a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

regression models for longitudinal binary responses with informative drop outs this paper reviews both likelihood based and non likelihood generalized estimating equations regression models for longitudinal binary responses when there are drop outs throughout it is assumed that the regression parameters for the marginal expectations of the binary responses are of primary scientific interest the association or time dependence between the responses is largely regarded as a nuisance characteristic of the data the performance of the methods is compared in terms of asymptotic bias under mis specification of the association between the responses and the missing data mechanism or drop out process

finite sample adjustments in estimating equations and covariance estimators for intracluster correlations bias corrected covariance estimators are introduced in the context of an estimating equations approach for intracluster correlations among binary outcomes simulation study results show that the bias corrected covariance estimators perform better than uncorrected sandwich estimators in terms of bias and coverage probabilities additionally introduction of a matrix based bias correction into the estimating equations considerably improves point and interval estimation for the intracluster correlations the methods are illustrated using data from a nested cross sectional cluster trial on reducing underage drinking

on a class of functionals invariant under a zn action abstract this document considers a system of ordinary differential equations of the form q v sub q t q f t where f and v are periodic in t v is periodic in the components of q q sub 1 q sub m and the mean value of f vanishes by showing that a corresponding functional is invariant under a natural z sub n action a simple variational argument yields at least n 1 distinct periodic solutions of more general versions of are also treated as is a class of neumann problems for semilinear elliptic partial differential equations

modelling multivariate binary data with alternating logistic regressions marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables and the association between pairs of responses when the former is the scientific focus a first order generalized estimating equation method liang zeger 1986 is easy to implement and gives efficient estimates of regression coefficients although estimates of the association among the binary outcomes can be inefficient when the association model is a focus simultaneous modelling of the responses and all pairwise products prentice 1988 using second order estimating equations gives more efficient estimates of association parameters as well however this procedure can become computationally infeasible as the cluster size gets large this paper proposes an alternative approach alternating logistic regressions for simultaneously regressing the response on explanatory variables as well as modelling the association among responses in terms of pairwise odds ratios this algorithm iterates between a logistic regression using first order generalized estimating equations to estimate regression coefficients and a logistic regression of each response on others from the same cluster using an appropriate offset to update the odds ratio parameters for clusters of size n alternating logistic regression involves evaluation and inversion of matrices of order n2 rather than n4 as required for second order generalized estimating equations the alternating logistic regression estimates are shown to be reasonably efficient relative to solutions of second order equations in a few problems the new method is illustrated with an analysis of neuropsychological tests on patients with epileptic seizures

modelling of covariance structures in generalised estimating equations for longitudinal data summary when used for modelling longitudinal data generalised estimating equations specify a working structure for the within subject covariance matrices aiming to produce efficient parameter estimators however misspecification of the working covariance structure may lead to a large loss of efficiency of the estimators of the mean parameters in this paper we propose an approach for joint modelling of the mean and covariance structures of longitudinal data within the framework of generalised estimating equations the resulting estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed real data analysis and simulation studies show that the proposed approach yields efficient estimators for both the mean and covariance parameters

a partial differential equation for the rank one convex envelope a partial differential equation pde for the rank one convex envelope is introduced the existence and uniqueness of viscosity solutions to the pde is established elliptic finite difference schemes are constructed and convergence of finite difference solutions to the viscosity solution of the pde is proven computational results are presented and laminates are computed from the envelopes results include the kohn strang example the classical four gradient example and an example with eight gradients which produces nontrivial laminates

convergent difference schemes for degenerate elliptic and parabolic equations hamilton jacobi equations and free boundary problems convergent numerical schemes for degenerate elliptic partial differential equations are constructed and implemented simple conditions are identified which ensure that nonlinear finite difference schemes are monotone and nonexpansive in the maximum norm explicit schemes endowed with an explicit cfl condition are built for time dependent equations and are used to solve stationary equations iteratively explicit and implicit formulations of monotonicity for first and second order equations are unified bounds on orders of accuracy are established an example of a scheme which is stable but nonmonotone and nonconvergent is presented schemes for hamilton jacobi equations obstacle problems one phase free boundary problems and stochastic games are built and computational results are presented

multivariate logistic models summary the multivariate logistic transform is a reparameterisation of cell probabilities in terms of marginal logistic contrasts it is known that an arbitrary set of logistic contrasts may not correspond to a valid joint distribution in this paper we present an efficient algorithm for detecting whether or not the inverse transform exists and for computing it if it does

working covariance model selection for generalized estimating equations we investigate methods for data based selection of working covariance models in the analysis of correlated data with generalized estimating equations we study two selection criteria gaussian pseudolikelihood and a geodesic distance based on discrepancy between model sensitive and model robust regression parameter covariance estimators the gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean variance relations for longitudinal data application is also made to a clinical dataset assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications and we describe open source software supporting this practice

