modeling tumor onset and multiplicity using transition models with latent variables summary we describe a method for modeling carcinogenicity from animal studies where the data consist of counts of the number of tumors present over time the research is motivated by applications to transgenic rodent studies which have emerged as an alternative to chronic bioassays for screening possible carcinogens in transgenic mouse studies the endpoint of interest is frequently skin papilloma with weekly examinations determining how many papillomas each animal has at a particular point in time it is assumed that each animal has two unobservable latent variables at each time point the first indicates whether or not the tumors are in a multiplying state and the second is the potential number of additional tumors if the tumors are in a multiplying state the product of these variables follows a zero inflated poisson distribution and the em algorithm can be used to maximize the observed data pseudo likelihood based on the latent variables a generalized estimating equations robust variance estimator adjusts for dependency among outcomes within individual animals the method is applied to testing for a dose related trend in both tumor incidence and multiplicity in carcinogenicity studies

numerical stability for a dynamic naghdi shell we consider an elastic model for a shell incorporating shear membrane bending and dynamic effects we make use of the theory proposed by arnold and brezzi 1 based on a locking free non standard mixed variational formulation this method is implemented in terms of the displacement and rotation variables as the minimization of an altered energy functional we extend this theory to the shell vibrations problem and establish optimal error estimates independent of the thickness thereby proving that shear and membrane locking is avoided we study the numerical stability both in static and dynamic regimes the approximation schemes are tested on specific examples and the numerical results confirm the estimates obtained from theory

semiparametric analysis of zero inflated count data medical and public health research often involve the analysis of count data that exhibit a substantially large proportion of zeros such as the number of heart attacks and the number of days of missed primary activities in a given period a zero inflated poisson regression model which hypothesizes a two point heterogeneity in the population characterized by a binary random effect is generally used to model such data subjects are broadly categorized into the low risk group leading to structural zero counts and high risk or normal group so that the counts can be modeled by a poisson regression model the main aim is to identify the explanatory variables that have significant effects on i the probability that the subject is from the low risk group by means of a logistic regression formulation and ii the magnitude of the counts given that the subject is from the high risk group by means of a poisson regression where the effects of the covariates are assumed to be linearly related to the natural logarithm of the mean of the counts in this article we consider a semiparametric zero inflated poisson regression model that postulates a possibly nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate a sieve maximum likelihood estimation method is proposed asymptotic properties of the proposed sieve maximum likelihood estimators are discussed under some mild conditions the estimators are shown to be asymptotically efficient and normally distributed simulation studies were carried out to investigate the performance of the proposed method for illustration purpose the method is applied to a data set from a public health survey conducted in indonesia where the variable of interest is the number of days of missed primary activities due to illness in a 4 week period

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

on mathematical programming with indicator constraints in this paper we review the relevant literature on mathematical optimization with logical implications i e where constraints can be either active or disabled depending on logical conditions to hold in the case of convex functions the theory of disjunctive programming allows one to formulate these logical implications as convex nonlinear programming problems in a space of variables lifted with respect to its original dimension we concentrate on the attempt of avoiding the issue of dealing with large nlps in particular we review some existing results that allow to work in the original space of variables for two relevant special cases where the disjunctions corresponding to the logical implications have two terms then we significantly extend these special cases in two different directions one involving more general convex sets and the other with disjunctions involving three terms computational experiments comparing disjunctive programming formulations in the original space of variables with straightforward bigm ones show that the former are computationally viable and promising

on the separation of disjunctive cuts disjunctive cuts for mixed integer linear programs mips were introduced by egon balas in the late 1970s and have been successfully exploited in practice since the late 1990s in this paper we investigate the main ingredients of a disjunctive cut separation procedure and analyze their impact on the quality of the root node bound for a set of instances taken from miplib library we compare alternative normalization conditions and try to better understand their role in particular we point out that constraints that become redundant because of the disjunction used can produce over weak cuts and analyze this property with respect to the normalization used finally we introduce a new normalization condition and analyze its theoretical properties and computational behavior along the way we make use of a number of small numerical examples to illustrate some basic and often misinterpreted disjunctive programming features

augmented weighted estimators dealing with practical positivity violation to causal inferences in a random coefficient model the inverse probability of treatment weighted iptw estimator can be used to make causal inferences under two assumptions 1 no unobserved confounders ignorability and 2 positive probability of treatment and of control at every level of the confounders positivity but is vulnerable to bias if by chance the proportion of the sample assigned to treatment or proportion of control is zero at certain levels of the confounders we propose to deal with this sampling zero problem also known as practical violation of the positivity assumption in a setting where the observed confounder is cluster identity i e treatment assignment is ignorable within clusters specifically based on a random coefficient model assumed for the potential outcome we augment the iptw estimating function with the estimated potential outcomes of treatment or of control for clusters that have no observation of treatment or control if the cluster specific potential outcomes are estimated correctly the augmented estimating function can be shown to converge in expectation to zero and therefore yield consistent causal estimates the proposed method can be implemented in the existing software and it performs well in simulated data as well as with real world data from a teacher preparation evaluation study

clustered mixed nonhomogeneous poisson process spline models for the analysis of recurrent event panel data summary a flexible semiparametric model for analyzing longitudinal panel count data arising from mixtures is presented panel count data refers here to count data on recurrent events collected as the number of events that have occurred within specific follow up periods the model assumes that the counts for each subject are generated by mixtures of nonhomogeneous poisson processes with smooth intensity functions modeled with penalized splines time dependent covariate effects are also incorporated into the process intensity using splines discrete mixtures of these nonhomogeneous poisson process spline models extract functional information from underlying clusters representing hidden subpopulations the motivating application is an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth mature moths arise from hidden but distinct subpopulations and monitoring the subpopulation responses was of interest within cluster random effects are used to account for correlation structures and heterogeneity common to this type of data an estimating equation approach to inference requiring only low moment assumptions is developed and the finite sample properties of the proposed estimating functions are investigated empirically by simulation

estimation of death rates in us states with small subpopulations in us states with small subpopulations the observed mortality rates are often zero particularly among young ages because in life tables death rates are reported mostly on a log scale zero mortality rates are problematic to overcome the observed zero death rates problem appropriate probability models are used using these models observed zero mortality rates are replaced by the corresponding expected values this enables logarithmic transformations and in some cases the fitting of the eight parameter heligman pollard model to produce mortality estimates for ages 0 130 years a procedure illustrated in terms of mortality data from several states copyright 2014 john wiley sons ltd

sur la convergence des methodes d elements finis nonconformes pour des problemes lineaires de coques minces in this paper we study the convergence of nonconforming finite element method for the approximation of general thin shell problems we give sufficient conditions of convergence for a large class of finite elements then we estimate the error on the displacements and on the stresses dans cet article nous etudions la convergence des methodes d elements finis nonconformes pour l approximation des problemes de coques minces generales nous etablissons des conditions suffisantes de convergence pour une large classe d elements finis puis nous donnons des estimations de l erreur sur les deplacements et les contraintes

the cphd filter with target spawning in its classical form the cardinalized probability hypothesis density cphd filter does not model the appearance of new targets through spawning yet there are applications for which spawning models more appropriately account for newborn objects when compared to spontaneous birth models in this paper we propose a principled derivation of the cphd filter prediction step including spontaneous birth and spawning a gaussian mixture implementation of the cphd filter with spawning is then presented illustrated with three applicable spawning models on a simulated scenario involving two parent targets spawning a total of five objects

multivariate bernoulli mixture models with application to postmortem tissue studies in schizophrenia a novel mixture model is presented for repeated measurements in which correlation among repeated observations on the same subject is induced via correlated unobservable component indicators the mixture components in our model are linear regressions and the mixing proportions are logits with random effects inference is facilitated by sampling from the posterior distribution of the parameters via markov chain monte carlo methods the model is applied to a neuronal postmortem brain tissue study to examine the differences in neuron volumes between schizophrenic and control subjects

a score test for zero inflation in a poisson distribution when analyzing poisson count data sometimes a lot of zeros are observed when there are too many zeros a zero inflated poisson distribution can be used a score test is presented to test whether the number of zeros is too large for a poisson distribution to fit the data well

bilevel programming and the separation problem in recent years branch and cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs milps methods for automatically generating inequalities valid for the convex hull of solutions to such milps are a critical element of branch and cut this paper examines the nature of the so called separation problem which is that of generating a valid inequality violated by a given real vector usually arising as the solution to a relaxation of the original problem we show that the problem of generating a maximally violated valid inequality often has a natural interpretation as a bilevel program in some cases this bilevel program can be easily reformulated as a simple single level mathematical program yielding a standard mathematical programming formulation for the separation problem in other cases no such polynomial size single level reformulation exists unless the polynomial hierarchy collapses to its first level an event considered extremely unlikely in computational complexity theory we illustrate our insights by considering the separation problem for two well known classes of valid inequalities

bootstrap tests for overdispersion in a zero inflated poisson regression model summaryridout hinde and demetrio 2001 biometrics57 219 223 derived a score test for testing a zero inflated poisson zip regression model against zero inflated negative binomial zinb alternatives they mentioned that the score test using the normal approximation might underestimate the nominal significance level possibly for small sample cases to remedy this problem a parametric bootstrap method is proposed it is shown that the bootstrap method keeps the significance level close to the nominal one and has greater power uniformly than the existing normal approximation for testing the hypothesis

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

a locking free finite element method for naghdi shells abstract in this paper a locking free method using mixed finite elements is introduced to approximate the solution of naghdi shell problems with small parameter t the thickness of the shell the approach of arnold and brezzi 1997 is employed with some important changes instead of proving the discrete inf sup condition for arbitrary geometric coefficients which does not seem possible we prove a weaker stability condition for smooth enough geometrically dependent coefficients which is sufficient for deducing the optimal error estimate as long as h 2 t is uniformly bounded for extremely small t we can relax this condition either using a larger bubble space or stabilizing the problem by replacing t2 by t2 h4 in either case an optimal error estimate still holds

hierarchical mixtures of experts and the em algorithm we present a tree structured architecture for supervised learning the statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models glim s learning is treated as a maximum likelihood problem in particular we present an expectation maximization em algorithm for adjusting the parameters of the architecture we also develop an on line learning algorithm in which the parameters are updated incrementally comparative simulation results are presented in the robot dynamics domain

bayesian inference in mixtures of experts and hierarchical mixtures of experts models with an application to speech recognition abstract machine classification of acoustic waveforms as speech events is often difficult due to context dependencies here a vowel recognition task with multiple speakers is studied via the use of a class of modular and hierarchical systems referred to as mixtures of experts and hierarchical mixtures of experts models the statistical model underlying the systems is a mixture model in which both the mixture coefficients and the mixture components are generalized linear models a full bayesian approach is used as a basis of inference and prediction computations are performed using markov chain monte carlo methods a key benefit of this approach is the ability to obtain a sample from the posterior distribution of any functional of the parameters of the given model in this way more information is obtained than can be provided by a point estimate also avoided is the need to rely on a normal approximation to the posterior as the basis of inference this is particularly important in cases where the posteri

a modified lift and project procedure in recent years the lift and project approach has been used successfully within a branch and cut framework to solve large difficult pure and mixed 0 1 programs that have resisted solution efforts by pure branch and bound codes the approach uses a linear description in a higher dimensional space of the convex hull of the disjunctive set created by imposing one or several 0 1 conditions by solving a linear program derived from this higher dimensional representation the cut generating linear program cglp the standard lift and project procedure obtains a deepest cut in a well defined sense we propose a modification of cglp that allows us to generate not just one deepest cut but a class of cuts with desirable properties each at the cost of one extra pivot in the optimal tableau of the modified cglp

bayesian semiparametric analysis of developmental toxicology data modeling of developmental toxicity studies often requires simple parametric analyses of the dose response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure this article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations we approach our analysis using a bayesian semiparametric model that we tailored specifically to developmental toxicology studies it combines parametric dose response relationships with a flexible nonparametric specification of the distribution of the response obtained via a product of dirichlet process mixtures approach pdpm our formulation achieves three goals 1 the distribution of the response is modeled in a general way 2 the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data and 3 the marginal posterior distribution of the parameters of interest is available in closed form the logistic regression model as well as many of its extensions such as the beta binomial model and finite mixture models are special cases in the context of the two motivating examples and a simulated example we provide model comparisons illustrate overdispersion diagnostics that can assist model specification show how to derive posterior distributions of the effective dose parameters and predictive distributions of response and discuss the sensitivity of the results to the choice of the prior distribution

confidence intervals for intraclass correlation coefficients in a nonlinear dose response meta analysis this work is motivated by a meta analysis case study on antipsychotic medications the michaelis menten curve is employed to model the nonlinear relationship between the dose and d2 receptor occupancy across multiple studies an intraclass correlation coefficient icc is used to quantify the heterogeneity across studies to interpret the size of heterogeneity an accurate estimate of icc and its confidence interval is required the goal is to apply a recently proposed generic beta approach for construction the confidence intervals on iccs for linear mixed effects models to nonlinear mixed effects models using four estimation methods these estimation methods are the maximum likelihood second order generalized estimating equations and two two step procedures the beta approach is compared with a large sample normal approximation delta method and bootstrapping the confidence intervals based on the delta method and the nonparametric percentile bootstrap with various resampling strategies failed in our settings the beta approach demonstrates good coverages with both two step estimation methods and consequently it is recommended for the computation of confidence interval for iccs in nonlinear mixed effects models for small studies

models for zero inflated correlated count data with extra heterogeneity when is it too complex statistical analysis of count data typically starts with a poisson regression however in many real life applications it is observed that the variation in the counts is larger than the mean and one needs to deal with the problem of overdispersion in the counts several factors may contribute to overdispersion 1 unobserved heterogeneity due to missing covariates 2 correlation between observations such as in longitudinal studies and 3 the occurrence of many zeros more than expected from the poisson distribution in this paper we discuss a model that allows one to explicitly take each of these factors into consideration the aim of this paper is twofold 1 investigate whether we can identify the cause of overdispersion via model selection and 2 investigate the impact of a misspecification of the model on the power of a covariate the paper is motivated by a study of the occurrence of drug induced arrhythmia in beagle dogs based on electrocardiogram recordings with the objective to evaluate the effect of potential drugs on the heartbeat irregularities copyright 2016 john wiley sons ltd

a general maximum likelihood analysis of variance components in generalized linear models this paper describes an em algorithm for nonparametric maximum likelihood ml estimation in generalized linear models with variance component structure the algorithm provides an alternative analysis to approximate mql and pql analyses mcgilchrist and aisbett 1991 biometrical journal 33 131 141 breslow and clayton 1993 journal of the american statistical association 88 9 25 mcgilchrist 1994 journal of the royal statistical society series b 56 61 69 goldstein 1995 multilevel statistical models and to gee analyses liang and zeger 1986 biometrika 73 13 22 the algorithm first given by hinde and wood 1987 in longitudinal data analysis 110 126 is a generalization of that for random effect models for overdispersion in generalized linear models described in aitkin 1996 statistics and computing 6 251 262 the algorithm is initially derived as a form of gaussian quadrature assuming a normal mixing distribution but with only slight variation it can be used for a completely unknown mixing distribution giving a straightforward method for the fully nonparametric ml estimation of this distribution this is of value because the ml estimates of the glm parameters can be sensitive to the specification of a parametric form for the mixing distribution the nonparametric analysis can be extended straightforwardly to general random parameter models with full npml estimation of the joint distribution of the random parameters this can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters a simple method is described for obtaining correct standard errors for parameter estimates when using the em algorithm several examples are discussed involving simple variance component and longitudinal models and small area estimation

locking free finite element methods for shells we propose a new family of finite element methods for the naghdi shell model one method associated with each nonnegative integer k the methods are based on a nonstandard mixed formulation and the kth method employs triangular lagrange finite elements of degree k 2 augmented by bubble functions of degree k 3 for both the displacement and rotation variables and discontinuous piecewise polynomials of degree k for the shear and membrane stresses this method can be implemented in terms of the displacement and rotation variables alone as the minimization of an altered energy functional over the space mentioned the alteration consists of the introduction of a weighted local projection into part but not all of the shear and membrane energy terms of the usual naghdi energy the relative error in the method measured in a norm which combines the h i norm of the displacement and ro tation fields and an appropriate norm of the shear and membrane stress fields converges to zero with order k 1 uniformly with respect to the shell thickness for smooth solutions at least under the assumption that certain geometrical coefficients in the nagdhi model are replaced by piecewise constants

an application of harrell s c index to ph frailty models frailty models are encountered in many medical applications yet little research has been devoted to develop measures that quantify the predictive ability of these models in this paper we elaborate on the concept of the concordance probability to clustered data resulting in an overall conditional c index or bfc o c and an overall marginal c index or c o m both overall c indices can be split up into a between conditional or c b c and a between marginal c index or c b m and into a within conditional or c w c and a within marginal c index or c w m for ph frailty models of the power variance family c w c and c w m are equivalent resulting in one within c index c w we propose an application of harrell s c index to estimate the proposed indices within a likelihood and a bayesian context and the performances of their point estimates and confidence credible intervals are compared in an extensive simulation study this simulation study shows that the point estimates of c w and c b m perform good within both a likelihood and bayesian context but that the point estimates of c b c show less bias for the bayesian approach than for the likelihood approach the 95 per cent confidence credible intervals also possess good coverage properties given that the point estimates perform good the performance of the c indices is evaluated on a real data set

tests for informative cluster size using a novel balanced bootstrap scheme clustered data are often encountered in biomedical studies and to date a number of approaches have been proposed to analyze such data however the phenomenon of informative cluster size ics is a challenging problem and its presence has an impact on the choice of a correct analysis methodology for example dutta and datta 2015 biometrics presented a number of marginal distributions that could be tested depending on the nature and degree of informativeness of the cluster size these marginal distributions may differ as do the choices of the appropriate test in particular they applied their new test to a periodontal data set where the plausibility of the informativeness was mentioned but no formal test for the same was conducted we propose bootstrap tests for testing the presence of ics a balanced bootstrap method is developed to successfully estimate the null distribution by merging the re sampled observations with closely matching counterparts relying on the assumption of exchangeability within clusters the proposed procedure performs well in simulations even with a small number of clusters at different distributions and against different alternative hypotheses thus making it an omnibus test we also explain how to extend the ics test to a regression setting and thereby enhancing its practical utility the methodologies are illustrated using the periodontal data set mentioned earlier copyright 2017 john wiley sons ltd

bending dominated deformation of thin spherical shells analysis and finite element approximation in this paper the bending dominated deformation of a linearly elastic thin spherical shell is considered it is shown that the displacements converge to the solution of a constrained variational problem as the thickness of the shell tends to zero the order of the convergence is estimated and regularity results for the limit problem are derived for the numerical approximation of this limit problem a low order finite element method with a penalty term that generalizes the concept of the discrete kirchhoff triangle elements for plate bending problems is presented the application of the second strang lemma yields error estimates in the energy norm

a score type test for heterogeneity in zero inflated models in a stratified population we propose a score type statistic to evaluate heterogeneity in zero inflated models for count data in a stratified population where heterogeneity is defined as instances in which the zero counts are generated from two sources evaluating heterogeneity in this class of models has attracted considerable attention in the literature but existing testing procedures have primarily relied on the constancy assumption under the alternative hypothesis in this paper we extend the literature by describing a score type test to evaluate homogeneity against general alternatives that do not neglect the stratification information under the alternative hypothesis the limiting null distribution of the proposed test statistic is a mixture of chi squared distributions which can be well approximated by a simple parametric bootstrap procedure our numerical simulation studies show that the proposed test can greatly improve efficiency over tests of heterogeneity that ignore the stratification information an empirical application to dental caries data in early childhood further shows the importance and practical utility of the methodology in using the stratification profile to detect heterogeneity in the population

non parametric bootstrap confidence intervals for the intraclass correlation coefficient the intraclass correlation coefficient rho plays a key role in the design of cluster randomized trials estimates of rho obtained from previous cluster trials and used to inform sample size calculation in planned trials may be imprecise due to the typically small numbers of clusters in such studies it may be useful to quantify this imprecision this study used simulation to compare different methods for assigning bootstrap confidence intervals to rho for continuous outcomes from a balanced design data were simulated for combinations of numbers of clusters 10 30 50 intraclass correlation coefficients 0 001 0 01 0 05 0 3 and outcome distributions normal non normal continuous the basic bootstrap t percentile bias corrected and bias corrected accelerated bootstrap intervals were compared with new methods using the basic and bootstrap t intervals applied to a variance stabilizing transformation of rho the standard bootstrap methods provided coverage levels for 95 per cent intervals that were markedly lower than the nominal level for data sets with only 10 clusters and only provided close to 95 per cent coverage when there were 50 clusters application of the bootstrap t method to the variance stabilizing transformation of rho improved upon the performance of the standard bootstrap methods providing close to nominal coverage

mixed 0 1 programming by lift and project in a branch and cut framework we investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0 1 programs into a branch and cut framework the cuts we use are of the lift and project variety some of the issues addressed have a theoretical answer but others are of an experimental nature and are settled by comparing alternatives on a set of test problems the resulting code is a robust solver for mixed 0 1 programs we compare it with several existing codes on a wide range of test problems it performs as well as or better than some of the best currently available mixed integer programming codes

a zero inefficiency stochastic frontier estimator traditional stochastic frontier models impose inefficient behavior on all firms in the sample of interest if the data under investigation represent a mixture of both fully efficient and inefficient firms then off the shelf frontier models are statistically inadequate we introduce the zero inefficiency stochastic frontier model which can accommodate the presence of both efficient and inefficient firms in the sample we derive the corresponding log likelihood function conditional mean of inefficiency to estimate observation specific inefficiency and discuss testing for the presence of fully efficient firms we provide both simulated evidence as well as an empirical example which demonstrates the applicability of the proposed method jel classification no c13 c23 c33

marginal regression models for clustered count data based on zero inflated conway maxwell poisson distribution with applications community water fluoridation is an important public health measure to prevent dental caries but it continues to be somewhat controversial the iowa fluoride study ifs is a longitudinal study on a cohort of iowa children that began in 1991 the main purposes of this study http www dentistry uiowa edu preventive fluoride study were to quantify fluoride exposures from both dietary and nondietary sources and to associate longitudinal fluoride exposures with dental fluorosis spots on teeth and dental caries cavities we analyze a subset of the ifs data by a marginal regression model with a zero inflated version of the conway maxwell poisson distribution for count data exhibiting excessive zeros and a wide range of dispersion patterns in general we introduce two estimation methods for fitting a zicmp marginal regression model finite sample behaviors of the estimators and the resulting confidence intervals are studied using extensive simulation studies we apply our methodologies to the dental caries data our novel modeling incorporating zero inflation clustering and overdispersion sheds some new light on the effect of community water fluoridation and other factors we also include a second application of our methodology to a genomic next generation sequencing dataset that exhibits underdispersion

bootstrapping robust estimates for clustered data in mixed models the use of robust estimates raises several interesting inferential challenges one of these challenges arises from the realization that the effect of contamination is to increase the variability in the data but robust estimates of variance components are usually smaller than their nonrobust counterparts the robust estimates reflect the variability of the bulk of the data which is not the same as the variability in the data generating process this means that the naive implementation of bootstrap procedures might not work in this article we consider several bootstrap procedures including random effect transformation and weighted bootstraps we give conditions for the asymptotic validity of the bootstraps and assess their performance via a small simulation study both the transformation and generalized cluster bootstrap perform well and are asymptotically valid under reasonable conditions

optimizing over the split closure the polyhedron defined by all the split cuts obtainable directly i e without iterated cut generation from the lp relaxation p of a mixed integer program mip is termed the elementary or rank 1 split closure of p this paper deals with the problem of optimizing over the elementary split closure this is accomplished by repeatedly solving the following separation problem given a fractional point say x find a rank 1 split cut violated by x or show that none exists following caprara and letchford 17 we formulate this separation problem as a nonlinear mixed integer program that can be treated as a parametric mixed integer linear program pmilp with a single parameter in the objective function and the right hand side we develop an algorithmic framework to deal with the resulting pmilp by creating and maintaining a dynamically updated grid of parameter values and use the corresponding mixed integer programs to generate rank 1 split cuts our approach was implemented in the coin or framework using cplex 9 0 as a general purpose mip solver we report our computational results on well known benchmark instances from miplib 3 0 and several classes of structured integer and mixed integer problems our computational results show that rank 1 split cuts close more than 98 of the duality gap on 15 out of 41 mixed integer instances from miplib 3 0 more than 75 of the duality gap can be closed on an additional 10 instances the average gap closed over all 41 instances is 72 78 in the pure integer case rank 1 split cuts close more than 75 of the duality gap on 13 out of 24 instances from miplib 3 0 on average rank 1 split cuts close about 72 of the duality gap on these 24 instances we also report results on several classes of structured problems capacitated versions of warehouse location single source facility location p median fixed charge network flow multi commodity network design with splittable and unsplittable flows and lot sizing the fraction of the integrality gap closed varies for these problem classes between 100 and 67 we also gathered statistics on the average coefficient size absolute value of the disjunctions generated they turn out to be surprisingly small

a resampling procedure for complex survey data abstract in complex survey data often the sampling design induces a non iid structure to the data e g without replacement sampling stratification multistage or unequal probability of selection though techniques for variance estimation and confidence intervals do exist they often are cumbersome to implement or do not extend to complex designs it would be desirable to have resampling methods that reuse the existing estimation system repeatedly using computing power to avoid theoretical work and that can be applied to such data in recognition of this need various resampling procedures for variance estimation and confidence intervals in sample survey data where the sampling is without replacement have been proposed in the literature these include the jackknife the with replacement bootstrap bwr the without replacement bootstrap bwo and the rescaling bootstrap the bwr and bwo are applicable only to simple sampling designs others have shown the asymptotic consistency of jackknife vari

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

a precise correspondence between lift and project cuts simple disjunctive cuts and mixed integer gomory cuts for 0 1 programming we establish a precise correspondence between lift and project cuts for mixed 0 1 programs simple disjunctive cuts intersection cuts and mixed integer gomory cuts the correspondence maps members of one family onto members of the others it also maps bases of the higher dimensional cut generating linear program cglp into bases of the linear programming relaxation it provides new bounds on the number of facets of the elementary closure and on the rank of the standard linear programming relaxation of the mixed 0 1 polyhedron with respect to the above families of cutting planes

marginal analysis of panel counts through estimating functions we develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations using two types of self consistent estimating equations the first is derived from the likelihood studied in wellner zhang 2000 assuming a poisson counting process and gives a nondecreasing estimator which is the same as the nonparametric maximum likelihood estimator of wellner zhang and thus is consistent without the poisson assumption motivated by the construction of parametric generalized estimating equations the second type is a set of data adaptive quasi score functions which are likelihood estimating functions under a mixed poisson assumption we evaluate the procedures via simulation and illustrate them with the data from a bladder cancer study

a bayesian approach for analyzing zero inflated clustered count data with dispersion in practice count data may exhibit varying dispersion patterns and excessive zero values additionally they may appear in groups or clusters sharing a common source of variation we present a novel bayesian approach for analyzing such data to model these features we combine the conway maxwell poisson distribution which allows both overdispersion and underdispersion with a hurdle component for the zeros and random effects for clustering we propose an efficient markov chain monte carlo sampling scheme to obtain posterior inference from our model through simulation studies we compare our hurdle conway maxwell poisson model with a hurdle poisson model to demonstrate the effectiveness of our conway maxwell poisson approach furthermore we apply our model to analyze an illustrative dataset containing information on the number and types of carious lesions on each tooth in a population of 9 year olds from the iowa fluoride study which is an ongoing longitudinal study on a cohort of iowa children that began in 1991

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

generalized partially linear single index model for zero inflated count data count data often arise in biomedical studies while there could be a special feature with excessive zeros in the observed counts the zero inflated poisson model provides a natural approach to accounting for the excessive zero counts in the semiparametric framework we propose a generalized partially linear single index model for the mean of the poisson component the probability of zero or both we develop the estimation and inference procedure via a profile maximum likelihood method under some mild conditions we establish the asymptotic properties of the profile likelihood estimators the finite sample performance of the proposed method is demonstrated by simulation studies and the new model is illustrated with a medical care dataset

a longitudinal measurement error model with a semicontinuous covariate covariate measurement error in regression is typically assumed to act in an additive or multiplicative manner on the true covariate value however such an assumption does not hold for the measurement error of sleep disordered breathing sdb in the wisconsin sleep cohort study wscs the true covariate is the severity of sdb and the observed surrogate is the number of breathing pauses per unit time of sleep which has a nonnegative semicontinuous distribution with a point mass at zero we propose a latent variable measurement error model for the error structure in this situation and implement it in a linear mixed model the estimation procedure is similar to regression calibration but involves a distributional assumption for the latent variable modeling and model fitting strategies are explored and illustrated through an example from the wscs

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

marginal regression analysis of recurrent events with coarsened censoring times motivated by an ongoing pediatric mental health care pmhc study this article presents weakly structured methods for analyzing doubly censored recurrent event data where only coarsened information on censoring is available the study extracted administrative records of emergency department visits from provincial health administrative databases the available information of each individual subject is limited to a subject specific time window determined up to concealed data to evaluate time dependent effect of exposures we adapt the local linear estimation with right censored survival times under the cox regression model with time varying coefficients cf cai and sun scandinavian journal of statistics 2003 30 93 111 we establish the pointwise consistency and asymptotic normality of the regression parameter estimator and examine its performance by simulation the pmhc study illustrates the proposed approach throughout the article

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

nonanticipative duality relaxations and formulations for chance constrained stochastic programs we propose two new lagrangian dual problems for chance constrained stochastic programs based on relaxing nonanticipativity constraints we compare the strength of the proposed dual bounds and demonstrate that they are superior to the bound obtained from the continuous relaxation of a standard mixed integer programming mip formulation for a given dual solution the associated lagrangian relaxation bounds can be calculated by solving a set of single scenario subproblems and then solving a single knapsack problem we also derive two new primal mip formulations and demonstrate that for chance constrained linear programs the continuous relaxations of these formulations yield bounds equal to the proposed dual bounds we propose a new heuristic method and two new exact algorithms based on these duals and formulations the first exact algorithm applies to chance constrained binary programs and uses either of the proposed dual bounds in concert with cuts that eliminate solutions found by the subproblems the second exact method is a branch and cut algorithm for solving either of the primal formulations our computational results indicate that the proposed dual bounds and heuristic solutions can be obtained efficiently and the gaps between the best dual bounds and the heuristic solutions are small

chva tal closures for mixed integer programming problems chvatal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality this viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems the basic ingredient in these cutting plane proofs is that for a polyhedronp and integral vectorw if max wx x p wx integer t thenwx t is valid for all integral vectors inp we consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that bar wx be integer for some other integral vector bar w the cutting plane proofs thus obtained may be seen either as an abstraction of gomory s mixed integer cutting plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by balas and jeroslow our main result is that for a given polyhedronp the set of vectors that satisfy every cutting plane forp with respect to a specified subset of integer variables is again a polyhedron this allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron analogous to the process of repeatedly taking chvatal closures in the integer programming case these results are illustrated with a number of examples from combinatorial optimization our work can be seen as a continuation of that of nemhauser and wolsey on mixed integer cutting planes

nonparametric analysis of clustered multivariate data there is wide interest in extending univariate and multivariate nonparametric procedures to clustered and hierarchical data traditionally parametric mixed models have been used to account for the correlation structures among the dependent observational units in this work we extend multivariate nonparametric procedures for one sample and several sample location problems to clustered data settings the results are given for a general score function but with an emphasis on spatial sign and rank methods mixed models notation involving design matrices for fixed and random effects is used throughout the asymptotic variance formulas and limiting distributions of the test statistics under the null hypothesis and under a sequence of alternatives are derived as are the limiting distributions for the corresponding estimates the approach based on a general score function also shows for example how m estimates behave with clustered data efficiency studies demonstrate the practical advantages and disadvantag

a semiparametric marginal mixture cure model for clustered survival data we consider a marginal model for the regression analysis of clustered failure time data with a cure fraction we propose to use novel generalized estimating equations in an expectation maximization algorithm to estimate regression parameters in a semiparametric proportional hazards mixture cure model the dependence among the cure statuses and among the survival times of uncured patients within clusters are modeled by working correlation matrices in the estimating equations we use a bootstrap method to obtain the variances of the estimates we report a simulation study to demonstrate a substantial efficiency gain of the proposed method over an existing marginal method finally we apply the model and the proposed method to a set of data from a multi institutional study of tonsil cancer patients treated with a radiation therapy

variance estimation in inverse probability weighted cox models inverse probability weighted cox models can be used to estimate marginal hazard ratios under different point treatments in observational studies to obtain variance estimates the robust sandwich variance estimator is often recommended to account for the induced correlation among weighted observations however this estimator does not incorporate the uncertainty in estimating the weights and tends to overestimate the variance leading to inefficient inference here we propose a new variance estimator that combines the estimation procedures for the hazard ratio and weights using stacked estimating equations with additional adjustments for the sum of terms that are not independently and identically distributed in a cox partial likelihood score equation we prove analytically that the robust sandwich variance estimator is conservative and establish the asymptotic equivalence between the proposed variance estimator and one obtained through linearization by hajage et al in 2018 in addition we extend our proposed variance estimator to accommodate clustered data we compare the finite sample performance of the proposed method with alternative methods through simulation studies we illustrate these different variance methods in both independent and clustered data settings using a bariatric surgery dataset and a multiple readmission dataset respectively to facilitate implementation of the proposed method we have developed an r package ipwcoxcsv

bootstrapping clustered data summary various bootstraps have been proposed for bootstrapping clustered data from one way arrays the simulation results in the literature suggest that some of these methods work quite well in practice the theoretical results are limited and more mixed in their conclusions for example mccullagh reached negative conclusions about the use of non parametric bootstraps for one way arrays the purpose of this paper is to extend our understanding of the issues by discussing the effect of different ways of modelling clustered data the criteria for successful bootstraps used in the literature and extending the theory from functions of the sample mean to include functions of the between and within sums of squares and non parametric bootstraps to include model based bootstraps we determine that the consistency of variance estimates for a bootstrap method depends on the choice of model with the residual bootstrap giving consistency under the transformation model whereas the cluster bootstrap gives consistent estimates under both the transformation and the random effect model in addition we note that the criteria based on the distribution of the bootstrap observations are not really useful in assessing consistency

on the efficiency of score tests for homogeneity in two component parametric models for discrete data in many applications of two component mixture models for discrete data such as zero inflated models it is often of interest to conduct inferences for the mixing weights score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose but the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model in this article we develop a score test of homogeneity that overcomes the limitations of existing procedures the technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation we exploit this decomposition to lay the foundation of the test simulation results show that the proposed covariate adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights a real life example in dental caries research is used to illustrate the methodology

time dependent tree structured survival analysis with unbiased variable selection through permutation tests incorporating time dependent covariates into tree structured survival analysis tssa may result in more accurate prognostic models than if only baseline values are used available time dependent tssa methods exhaustively test every binary split on every covariate however this approach may result in selection bias towards covariates with more observed values we present a method that uses unbiased significance levels from newly proposed permutation tests to select the time dependent or baseline covariate with the strongest relationship with the survival outcome the specific splitting value is identified using only the selected covariate simulation results show that the proposed time dependent tssa method produces tree models of equal or greater accuracy as compared to baseline tssa models even with high censoring rates and large within subject variability in the time dependent covariate to illustrate the proposed method is applied to data from a cohort of bipolar youth to identify subgroups at risk for self injurious behavior

generalized intersection cuts and a new cut generating paradigm intersection cuts are generated from a polyhedral cone and a convex set s whose interior contains no feasible integer point we generalize these cuts by replacing the cone with a more general polyhedron c the resulting generalized intersection cuts dominate the original ones this leads to a new cutting plane paradigm under which one generates and stores the intersection points of the extreme rays of c with the boundary of s rather than the cuts themselves these intersection points can then be used to generate in a non recursive fashion cuts that would require several recursive applications of some standard cut generating routine a procedure is also given for strengthening the coefficients of the integer constrained variables of a generalized intersection cut the new cutting plane paradigm yields a new characterization of the closure of intersection cuts and their strengthened variants this characterization is minimal in the sense that every one of the inequalities it uses defines a facet of the closure

semiparametric estimation in generalized linear mixed models with auxiliary covariates a pairwise likelihood approach auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects this article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data we propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation based inference procedure by treating both the error structure and random effects as nuisance parameters this method is robust against misspecification of either error structure or random effects distribution and allows for dependence between random effects and covariates we show that the resulting estimators are consistent and asymptotically normal extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method we illustrate the method with two real data examples

on the approximation rate of hierarchical mixtures of experts for generalized linear models we investigate a class of hierarchical mixtures of experts hme models where generalized linear models with nonlinear mean functions of the form xt are mixed here is the inverse link function it is shown that mixtures of such mean functions can approximate a class of smooth functions of the form h x where h e w 2 k a sobolev class over 0 1 s as the number of experts m in the network increases an upper bound of the approximation rate is given as o m 2 s in lp norm this rate can be achieved within the family of hme structures with no more than s layers where s is the dimension of the predictor x

stabilized finite element formulations for shells in a bending dominated state we consider the design of finite element methods for the naghdi shell model in the case when the deformation is bending dominated two formulations based on stabilizing techniques are introduced and it is proved that they are stable hence free from locking the theoretical estimates are confirmed by numerical benchmark studies

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

a multivariate test of interaction for use in clinical trials an important issue in clinical trials is whether the effect of treatment is essentially homogeneous as a function of baseline covariates covariates that have the potential for an interaction with treatment may be suspected on the basis of treatment mechanism or may be known risk factors as it is often thought that the sickest patients may benefit most from treatment if disease severity is more accurately determined by a collection of baseline covariates rather than a single risk factor methods that examine each covariate in turn for interaction may be inadequate we propose a procedure whereby treatment interaction is examined along a single severity index that is a linear combination of baseline covariates formally we derive a likelihood ratio test based on the null beta0 beta1 versus the alternative abeta0 beta1 where x beta k k 0 1 corresponds to the severity index in arm k and x is a vector of baseline covariates while our explicit test requires a gaussian response it can be readily implemented whenever the estimates of beta0 beta1 are approximately multivariate normal for example it is appropriate for large clinical trials where beta k is based on a logisitic or cox regression of response on x

mixtures of proportional hazards regression models this paper presents a mixture model which combines features of the usual cox proportional hazards model with those of a class of models known as mixtures of experts the resulting model is more flexible than the usual cox model in the sense that the log hazard ratio is allowed to vary non linearly as a function of the covariates thus it provides a flexible approach to both modelling survival data and model checking the method is illustrated with simulated data as well as with multiple myeloma data

facet separation with one linear program given polyhedron p and and a point x the separation problem for polyhedra asks to certify that x in p and if not to determine an inequality that is satisfied by p and violated by x this problem is repeatedly solved in cutting plane methods for integer programming and the quality of the violated inequality is an essential feature in the performance of such methods in this paper we address the problem of finding efficiently an inequality that is violated by x and either defines an improper face or a facet of p we show that by solving a single linear program one almost surely obtains such an improper face or facet

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

on the membrane locking of h p finite elements in a cylindrical shell problem we study the performance of high order h p finite clement schemes in approximating the nearly inexlensional deformation state of a thin cylindrical shell roof with both ends free severe locking is demonstrated for both quadratic and cubic elements and even for higher order if the grid is not aligned with the axis of the cylinder carefully designed selective reduced integration is shown to improve the accuracy of the finite element approximation at low and moderately high orders however so far this technique seems to work well only on aligned grids

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea