages of the three methods copyright 2005 john wiley sons ltd

confidence intervals for differnces in correlated binary proportions by w l may and w d johnson statistics in medicine 16 2127 2136 1997

a comparison of methods for the construction of confidence interval for relative risk in stratified matched pair designs a stratified matched pair study is often designed for adjusting a confounding effect or effect of different trails centers groups in modern medical studies the relative risk is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials in this paper we propose seven confidence interval estimators for the common relative risk and three simultaneous confidence interval estimators for the relative risks in stratified matched pair designs the performance of the proposed methods is evaluated with respect to their type i error rates powers coverage probabilities and expected widths our empirical results show that the percentile bootstrap confidence interval and bootstrap resampling based bonferroni simultaneous confidence interval behave satisfactorily for small to large sample sizes in the sense that i their empirical coverage probabilities can be well controlled around the pre specified nominal confidence level with reasonably shorter confidence widths and ii the empirical type i error rates of their associated test statistics are generally closer to the pre specified nominal level with larger powers they are hence recommended two real examples from clinical laboratory studies are used to illustrate the proposed methodologies

a semi analytical integration method for j2 flow theory of plasticity with linear isotropic hardening abstract in this paper an exact time integration scheme is presented for von mises elastoplasticity with linear isotropic hardening at small deformations the method is based on the constant strain rate assumption which is widely accepted in displacement based finite element applications the deviatoric form of the rate equation using the method proposed by krieg and krieg in r d krieg d b krieg accuracies of numerical solution methods for the elastic perfectly plastic model j press vess technol trans asme 99 1977 510 515 is rewritten to a system of nonlinear odes with two scalar functions the radius of the mises circle and an angle obtained by using the scalar product of the stress deviator and the strain rate the time integration of these functions gives an exact solution in implicit form using the incomplete beta function in addition by the exact linearization of this new semi analytical solution a stress updating algorithm and the consistent tangent operator are derived the numerical performance and accuracy of the proposed method are illustrated on numerical examples moreover a comparison of the proposed method with the well known radial return method is included

saddlepoint expansions for directional test probabilities an expansion is derived for the conditional tail probability of a multivariate random variable given its direction from the expected value in particular if the score function of a statistical model is chosen as this variable such a conditional probability gives a test for a simple hypothesis which is asymptotically equivalent to the likelihood ratio test the expansion is of the large deviation type and is derived through the use of saddlepoint methods thus the relative error of the test probability is o n1 uniformly in a bounded set for an average of n independent replications the approximation is based on the cumulant transform for the random variable but is otherwise a simple expression in terms of chi squared distributions in the one dimensional case it reduces to the expansion obtained by lugannani and rice numerical examples show an excellent fit comparable with other saddlepoint expansions when the dimension is low even for very small sample sizes but for higher dimensions more replications are required to give a similar approximation

construction of confidence limits about effect measures a general approach it is widely accepted that confidence interval construction has important advantages over significance testing for the presentation of research results as now facilitated by readily available software however for a number of effect measures procedures are either not available or not satisfactory in samples of small to moderate size in this paper we describe a general approach for estimating a difference between effect measures which can also be used to obtain confidence limits for a risk ratio and a lognormal mean numerical evaluation shows that this closed form procedure outperforms existing methods including the bootstrap

multiple imputation for the comparison of two screening tests in two phase alzheimer studies two phase designs are common in epidemiological studies of dementia and especially in alzheimer research in the first phase all subjects are screened using a common screening test s while in the second phase only a subset of these subjects is tested using a more definitive verification assessment i e golden standard test when comparing the accuracy of two screening tests in a two phase study of dementia inferences are commonly made using only the verified sample it is well documented that in that case there is a risk for bias called verification bias when the two screening tests have only two values e g positive and negative and we are trying to estimate the differences in sensitivities and specificities of the tests one is actually estimating a confidence interval for differences of binomial proportions estimating this difference is not trivial even with complete data it is well documented that it is a tricky task in this paper we suggest ways to apply imputation procedures in order to correct the verification bias this procedure allows us to use well established complete data methods to deal with the difficulty of the estimation of the difference of two binomial proportions in addition to dealing with incomplete data we compare different methods of estimation and evaluate the use of multiple imputation in this case our simulation results show that the use of multiple imputation is superior to other commonly used methods we demonstrate our finding using alzheimer data

estimating functions and approximate conditional likelihood summary the approximate conditional likelihood method proposed by cox reid 1987 is applied to the estimation of a scalar parameter 0 in the presence of nuisance parameters the estimating function of 0 based on the approximate conditional likelihood is shown to be preferable to that based on the profile likelihood a sufficient condition for both approaches to be equivalent is given the role of parameter orthogonality is emphasized several examples including bivariate normal means with known coefficient of variation are presented

improved confidence intervals for the difference between binomial proportions based on paired data existing methods for setting confidence intervals for the difference theta between binomial proportions based on paired data perform inadequately the asymptotic method can produce limits outside the range of validity the exact conditional method can yield an interval which is effectively only one sided both these methods also have poor coverage properties better methods are described based on the profile likelihood obtained by conditionally maximizing the proportion of discordant pairs a refinement methods 5 and 6 which aligns 1 alpha with an aggregate of tail areas produces appropriate coverage properties a computationally simpler method based on the score interval for the single proportion also performs well method 10

rotationally invariant distortion resistant finite elements the predictive capability of conventional iso parametric finite elements deteriorates with mesh distortion in the case of geometrically non linear analysis changes in geometry causing severe distortion can result in negative jacobian mapping between the local and global systems resulting in numerical breakdown this paper presents a finite element formulation that is resistant to irregular mesh geometries and large element distortions whilst remaining invariant to rigid body motion the predictive capabilities of the family of finite elements are demonstrated using a series of geometrically non linear analyses including an elastic cantilever beam and an elasto plastic double notched specimen

exact and approximate unconditional confidence intervals for proportion difference in the presence of incomplete data confidence interval ci construction with respect to proportion rate difference for paired binary data has become a standard procedure in many clinical trials and medical studies when the sample size is small and incomplete data are present asymptotic cis may be dubious and exact cis are not yet available in this article we propose exact and approximate unconditional test based methods for constructing ci for proportion rate difference in the presence of incomplete paired binary data approaches based on one and two sided wald s tests will be considered unlike asymptotic ci estimators exact unconditional ci estimators always guarantee their coverage probabilities at or above the pre specified confidence level our empirical studies further show that i approximate unconditional ci estimators usually yield shorter expected confidence width ecw with their coverage probabilities being well controlled around the pre specified confidence level and ii the ecws of the unconditional two sided test based ci estimators are generally narrower than those of the unconditional one sided test based ci estimators moreover ecws of asymptotic cis may not necessarily be narrower than those of two sided based exact unconditional cis two real examples will be used to illustrate our methodologies

confidence intervals for a ratio of binomial proportions based on paired data four interval estimation methods for the ratio of marginal binomial proportions are compared in terms of expected interval width and exact coverage probability two new methods are proposed that are based on combining two wilson score intervals the new methods are easy to compute and perform as well or better than the method recently proposed by nam and blackwelder two sample size formulas are proposed to approximate the sample size required to achieve an interval estimate with desired confidence level and width

multivariate extensions of mcnemar s test this article considers global tests of differences between paired vectors of binomial probabilities based on data from two dependent multivariate binary samples difference is defined as either an inhomogeneity in the marginal distributions or asymmetry in the joint distribution for detecting the first type of difference we propose a multivariate extension of mcnemar s test and show that it is a generalized score test under a generalized estimating equations gee approach univariate features such as the relationship between the wald and score tests and the dropout of pairs with the same response carry over to the multivariate case and the test does not depend on the working correlation assumption among the components of the multivariate response for sparse or imbalanced data such as occurs when the number of variables is large or the proportions are close to zero the test is best implemented using a bootstrap and if this is computationally too complex a permutation distribution we apply the test to safety data for a drug in which two doses are evaluated by comparing multiple responses by the same subjects to each one of them

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

on the choice of prior distribution for the box cox transformed linear model summary the noninformative prior distribution for the parameters of the linear model transformed following box cox 1964 has the non bayesian property of depending to some extent on the data an alternative choice of prior which is not outcome dependent was suggested by pericchi 1981 but it is argued here that this prior has some undesirable features an alternative family of non outcome dependent priors is suggested leading to a noninformative prior which is closer in spirit to that proposed by box cox the posterior consequences of adopting this prior are fully explored and an example discussed

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

recommended tests and confidence intervals for paired binomial proportions we describe evaluate and recommend statistical methods for the analysis of paired binomial proportions a total of 24 methods are considered the best tests for association include the asymptotic mcnemar test and the mcnemar mid p test for the difference between proportions we recommend two simple confidence intervals with closed form expressions and the asymptotic score interval the asymptotic score interval is also recommended for the ratio of proportions as is an interval with closed form expression based on combining two wilson score intervals for the single proportion for the odds ratio we recommend a transformation of the wilson score interval and a transformation of the clopper pearson mid p interval we illustrate the practical application of the methods using data from a recently published study of airway reactivity in children before and after stem cell transplantation and a matched case control study of the association between floppy eyelid syndrome and obstructive sleep apnea hypopnea syndrome

confidence intervals for a binomial proportion thirteen methods for computing binomial confidence intervals are compared based on their coverage properties widths and errors relative to exact limits the use of the standard textbook method x n 1 96 square root of x n 1 x n n or its continuity corrected version is strongly discouraged a commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p is such that np and n 1 p both exceed 5 does not ensure adequate accuracy score limits are easily calculated from closed form solutions to quadratic equations and can be used at all times based on coverage functions the continuity corrected score method is recommended over exact methods its conservative nature should be kept in mind as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

a simple predictive density function abstract an easily computable predictive density is considered although involving a plain maximum likelihood technique it coincides with the posterior predictive density with a noninformative prior for standard situations achievements are comparable with classical inference

an integration scheme for prandtl reuss elastoplastic constitutive equations we investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure independent yield criteria the incremental equations are divided into one scalar hydrostatic pressure dilation rate equation and a stress deviator strain rate deviator tensorial equation this formulation is applied to two classical problems bulging of a tube under internal pressure and tension test on a notched specimen

confidence intervals for an effect size measure based on the mann whitney statistic part 2 asymptotic methods and evaluation several asymptotic confidence interval methods for u mn the mann whitney u statistic divided by the product of the two sample sizes are developed and evaluated alongside published methods novel methods derived from gaussian and beta models perform well though overall a modification of the hanley mcneil approach method 5 in this evaluation performed better and is recommended for calculating confidence intervals for u mn for continuously distributed data

rapid non linear finite element analysis of continuous and discontinuous galerkin methods in matlab matlab is adept at the development of concise finite element fe routines however it is commonly perceived to be too inefficient for high fidelity analysis this paper aims to challenge this preconception by presenting two optimised fe codes for both continuous galerkin cg and discontinuous galerkin dg methods although this has previously been achieved for linear elastic problems no such optimised matlab script currently exists which includes the effects of material non linearity to incorporate these elasto plastic effects the externally applied load is split into a discrete number of loadsteps equilibrium is determined at each loadstep between the externally applied load and the arising internal forces using the newton raphson method the optimisation of the scripts is primarily achieved using vectorised blocking algorithms which minimise ram to cache overheads and maximise cache reuse the optimised codes yielded maximum speed gains of 25 7 and 10 1 when compared to the corresponding unoptimised scripts for cg and dg respectively it was identified that with increasing refinement of the mesh the solver time begins to dominate the overall simulation time this bottleneck has a greater disadvantage on the dg code predominantly due the asymmetric nature of the global stiffness matrix the implementation of an efficient solver would see further improvement to the overall run times particularly for large problems

confidence intervals for a difference between proportions based on paired data we construct several explicit asymptotic two sided confidence intervals cis for the difference between two correlated proportions using the method of variance of estimates recovery mover the basic idea is to recover variance estimates required for the proportion difference from the confidence limits for single proportions the ci estimators for a single proportion which are incorporated with the mover include the agresti coull the wilson and the jeffreys cis our simulation results show that the mover type cis based on the continuity corrected coefficient and the tango score ci perform satisfactory in small sample designs and spare data structures we illustrate the proposed cis with several real examples copyright 2009 john wiley sons ltd

confidence intervals for the mean of a variable taking the values 0 1 and 2 the problem of setting a confidence interval for the mean of a variable on 0 1 2 arises in three contexts paired organ procedure rates estimation of gene frequency and three point likert scales an effective approach to its estimation may be based on a good interval for a paired difference of proportions four good methods due to newcombe and tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications

confidence intervals for differences in correlated binary proportions an experiment to assess the efficacy of a particular treatment or process often produces dichotomous responses either favourable or unfavourable when we administer the treatment on two occasions to the same subjects we often use mcnemar s test to investigate the hypothesis of no difference in the proportions on the two occasions that is the hypothesis of marginal homogeneity a disadvantage in using mcnemar s statistic is that we estimate the variance of the sample difference under the restriction that the marginal proportions are equal a competitor to mcnemar s statistic is a wald statistic that uses an unrestricted estimator of the variance because the wald statistic tends to reject too often in small samples we investigate an adjusted form that is useful for constructing confidence intervals quesenberry and hurst and goodman discussed methods of construction that we adapt for constructing confidence intervals for the differences in correlated proportions we empirically compare the coverage probabilities and average interval lengths for the competing methods through simulation and give recommendations based on the simulation results

estimating the difference between differences measurement of additive scale interaction for proportions a simple effective closed form method to calculate a confidence interval for the difference between two differences of proportions is proposed the method is based on the wilson score interval for the single proportion and may be used to compare either unpaired or paired differences it is equally applicable whether cell frequencies are large or small and coverage properties are favourable it is easily adapted to give a confidence interval for the treatment effect for a binary outcome in a two period cross over trial

unconditional exact tests for equivalence or noninferiority for paired binary endpoints problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions when the sample size is small the asymptotic tests may not be reliable this article proposes an unconditional exact test procedure to assess equivalence or noninferiority two statistics a sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to define the rejection region of the exact test are considered we show the p value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits we also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics a typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods the p value from the unconditional exact tests is generally larger than the p value from the asymptotic tests in other words an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

an implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto plastic analyses abstract implicit boundary methods which enrich the interpolation structure with implicit weight functions are straightforward methods for the enforcement of dirichlet boundary conditions in this article we follow the implicit boundary method that uses approximate step functions the step boundary method developed by kumar et al and provide modifications that have several advantages roller boundary conditions have wide practical applications in engineering however the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations thus we provide a complete derivation that leads to simplified stiffness matrices compared to the original approach which can be implemented directly in fictitious domain finite element analysis the approach is then extended we believe for the first time to the nonlinear cases of frictional boundary conditions and elasto plastic material behaviour the proposed formulation and procedures are validated on a number of example problems that test different aspects of the method

nurbs plasticity yield surface representation and implicit stress integration for isotropic inelasticity in numerical analysis the failure of engineering materials is controlled through specifying yield envelopes or surfaces that bound the allowable stress in the material however each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case these equations impact on the numerical implementation specifically relating to stress integration of the models and therefore a separate algorithm must be constructed for each model this paper presents for the first time a way to construct yield surfaces using techniques from non uniform rational basis spline nurbs surfaces such that any isotropic convex yield envelope can be represented within the same framework these surfaces are combined with an implicit backward euler type stress integration algorithm to provide a flexible numerical framework for computational plasticity the algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration the performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

the validity and power of tests for equality of two correlated proportions with measurements taken on subjects over time on matched pairs of subjects or on clusters of subjects the data often contain pairs of correlated dichotomous responses mcnemar s test is perhaps the best known test to compare two correlated binomial proportions the salient feature of mcnemar s test is that we compute the variance of the contrast estimator under the restriction that the null hypothesis is true wald s test on the other hand does not require that restriction as a consequence wald s statistic is always greater in magnitude than mcnemar s statistic when the marginal proportions are unequal but there is a problem with the validity of both mcnemar s test and wald s test with small to moderate samples there have been various modifications suggested for mcnemar s test to improve its performance we propose a modified wald s test that is valid in small to moderate samples and maintains good power we also evaluate the performance of mcnemar s test and wald s test with and without modifications to enhance validity as well as the performance of the large sample likelihood ratio test and an exact test of the equality of correlated binomial proportions in a smaller study we compare the behaviour of a test based on the james stein estimator of the common odds ratio proposed by liang and zeger to mcnemar s test and wald s test

interval estimation of the difference in proportions under m to one matching when the number of potential controls is large relative to the number of available cases or when little effort needs to be expended in collecting the relevant information on the controls we often apply multiple matching to attain the validity or increase the efficiency of our inference in epidemiological studies in this paper we focus interval estimation on the difference in proportions for m to one matching we consider four asymptotic interval estimators including the estimator directly using the mantel haenszel mh point estimator the estimator using the tanh 1 x transformation the estimator derived from the cochran mantel haenszel cmh test statistic and the estimator derived from the quadratic inequality developed in this paper to evaluate and compare the performance of these estimators we employ monte carlo simulation we find that the estimator directly using the mh estimator can have the coverage probability less than the desired confidence level when the number of matched sets is small we note that the estimator derived from the quadratic inequality can perform well when the underlying difference is close to 0 even for a small number of matched sets however this estimator tends to have the coverage probability less than the desired confidence level as well when the underlying difference in proportions is large by contrast the estimator using the cmh statistic tends to have the coverage probability larger than the desired confidence level when the underlying difference is small we also find that the estimator using the tanh 1 x transformation consistently outperforms the interval estimator directly using the mh estimator we use the data regarding the association between induced abortions and ectopic pregnancy to illustrate the use of these estimators copyright 2005 john wiley sons ltd

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

a unified numerical integration formula for the perfectly plastic von mises model the accuracy of numerical integration of the perfectly plastic constitutive equation of von mises is examined based on the analysis of the three existing numerical integration schemes a unified numerical integration formula unif is derived which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately according to the unif there are in fact many integration schemes depending on the direction of the trial stress the validity of the unif is verified by presenting ten contours of constant angular error calculated with the unif we then come to the conclusion that the three widely used schemes are by no means the most accurate ones some other schemes with better accuracy are thereby suggested the determination of the number of substeps is also discussed in conjunction with the unif when a multi step method is used

finite element analysis of diffusion with reaction at a moving boundary abstract we consider the model problem of mass transport by diffusion with chemical reaction at a moving boundary the objective is to model the chemical process by predicting the location of the boundary as the reaction proceeds in time a finite element analysis is formulated in one dimension using moving elements to follow the boundary motion and an iterative linearization method is developed to uncouple and solve the diffusion and reaction equations the semidiscrete system for the transport process is integrated using a predictor corrector scheme and its accuracy and stability are examined in numerical experiments numerical results are compared with an analytic solution for the quasi steady case in which diffusion is very rapid in comparison to reaction and to a perturbation solution for the unsteady case other supporting numerical studies are made to examine the sensitivity of the solution and boundary motion to changes in diffusion and reaction rate for both linear and nonlinear reactions

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

interval estimation for the difference between independent proportions comparison of eleven methods several existing unconditional methods for setting confidence intervals for the difference between binomial proportions are evaluated computationally simpler methods are prone to a variety of aberrations and poor coverage properties the closely interrelated methods of mee and miettinen and nurminen perform well but require a computer program two new approaches which also avoid aberrations are developed and evaluated a tail area profile likelihood based method produces the best coverage properties but is difficult to calculate for large denominators a method combining wilson score intervals for the two proportions to be compared also performs well and is readily implemented irrespective of sample size

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

assessing equivalence or non inferiority in screening tests with paired and independent binomial endpoints through confidence intervals for the odds ratio the confidence interval ci on the population average pa odds ratio or is a useful measure of agreement among different diagnostic methods when no gold standard is available it can be calculated by the repeated measures logistic regression procedure genmod sas we compare the width of cis from paired and independent samples with an identical number of measurements and an identical probability of positive response among them for two and three diagnostic methods with binomial endpoints the best performing sampling strategy is analytically described the asymptotic formulae of the ratio of the ci widths for paired and independent samples are provided we numerically study the dependence of the width of the cis on the number of positive concordant outcomes the width of cis from independent samples is an increasing function of the sample size with a saturation asymptote and rather weak dependence on the argument the width of cis from paired samples is a decreasing function of the sample size with a saturation asymptote and significant dependence on the argument when the sample size is small if curves for paired and independent samples intersect a critical sample size exists at this point a small change in the sample size can reverse the choice of the best performing sampling policy we numerically validated the robustness of the critical point to variations of the conditional or

two sided confidence intervals for the single proportion comparison of seven methods simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals criteria appropriate to the evaluation of various proposed methods include closeness of the achieved coverage probability to its nominal value whether intervals are located too close to or too distant from the middle of the scale expected interval width avoidance of aberrations such as limits outside 0 1 or zero width intervals and ease of use whether by tables software or formulae seven methods for the single proportion are evaluated on 96 000 parameter space points intervals based on tail areas and the simpler score methods are recommended for use in each case methods are available that aim to align either the minimum or the mean coverage with the nominal 1 alpha

weighted profile likelihood based confidence interval for the difference between two proportions with paired binomial data inference on the difference between two binomial proportions in the paired binomial setting is often an important problem in many biomedical investigations tang et al 2010 statistics in medicine discussed six methods to construct confidence intervals henceforth we abbreviate it as ci for the difference between two proportions in paired binomial setting using method of variance estimates recovery in this article we propose weighted profile likelihood based cis for the difference between proportions of a paired binomial distribution however instead of the usual likelihood we use weighted likelihood that is essentially making adjustments to the cell frequencies of a 2 2 table in the spirit of agresti and min 2005 statistics in medicine we then conduct numerical studies to compare the performances of the proposed cis with that of tang et al and agresti and min in terms of coverage probabilities and expected lengths our numerical study clearly indicates that the weighted profile likelihood based intervals and jeffreys interval cf tang et al are superior in terms of achieving the nominal level and in terms of expected lengths they are competitive finally we illustrate the use of the proposed cis with real life examples copyright 2014 john wiley sons ltd

sample size determination for establishing equivalence noninferiority via ratio of two proportions in matched pair design summary in this article we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match pairs design using the ratio of two proportions as the equivalence measure we derive sample size formulas based on a score statistic for two types of analyses hypothesis testing and confidence interval estimation depending on the purpose of a study these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level our empirical results confirm that these score methods are reliable in terms of true size coverage probability and skewness a liver scan detection study is used to illustrate the proposed methods

nurbs plasticity yield surface evolution and implicit stress integration for isotropic hardening this paper extends the non uniform rational basis spline nurbs plasticity framework of coombs et al 2016 to include isotropic hardening of the yield surfaces the approach allows any smooth isotropic yield envelope to be represented by a nurbs surface the key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material the model is integrated using a fully implicit backward euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations this provides a powerful framework for elasto plastic constitutive models where unlike the majority of models presented in the literature the underlying numerical algorithm and implemented code remains unchanged for different yield surfaces the performance of the algorithm is demonstrated and validated using both material point and boundary values simulations including plane stress plane strain and three dimensional examples for different yield criteria

a new exact and more powerful unconditional test of no treatment effect from binary matched pairs we consider the problem of testing for a difference in the probability of success from matched binary pairs starting with three standard inexact tests the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization producing what i call an e m p value the e m p value based on mcnemar s statistic is shown numerically to dominate previous suggestions including partially maximized p values as described in berger and sidik 2003 statistical methods in medical research 12 91 108 the latter method however may have computational advantages for large samples

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

error estimates for fully discrete approximation to a free boundary problem in polymer technology in this paper we construct and analyze fully discrete method for a free boundary problem arising in polymer technology this method is based on a galerkin finite element formulation in space and a backward euler time stepping technique we derive optimal error estimates in the spatial and temporal directions in l 2 h 1 normed spaces

confidence intervals from the difference between two correlated proportions abstract when data arise as matched binary pairs it is often of interest to test whether or not the probabilities of an odd pair of each type are equal construction of a small sample confidence interval for the difference in these probabilities is more difficult and either approximate or conservative methods need be resorted to two methods are suggested in this article one a natural asymptotic method and the other a more generally applicable conservative method the coverage probability and average width are studied for small and moderate sample sizes

simple improved confidence intervals for comparing matched proportions for binary matched pairs data this article discusses interval estimation of the difference of probabilities and an odds ratio for comparing success probabilities we present simple improvements of the commonly used wald confidence intervals for these parameters the improvement of the interval for the difference of probabilities is to add two observations to each sample before applying it the improvement for estimating an odds ratio transforms a confidence interval for a single proportion

confidence limits for the ratio of two rates based on likelihood scores non iterative method this paper describes a method for creating a confidence interval for the ratio of rates using the score statistic this non iterative and easy to apply procedure produces confidence intervals that are suitable for use with poisson data and simulation results indicate that it is close to the nominal level for a wide range of scenarios

on the sample size for one sided equivalence of sensitivities based upon mcnemar s test in this paper we formalize the problem of testing the one sided equivalence in the sensitivities of two medical diagnostic tests under a matched pair study design we derive conditional and unconditional sample size formulae which are decreasing functions of the probability of being diagnosed by both tests we calculate upper boundary and midpoint sample sizes results of a monte carlo simulation study that compares the proposed sample size formulae with that of lachenbruch suggest that our midpoint conditional sample size is the best choice to obtain the desired power for the type of equivalence studies discussed in the paper