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

estimates for numerical approximations of rank one convex envelopes summary we present a convergence analysis of an algorithm for the numerical computation of the rank one convex envelope of a function f mathrm m m times n rightarrow mathbb r a rate of convergence for the scheme is established and numerical experiments are presented to illustrate the analytical results and applications of the algorithm

mixed effects models with bivariate and univariate association parameters for longitudinal bivariate binary response data summary when two binary responses are measured for each study subject across time it may be of interest to model how the bivariate associations and marginal univariate risks involving the two responses change across time to achieve such a goal marginal models with bivariate log odds ratio and univariate logit components are extended to include random effects for all components specifically separate normal random effects are specified on the log odds ratio scale for bivariate responses and on the logit scale for univariate responses assuming conditional independence given the random effects facilitates the modeling of bivariate associations across time with missing at random incomplete data we fit the model to a dataset for which such structures are feasible a longitudinal randomized trial of a cardiovascular educational program where the responses of interest are change in hypertension and hypercholestemia status the proposed model is compared to a naive bivariate model that assumes independence between time points and univariate mixed effects logit models

bayesian multivariate logistic regression bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes in addition difficulties arise when simple noninformative priors are chosen for the covariance parameters motivated by these problems we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data the model for individual outcomes has a marginal logistic structure simplifying interpretation we follow a bayesian approach to estimation and inference developing an efficient data augmentation algorithm for posterior computation the method is illustrated with application to a neurotoxicology study

periodic solutions of classical hamiltonian systems without palais smale condition abstract in this paper we study the existence of periodic solutions for classical hamiltonian systems without the palais smale condition we prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions moreover we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function v

on the computation of the rank one convex hull of a function we report on several numerical experiments where the rank one convexification of an energy density is computed the explicit examples cover a whole spectrum of typical situations one may encounter one of those is especially relevant for the computation of microstructures in crystalline solids

smoothing spline anova for multivariate bernoulli observations with application to ophthalmology data we combine a smoothing spline analysis of variance ss anova model and a log linear model to build a partly flexible model for multivariate bernoulli data the joint distribution conditioning on the predictor variables is estimated the log odds ratio is used to measure the association between outcome variables a numerical scheme based on the block one step successive over relaxation sor newton ralphson algorithm is proposed to obtain an approximate solution for the variational problem we extend the generalized approximate cross validation gacv and the randomized gacv for choosing smoothing parameters to the case of multivariate bernoulli responses the randomized version is fast and stable to compute and is used to adaptively select smoothing parameters in each block onestep sor iteration approximate bayesian confidence intervals are obtained for the flexible estimates of the conditional logit functions simulation studies are conducted to check the performance of the proposed method using the com

reliable and efficient approximation of polyconvex envelopes an iterative algorithm that approximates the polyconvex envelope fpc of a given function f mathbb r n times m to mathbb r i e the largest function below f which is convex in all minors is established also presented are a rigorous error analysis with a focus on reliability and optimal orders of convergence an efficient strategy that reduces the large number of unknowns as well as numerical experiments

front propagation problems with nonlocal terms ii abstract we study the propagation of hyper surfaces t of r n satisfying the equation v h x t where v is the normal velocity of t at x t is the interior of t and h is a given evolution law we prove the existence of generalized solutions and an inclusion principle for these generalized solutions copyright 2001 academic press dans cet article nous etudions certains problemes de propagation d hypersurfaces t de r n suivant des lois de la forme v h x t ou v est la vitesse normale a t en x t est l interieur de t et h est une loi d evolution on definit une notion de solutions generalisees et on montre l existence de telles solutions de plus on demontre un principe d inclusion pour ces solutions

on the smoothness of convex envelopes we examine differentiability properties of the convex envelope conv e of a given function e rn cc cc in terms of properties of e it is shown that c1 as well as optimal c1 a regularity results 0 a 1 can be obtained under general conditions

marginal methods for correlated binary data with misclassified responses misclassification is a longstanding concern in medical research although there has been much research concerning error prone covariates relatively little work has been directed to problems with response variables subject to error in this paper we focus on misclassification in clustered or longitudinal outcomes we propose marginal analysis methods to handle binary responses which are subject to misclassification the proposed methods have several appealing features including simultaneous inference for both marginal mean and association parameters and they can handle misclassified responses for a number of practical scenarios such as the case with a validation subsample or replicates furthermore the proposed methods are robust to model misspecification in a sense that no full distributional assumptions are required numerical studies demonstrate satisfactory performance of the proposed methods under a variety of settings copyright 2011 oxford university press

alternating logistic regressions with improved finite sample properties alternating logistic regressions is an estimating equations procedure used to model marginal means of correlated binary outcomes while simultaneously specifying a within cluster association model for log odds ratios of outcome pairs a recent generalization of alternating logistic regressions known as orthogonalized residuals is extended to incorporate finite sample adjustments in the estimation of the log odds ratio model parameters for when there is a moderately small number of clusters bias adjustments are made both in the sandwich variance estimators and in the estimating equations for the association parameters the proposed methods are demonstrated in a repeated cross sectional cluster trial to reduce underage drinking in the united states and in an analysis of dental caries incidence in a cluster randomized trial of 30 aboriginal communities in the northern territory of australia a simulation study demonstrates improved performance with respect to bias and coverage of their estimators relative to those based on the uncorrected orthogonalized residuals procedure

numerical approximation of non homogeneous non convex vector variational problems in this paper we study a numerical scheme for non convex vector variational problems allowing for microstructure based on the approximation of gradient young measures we present a convergence result and some numerical experiments

marginal methods for incomplete longitudinal data arising in clusters inverse probability weighted generalized estimating equations are commonly used to deal with incomplete longitudinal data arising from a missing at random mechanism when the marginal means are of primary interest in many cases however the repeated measurements themselves may arise in clusters which leads to both a cross sectional and a longitudinal correlation structure in some applications the degree of these types of correlation may become of scientific interest here we develop inverse probability weighted second order estimating equations for monotone missing data patterns which under specified assumptions facilitate consistent estimation of the marginal mean parameters and association parameters here the missing data model accommodates cross sectional clustering in the missing data indicators and the probabilities are estimated under a multivariate plackett model for computational reasons we also consider using the alternating logistic regression algorithm for estimation of the associatio

interior w 2 p estimates for solutions of the monge ampere equation in this work we adapt the techniques developed in c1 to prove interior estimates for solutions of perturbations of the monge ampere equation

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

the analysis of binary longitudinal data with time dependent covariates we consider longitudinal studies with binary outcomes that are measured repeatedly on subjects over time the goal of our analysis was to fit a logistic model that relates the expected value of the outcomes with explanatory variables that are measured on each subject however additional care must be taken to adjust for the association between the repeated measurements on each subject we propose a new maximum likelihood method for covariates that may be fixed or time varying we also implement and make comparisons with two other approaches generalized estimating equations which may be more robust to misspecification of the true correlation structure and alternating logistic regression which models association via odds ratios that are subject to less restrictive constraints than are correlations the proposed estimation procedure will yield consistent and asymptotically normal estimates of the regression and correlation parameters if the correlation on consecutive measurements on a subject is correctly specified simulations demonstrate that our approach can yield improved efficiency in estimation of the regression parameter for equally spaced and complete data the gains in efficiency were greatest for the parameter associated with a time by group interaction term and for stronger values of the correlation for unequally spaced data and with dropout according to a missing at random mechanism mark1ml with correctly specified consecutive correlations yielded substantial improvements in terms of both bias and efficiency we present an analysis to demonstrate application of the methods we consider we also offer an r function for easy implementation of our approach copyright 2012 john wiley sons ltd

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

the dirichlet problem for the convex envelope the convex envelope of a given function was recently characterized as the solution of a fully nonlinear partial differential equation pde in this article we study a modified problem the dirichlet problem for the underlying pde the main result is an optimal regularity result differentiability c1 regularity of the boundary data implies the corresponding result for the solution in the interior despite the fact that the solution need not be continuous up to the boundary secondary results are the characterization of the convex envelope as i the value function of a stochastic control problem and ii the optimal underestimator for a class of nonlinear elliptic pdes

permutation invariance of alternating logistic regression for multivariate binary data summary a practically important but not so obvious result is that alternating logistic regression is invariant to permutations of the response variables within clusters in this note we give a short proof of the invariance result using a pairwise likelihood argument the same proof can be used to establish invariance for a more general class of estimating equations based on conditional residuals as it stands the invariance theory is incomplete because existing standard error estimates are not invariant to permutations to solve this problem we present a symmetrised version of the estimating equation and use it to obtain permutation invariant standard errors

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

numerical computation of rank one convex envelopes we describe an algorithm for the numerical computation of the rank one convex envelope of a function f mm m times n rightarrow rr we prove its convergence and an error estimate in l infty

intra cluster correlation selection for cluster randomized trials in this paper we give focus to cluster randomized trials also known as group randomized trials which randomize clusters or groups of subjects to different trial arms such as intervention or control outcomes from subjects within the same cluster tend to exhibit an exchangeable correlation measured by the intra cluster correlation coefficient icc our primary interest is to test if the intervention has an impact on the marginal mean of an outcome using recently developed methods we propose how to select a working icc structure with the goal of choosing the structure that results in the smallest standard errors for regression parameter estimates and thus the greatest power for this test specifically we utilize small sample corrections for the estimation of the covariance matrix of regression parameter estimates this matrix is incorporated within correlation selection criteria proposed in the generalized estimating equations literature to choose one of multiple working icc structures under consideration we demonstrate the potential power and utility of this approach when used in cluster randomized trial settings via a simulation study and application example and we discuss practical considerations for its use in practice copyright 2016 john wiley sons ltd

improving small sample inference in group randomized trials with binary outcomes group randomized trials grts randomize groups of people to treatment or control arms instead of individually randomizing subjects when each subject has a binary outcome over dispersed binomial data may result quantified as an intra cluster correlation icc typically grts have a small number bin of independent clusters each of which can be quite large treating the icc as a nuisance parameter inference for a treatment effect can be done using quasi likelihood with a logistic link a wald statistic which under standard regularity conditions has an asymptotic standard normal distribution can be used to test for a marginal treatment effect however we have found in our setting that the wald statistic may have a variance less than 1 resulting in a test size smaller than its nominal value this problem is most apparent when marginal probabilities are close to 0 or 1 particularly when n is small and the icc is not negligible when the icc is known we develop a method for adjusting the estimated standard error appropriately such that the wald statistic will approximately have a standard normal distribution we also propose ways to handle non nominal test sizes when the icc is estimated we demonstrate the utility of our methods through simulation results covering a variety of realistic settings for grts

convergent filtered schemes for the monge ampere partial differential equation the theory of viscosity solutions has been effective for representing and approximating weak solutions to fully nonlinear partial differential equations such as the elliptic monge ampere equation the approximation theory of barles and souganidis asymptotic anal 4 1991 pp 271 283 requires that numerical schemes be monotone or elliptic in the sense of a m oberman siam j numer anal 44 2006 pp 879 895 but such schemes have limited accuracy in this article we establish a convergence result for filtered schemes which are nearly monotone this allows us to construct finite difference discretizations of arbitrarily high order we demonstrate that the higher accuracy is achieved when solutions are sufficiently smooth in addition the filtered scheme provides a natural detection principle for singularities we employ this framework to construct a formally second order scheme for the monge ampere equation and present computational results on smooth and singular solutions

on the periodic nonlinearity and the multiplicity of solutions abstract this document studies the multiplicity of solutions for semilinear elliptic systems as well as hamiltonian systems in which the nonlinear terms are periodic in certain variables the cuplength for cohomology rings of the torus is used our results generalize and unify several recent works by conley zehnder rabinowitz mawhin willem pucci serrin etc in particular the resonance problems and indefinite problems are studied keywords critical point neumann problem periodic solution

analysis of multivariate probit models summary this paper provides a practical simulation based bayesian and non bayesian analysis of correlated binary data using the multivariate probit model the posterior distribution is simulated by markov chain monte carlo methods and maximum likelihood estimates are obtained by a monte carlo version of the em algorithm a practical approach for the computation of bayes factors from the simulation output is also developed the methods are applied to a dataset with a bivariate binary response to a four year longitudinal dataset from the six cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the panel survey of income dynamics

marginal regression models for clustered ordinal measurements abstract this article constructs statistical models for clustered ordinal measurements we specify two regression models one for the marginal means and one for the marginal pairwise global odds ratios of particular interest are problems in which the odds ratio regression is a focus simple assumptions about higher order conditional moments give a quadratic exponential likelihood function with second order estimating equations gee2 as score equations but computational difficulty can arise for large clusters when both the mean response and the association between measures is of interest first we present gee1 as an alternative estimation strategy second we extend to repeated ordinal measurements the method developed by carey et al for binary observations that is based on alternating logistic regressions alr for the marginal mean parameters and the pairwise log odds ratio parameters we study the efficiency of gee1 and alr relative to full maximum likelihood we demonstrate the utility of our regr

periodic solutions for some nonautonomous second order hamiltonian systems the existence and multiplicity of periodic solutions are obtained for nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

using multiple imputation with gee with non monotone missing longitudinal binary outcomes this paper considers multiple imputation mi approaches for handling non monotone missing longitudinal binary responses when estimating parameters of a marginal model using generalized estimating equations gee gee has been shown to yield consistent estimates of the regression parameters for a marginal model when data are missing completely at random mcar however when data are missing at random mar the gee estimates may not be consistent the mi approaches proposed in this paper minimize bias under mar the first mi approach proposed is based on a multivariate normal distribution but with the addition of pairwise products among the binary outcomes to the multivariate normal vector even though the multivariate normal does not impute 0 or 1 values for the missing binary responses as discussed by horton et al am stat 57 229 232 2003 we suggest not rounding when filling in the missing binary data because it could increase bias the second mi approach considered is the fully conditional specification fcs approach in this approach we specify a logistic regression model for each outcome given the outcomes at other time points and the covariates typically one would only include main effects of the outcome at the other times as predictors in the fcs approach but we explore if bias can be reduced by also including pairwise interactions of the outcomes at other time point in the fcs in a study of asymptotic bias with non monotone missing data the proposed mi approaches are also compared to gee without imputation finally the proposed methods are illustrated using data from a longitudinal clinical trial comparing four psychosocial treatments from the national institute on drug abuse collaborative cocaine treatment study where patients cocaine use is collected monthly for 6 months during treatment

global cross ratio models for bivariate discrete ordered responses summary a family of statistical models is presented for bivariate discrete response to a regressor when both components of the response have ordered categories association between components is expressed in terms of global cross ratios cross product ratios of quadrant probabilities for each double dichotomy of the response table of probabilities into quadrants pearson and heron 1913 biometrika 9 159 315 these models are extensions to the work of plackett 1965 journal of the american statistical association 60 516 522 and mantel and brown 1973 biometrics 29 649 665 the marginal cumulative probabilities may satisfy linear logistic or other generalized linear models mccullagh 1980 journal of the royal statistical society series b 42 109 142 an analysis of patients postoperative pain level and medication frequency illustrates these methods

marginally specified logistic normal models for longitudinal binary data summary likelihood based inference for longitudinal binary data can be obtained using a generalized linear mixed model breslow n and clayton d g 1993 journal of the american statistical association88 9 25 wolfinger r and o connell m 1993 journal of statistical computation and simulation48 233 243 given the recent improvements in computational approaches alternatively fitzmaurice and laird 1993 biometrika80 141 151 molenberghs and lesaffre 1994 journal of the american statistical association89 633 644 and heagerty and zeger 1996 journal of the american statistical association91 1024 1036 have developed a likelihood based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and or marginal higher moment assumptions each of these marginal approaches is computationally intense and currently limited to small cluster sizes in this manuscript an alternative parameterization of the logistic normal random effects model is adopted and both likelihood and estimating equation approaches to parameter estimation are studied a key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual level predictions or contrasts an example is presented where scientific interest is in both the mean response and the covariance among repeated measurements

using second order generalized estimating equations to model heterogeneous intraclass correlation in cluster randomized trials in cluster randomized trials it is commonly assumed that the magnitude of the correlation among subjects within a cluster is constant across clusters however the correlation may in fact be heterogeneous and depend on cluster characteristics accurate modeling of the correlation has the potential to improve inference we use second order generalized estimating equations to model heterogeneous correlation in cluster randomized trials using simulation studies we show that accurate modeling of heterogeneous correlation can improve inference when the correlation is high or varies by cluster size we apply the methods to a cluster randomized trial of an intervention to promote breast cancer screening

a hybrid pairwise likelihood method a modification to the pairwise likelihood method is proposed which aims to improve the estimation of the marginal distribution parameters this is achieved by replacing the pairwise likelihood score equations for estimating such parameters by the optimal linear combinations of the marginal score functions a further advantage of the proposed estimator of marginal parameters over pairwise likelihood is that it is robust to misspecification of the bivariate distributions as long as the univariate marginal distributions are correctly specified while alternating logistic regression can be seen as a special case of the proposed method it is shown that an existing generalization of alternating logistic regression applicable to ordinal data is not the same as and is inferior to the proposed method because it replaces certain conditional densities by pseudodensities that assume working independence the fitting of the multivariate negative binomial distribution is another scenario involving intractable likelihood that calls for the use of pairwise likelihood methods and the superiority of the modified method is demonstrated in a simulation study two examples based on the analyses of salamander mating and patient controlled analgesia data demonstrate the usefulness of the proposed method the possibility of combining optimally the pairwise rather than marginal scores is also considered and its difficulty and potential are discussed

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

gee analysis of negatively correlated binary responses a caution the method of generalized estimating equations has become almost standard for analysing longitudinal and other correlated response data however we have found that if binary responses have less than binomial variation over clusters and are modelled using exchangeable correlations prevailing software implementations may give unreliable results bounding the negative correlation away from its theoretical minimum may not always be a satisfactory solution in such instances using the independence working correlation structure and robust ses is a more trustworthy alternative

optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations in this paper we prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients more precisely we deal with coefficients and right hand sides rhs in lq with q geq n this extends the result of caffarelli on the c loc 1 1 regularity of the convex envelope of supersolutions of fully nonlinear elliptic equations with bounded rhs moreover we also provide a regularity result with estimates for omega semiconvex functions that are supersolutions to the same type of equations with unbounded rhs i e rhs in l q q geq n by a completely different method our results here extend the recent regularity results obtained by braga et al adv math 334 184 242 2018 for q n as far as fully nonlinear pdes are concerned these results include in particular the apriori estimate obtained by caffarelli et al commun pure appl math 38 2 209 252 1985 on the modulus of continuity of the gradient of omega semiconvex supersolutions for linear equations and bounded rhs that have a holder modulus of semiconvexity

joint modeling of multiple ordinal adherence outcomes via generalized estimating equations with flexible correlation structure jiang z reprint author univ pittsburgh grad sch publ hlth dept biostat pittsburgh pa 15261 usa zhen jiang fda hhs gov

a likelihood based method for analysing longitudinal binary responses summary in this paper we discuss a likelihood based method for analysing correlated binary responses based on a multivariate model it is related to the pseudo maximum likelihood approach suggested recently by zhao prentice 1990 their parameterization results in a simple pairwise model in which the association between responses is modelled in terms of correlations while the present paper uses conditional log odds ratios with this approach higher order associations can be incorporated in a natural way one important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence we describe an iterative two stage procedure for obtaining the maximum likelihood estimates two examples are presented to illustrate this methodology

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

classification trees for multiple binary responses abstract multiple binary responses arise from many applications for which an array of health related symptoms are of primary interest these symptoms are usually correlated i generalize the tree based methodology for a single response to the case involving multiple binary responses in particular i apply the method to analyze building related occupant complaint syndrome based on a recently collected large database using the same database i compare the performance of several node splitting criteria for trees

a note on deletion diagnostics for estimating equations we describe an algorithm based upon the sherman morrison woodbury formula for the inversion of matrices with special structure that occur in formulae for deletion diagnostics substantial computational savings relative to a method based upon cholesky s decomposition are illustrated the result has broad application to regression diagnostics for clustered data

a generalized saddle point theorem abstract the well known saddle point theorem is extended to the case of functions defined on a product space x v where x is a banach space and v is a compact manifold under some linking conditions the existence of at least cuplength v 1 critical points is proved the abstract theorems are applied to the existence problems of periodic solutions of hamiltonian systems with periodic nonlinearity and or resonance

mixtures of marginal models summary in this paper we adapt a mixture model originally developed for regression models with independent data for the more general case of correlated outcome data which includes longitudinal data as a special case the estimation is performed by a generalisation of the em algorithm which we call the expectation solution es algorithm in this es algorithm the m step of the em algorithm is replaced by a step requiring the solution of a series of generalised estimating equations the es algorithm a general algorithm for solving generalised estimating equations with incomplete data is then applied to the present problem of mixtures of marginal models in addition to allowing for correlation inherent in correlated outcome data the systematic component of this mixture of marginal models is more flexible than the conventional linear function the methodology is applied in the contexts of normal and poisson response data some theory regarding the es algorithm is presented

bias in estimating association parameters for longitudinal binary responses with drop outs summary this paper considers the impact of bias in the estimation of the association parameters for longitudinal binary responses when there are drop outs a number of different estimating equation approaches are considered for the case where drop out cannot be assumed to be a completely random process in particular standard generalized estimating equations gee gee based on conditional residuals gee based on multivariate normal estimating equations for the covariance matrix and second order estimating equations geez are examined these different gee estimators are compared in terms of finite sample and asymptotic bias under a variety of drop out processes finally the relationship between bias in the estimation of the association parameters and bias in the estimation of the mean parameters is explored

testing for marginal independence between two categorical variables with multiple responses questions that ask respondents to choose all that apply from a set of items occur frequently in surveys categorical variables that summarize this type of survey data are called both pick any c variables and multiple response categorical variables it is often of interest to test for independence between two categorical variables when both categorical variables can have multiple responses traditional pearson chi square tests for independence should not be used because of the within subject dependence among responses an intuitively constructed version of the pearson statistic is proposed to perform the test using bootstrap procedures to approximate its sampling distribution first and second order adjustments to the proposed statistic are given in order to use a chi square distribution approximation a bonferroni adjustment is proposed to perform the test when the joint set of responses for individual subjects is unavailable simulations show that the bootstrap procedures hold the correct size more consistently than the other procedures

use of quasi least squares to adjust for two levels of correlation this article considers data with two levels of association our motivating example is an international intervention trial with repeated observations on subjects who reside within geographically defined clusters to account for the potential correlation within clusters and within the repeated measurements that pertain to each subject we apply a method based on generalized estimating equations for a correlation structure proposed by lefkopoulou moore and ryan 1989 journal of the american statistical association 84 810 815

regression analysis of correlated ordinal data using orthogonalized residuals semi parametric regression models for the joint estimation of marginal mean and within cluster pairwise association parameters are used in a variety of settings for population averaged modeling of multivariate categorical outcomes recently a formulation of alternating logistic regressions based on orthogonalized marginal residuals has been introduced for correlated binary data unlike the original procedure based on conditional residuals its covariance estimator is invariant to the ordering of observations within clusters in this article the orthogonalized residuals method is extended to model correlated ordinal data with a global odds ratio and shown in a simulation study to be more efficient and less biased with regards to estimating within cluster association parameters than an existing extension to ordinal data of alternating logistic regressions based on conditional residuals orthogonalized residuals are used to estimate a model for three correlated ordinal outcomes measured repeatedly in a longitudinal clinical trial of an intervention to improve recovery of patients perception of altered sensation following jaw surgery

weighted generalized estimating functions for longitudinal response and covariate data that are missing at random longitudinal studies often feature incomplete response and covariate data it is well known that biases can arise from naive analyses of available data but the precise impact of incomplete data depends on the frequency of missing data and the strength of the association between the response variables and covariates and the missing data indicators various factors may influence the availability of response and covariate data at scheduled assessment times and at any given assessment time the response may be missing covariate data may be missing or both response and covariate data may be missing here we show that it is important to take the association between the missing data indicators for these two processes into account through joint models inverse probability weighted generalized estimating equations offer an appealing approach for doing this here we develop these equations for a particular model generating intermittently missing at random data empirical studies demonstrate that the consistent e

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

efficient semiparametric mean association estimation for longitudinal binary responses semiparametric methods for longitudinal data with association within subjects have recently received considerable attention however existing methods for semiparametric longitudinal binary regression modeling i mainly concern mean structures with association parameters treated as nuisance ii generally require a correct specification of the covariance structure for misspecified covariance structure may lead to inefficient mean parameter estimates and iii usually run into computation and estimation problems when the time points are irregularly and possibly subject specific in this article we propose a semiparametric logistic regression model which simultaneously takes into account both the mean and response association structures via conditional log odds ratio for multivariate longitudinal binary outcomes our main interest lies in efficient estimation of both the marginal and association parameters the estimators of the parameters are obtained via the profile kernel approach we evaluate the proposed methodology through simulation studies and apply it to a real dataset both theoretical and empirical results demonstrate that the proposed method yields highly efficient estimators and performs satisfactorily copyright 2012 john wiley sons ltd

modelling and generating correlated binary variables summary many applications use simple parametric models for the correlation structure of binary responses which are observed in clusters the usual approach to use correlation models appropriate for normally distributed responses suffers from two drawbacks when the marginal probabilities within the clusters differ first as it does not explicitly take into account constraints on the second moments which must be satisfied for binary responses it may fail to model realistically the range of correlations present in the data secondly computer simulation of observations from these models is very difficult we present an alternative class of correlation models which reflect the binary nature of the responses and allow for simple simulation some key wor ds binary variable computer simulation correlation structure generalised estimating equation

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

properties of ideal point classification models for bivariate binary data the ideal point classification ipc model was originally proposed for analysing multinomial data in the presence of predictors in this paper we studied properties of the ipc model for analysing bivariate binary data with a specific focus on three quantities 1 the marginal probabilities 2 the association structure between the two binary responses and 3 the joint probabilities we found that the ipc model with a specific class point configuration represents either the marginal probabilities or the association structure however the ipc model is not able to represent both quantities at the same time we then derived a new parametrization of the model the bivariate ipc bipc model which is able to represent both the marginal probabilities and the association structure like the standard ipc model the results of the bipc model can be displayed in a biplot from which the effects of predictors on the binary responses and on their association can be read we will illustrate our findings with a psychological example relating personality traits to depression and anxiety disorders

periodic solutions of second order differential inclusions systems with p laplacian some existence results are obtained for periodic solutions of nonautonomous second order differential inclusions systems with p laplacian

logistic regression for autocorrelated data with application to repeated measures summary a stochastic model is proposed for the study of the influence of time dependent covariates on the marginal distribution of the binary response in serially correlated binary data markov chains are expressed in terms of transitional rather than marginal probabilities we show how to construct the model so that the covariates relate only to the mean value of the process independently of the association parameter after formulating the stochastic model for a simple sequence of data with possibly missing data the same approach is applied to a repeated measures setting and illustrated with a real data example

periodic solutions for nonautonomous second order systems with bounded nonlinearity some existence and multiplicity theorems are obtained for periodic solutions of nonautonomous second order systems with bounded nonlinearity by the minimax methods

estimating equations for measures of association between repeated binary responses moment based methods for analyzing repeated binary responses using the marginal odds ratio as a measure of association have been proposed by a number of authors carey zeger and diggle 1993 biometrika 80 517 526 have recently described how the marginal odds ratio can be estimated using generalized estimating equations gee based on conditional residuals deviations about conditional expectations in this paper we show that other measures of association between pairs of binary responses e g the correlation can also be estimated using conditional residuals we demonstrate that the estimator of the correlation based on conditional residuals is nearly efficient when compared with maximum likelihood or second order estimating equations gee2 except when the correlation is large this estimator also yields more efficient estimates of the correlation than the usual gee estimator that is based on unconditional residuals furthermore the gains in efficiency can be quite considerable when some of the responses are missing or incomplete or alternatively when cluster sizes are unequal in the clustered data setting

transition models for multivariate longitudinal binary data in many settings with longitudinal binary data interest lies in modeling covariate effects on transition probabilities of an underlying stochastic process when data from two or more processes are available the scientific focus may be on the degree to which changes in one process are associated with changes in another process analysis based on independent markov models permits separate examination of covariate effects on the transition probabilities for each process but no insight into between process associations is obtained we propose a method of estimation and inference based on joint transitional models for multivariate longitudinal binary data using gee2 or alternating logistic regression that allows modeling of covariate effects on marginal transition probabilities as well as the association parameters consistent estimates of regression coefficients and association parameters are obtained and efficiency gains for the parameters governing the marginal transition probabilities are realized when

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

a family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures