a density corrected quantum boltzmann equation binary correlations are a recognized part of the pair density operator but the influence of binary correlations on the singlet density operator is usually not emphasized here free motion and binary correlations are taken as independent building blocks for the structure of the nonequilibrium singlet and pair density operators binary correlations are assumed to arise from the collision of twofree particles together with the first bbgky equation and a retention of all terms that are second order in gas density a generalization of the boltzmann equation is obtained this is an equation for thefree particle density operator rather than for the full singlet density operator the form for the pressure tensor calculated from this equation reduces at equilibrium to give the correct beth uhlenbeck second virial coefficient in contrast to a previous quantum boltzmann equation which gave only part of the quantum second virial coefficient generalizations to include higher order correlations and collision types are indicated

checking the adequacy of the gamma frailty model for multivariate failure times summary multivariate failure time data arise when the sample consists of clusters and each cluster contains several dependent failure times the semiparametric gamma frailty model vaupel manton stallard 1979 clayton 1978 oakes 1982 for multivariate failure times characterises the intracluster dependence by the gamma frailty distribution while allowing the marginal distributions to be unspecified this paper develops both graphical and numerical techniques for checking the adequacy of this model the proposed techniques are based on the posterior expectation of the frailty given the observable data two examples from genetics are provided

estimating a weighted average of stratum specific parameters this article investigates estimators of a weighted average of stratum specific univariate parameters and compares them in terms of a design based estimate of mean squared error mse the research is motivated by a stratified survey sample of florida medicaid beneficiaries in which the parameters are population stratum means and the weights are known and determined by the population sampling frame assuming heterogeneous parameters it is common to estimate the weighted average with the weighted sum of sample stratum means under homogeneity one ignores the known weights in favor of precision weighting adaptive estimators arise from random effects models for the parameters we propose adaptive estimators motivated from these random effects models but we compare their design based performance we further propose selecting the tuning parameter to minimize a design based estimate of mean squared error this differs from the model based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means our design based approach effectively downweights strata with small weights in the assessment of homogeneity which can lead to a smaller mse we compare the standard random effects model with identically distributed parameters to a novel alternative which models the variances of the parameters as inversely proportional to the known weights we also present theoretical and computational details for estimators based on a general class of random effects models the methods are applied to estimate average satisfaction with health plan and care among florida beneficiaries just prior to medicaid reform

checking the marginal cox model for correlated failure time data summary correlated failure time data arise frequently in scientific investigations because there exists natural or artificial clustering of study subjects such that failure times within the same cluster are correlated it is convenient and useful to perform regression analysis by formulating the marginal distributions of the correlated failure times with the cox proportional hazards model in this paper we develop a class of graphical and numerical techniques for checking the adequacy of the marginal cox model the proposed methods are derived from cumulative sums of martingale based residuals over the failure time and or covariates the distributions of these stochastic processes under the assumed model can be approximated through simulating certain zero mean gaussian processes each observed residual pattern can then be compared objectively with a number of realisations from the approximating process an illustration with the diabetic retinopathy study is provided

test of marginal compatibility and smoothing methods for exchangeable binary data with unequal cluster sizes exchangeable binary data are often collected in developmental toxicity and other studies and a whole host of parametric distributions for fitting this kind of data have been proposed in the literature while these distributions can be matched to have the same marginal probability and intra cluster correlation they can be quite different in terms of shape and higher order quantities of interest such as the litter level risk of having at least one malformed fetus a sensible alternative is to fit a saturated model bowman and george 1995 journal of the american statistical association 90 871 879 using the expectation maximization em algorithm proposed by stefanescu and turnbull 2003 biometrics 59 18 24 the assumption of compatibility of marginal distributions is often made to link up the distributions for different cluster sizes so that estimation can be based on the combined data stefanescu and turnbull proposed a modified trend test to test this assumption their test however fails to take into account the variability of an estimated null expectation and as a result leads to inaccurate p values this drawback is rectified in this article when the data are sparse the probability function estimated using a saturated model can be very jagged and some kind of smoothing is needed we extend the penalized likelihood method simonoff 1983 annals of statistics 11 208 218 to the present case of unequal cluster sizes and implement the method using an em type algorithm in the presence of covariate we propose a penalized kernel method that performs smoothing in both the covariate and response space the proposed methods are illustrated using several data sets and the sampling and robustness properties of the resulting estimators are evaluated by simulations

estimation of covariate effects in generalized linear mixed models with informative cluster sizes in standard regression analyses of clustered data one typically assumes that the expected value of the response is independent of cluster size however this is often false for example in studies of surgical interventions investigators have frequently found surgery volume and outcomes to be related to the skill level of the surgeons this paper examines the effect of ignoring response dependent informative cluster sizes on standard analytical methods such as mixed effects models and conditional likelihood methods using analytic calculations simulation studies and an example from a study of periodontal disease we consider the case in which cluster sizes and responses share random effects which we assume to be independent of the covariates our focus is on maximum likelihood methods that ignore informative cluster sizes and we show that they exhibit little bias in estimating covariate effects that are uncorrelated with the random effects associated with cluster sizes however estimation of covariate effects that are associated with the random effects can be biased in particular for models with random intercepts only ignoring informative cluster sizes can yield biased estimators of the intercept but little bias in estimation of all covariate effects

weighted logrank tests for interval censored data when assessment times depend on treatment we consider weighted logrank tests for interval censored data when assessment times may depend on treatment and for each individual we only use the two assessment times that bracket the event of interest it is known that treating finite right endpoints as observed events can substantially inflate the type i error rate under assessment treatment dependence atd but the validity of several other implementations of weighted logrank tests score tests permutation tests multiple imputation tests has not been studied in this situation with a bounded number of unique assessment times the score test under the grouped continuous model retains the type i error rate asymptotically under atd however although the approximate permutation test based on the permutation central limit theorem is not asymptotically valid under every atd scenario we show through simulation that in many atd scenarios it retains the type i error rate better than the score test we show a case where the approximate permutation test retains the type i error rate when the exact permutation test does not we study and modify the multiple imputation logrank tests of huang lee and yu 2008 statistics in medicine 27 3217 3226 showing that the distribution of the rank like scores asymptotically does not depend on the assessment times we show through simulations that our modifications of the multiple imputation logrank tests retain the type i error rate in all cases studied even with atd and a small number of individuals in each treatment group simulations were performed using the interval r package us government work in the public domain

mean estimating equation approach to analysing cluster correlated data with nonignorable cluster sizes most methods for analysing cluster correlated biological data implicitly assume the ignorability of cluster sizes when this assumption fails the resulting inferences may be asymptotically invalid hoffman et al 2001 proposed a simple but computationally intensive method based on a large number of within cluster resamples and associated separate estimating equations that leads to asymptotically valid inferences whether the cluster sizes are ignorable or not we study a simple method based on a single inverse cluster size weighted estimating equation that avoids resampling and yet leads to asymptotically valid inferences simulation results are presented to assess the performance of the proposed method we also propose wald tests for ignorability of cluster sizes

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

a discrete survival model with random effects an application to time to pregnancy time to pregnancy the number of menstrual cycles it takes a couple to conceive and various covariates have been collected among couples ultimately achieving conception to assess the influence of the covariates we constructed a discrete survival model that allows time dependent covariates a random effect was included to account for unobserved heterogeneity the collected waiting times are obtained through retrospective ascertainment and are analyzed as truncated data maximum likelihood estimation was implemented by fisher scoring through iteratively reweighted least squares

a two grid discretization scheme of non conforming finite elements for transmission eigenvalues abstract in this paper for the helmholtz transmission eigenvalue problem we propose a two grid discretization scheme of non conforming finite elements with this scheme the solution of the transmission eigenvalue problem on a fine grid h is reduced to the solution of the primal and dual eigenvalue problem on a much coarser grid h and the solutions of two linear algebraic systems with the same positive definite hermitian and block diagonal coefficient matrix on the fine grid h we prove the resulting solution still maintains an asymptotically optimal accuracy and we report some numerical examples in two dimension and three dimension on the modified zienkiewicz element to validate the efficiency of our approach for solving transmission eigenvalues

a weighted multivariate sign test for cluster correlated data we consider the multivariate location problem with cluster correlated data a family of multivariate weighted sign tests is introduced for which observations from different clusters can receive different weights under weak assumptions the test statistic is asymptotically distributed as a chi squared random variable as the number of clusters goes to infinity the asymptotic distribution of the test statistic is also given for a local alternative model under multivariate normality optimal weights maximizing pitman asymptotic efficiency are provided these weights depend on the cluster sizes and on the intracluster correlation several approaches for estimating these weights are presented using pitman asymptotic efficiency we show that appropriate weighting can increase substantially the efficiency compared to a test that gives the same weight to each cluster a multivariate weighted t test is also introduced the finite sample performance of the weighted sign test is explored through a simulation study which shows that the proposed approach is very competitive a real data example illustrates the practical application of the methodology

weighted rank regression for clustered data analysis we consider ranked based regression models for clustered data analysis a weighted wilcoxon rank method is proposed to take account of within cluster correlations and varying cluster sizes the asymptotic normality of the resulting estimators is established a method to estimate covariance of the estimators is also given which can bypass estimation of the density function simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure presence absence of outliers and different correlation values the proposed methods appear to perform well in particular the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers a real example is provided for illustration

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

modeling survival data with informative cluster size analysis of clustered data focusing on inference of the marginal distribution may be problematic when the risk of the outcome is related to the cluster size termed as informative cluster size in the absence of censoring hoffman et al proposed a within cluster resampling method which is asymptotically equivalent to a weighted generalized estimating equations score equation we investigate the estimation of the marginal distribution for multivariate survival data with informative cluster size using cluster weighted weibull and cox proportional hazards models the cluster weighted cox model can be implemented using standard software simulation results demonstrate that the proposed methods produce unbiased parameter estimation in the presence of informative cluster size to illustrate the proposed approach we analyze survival data from a lymphatic filariasis study in recife brazil

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

survival model predictive accuracy and roc curves summary the predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model or r2 commonly used for continuous response models or using extensions of sensitivity and specificity which are commonly used for binary response models in this article we propose new time dependent accuracy summaries based on time specific versions of sensitivity and specificity calculated over risk sets we connect the accuracy summaries to a previously proposed global concordance measure which is a variant of kendall s tau in addition we show how standard cox regression output can be used to obtain estimates of time dependent sensitivity and specificity and time dependent receiver operating characteristic roc curves semiparametric estimation methods appropriate for both proportional and nonproportional hazards data are introduced evaluated in simulations and illustrated using two familiar survival data sets

doubly robust estimation optimally truncated inverse intensity weighting and increment based methods for the analysis of irregularly observed longitudinal data longitudinal data arising from routine follow up of patients will often have irregular measurement times existing methods for analysis include joint modelling of the outcome and measurement processes and inverse intensity weighting iiw this work extends previously proposed analysis of increments to the case of irregular follow up yielding a model for the increments that can be used as a stand alone method furthermore we propose two ways of combining the increments and iiw estimators first we use the increment model to select the truncation point for the inverse intensity weights that minimises the mean squared error of the iiw estimator second we use the increment model to augment the usual iiw estimating equations to form a doubly robust estimator we evaluate the methods through simulation and apply these to a recent study of juvenile dermatomyositis

likelihood methods for binary responses of present components in a cluster in some biomedical studies involving clustered binary responses say disease status the cluster sizes can vary because some components of the cluster can be absent when both the presence of a cluster component as well as the binary disease status of a present component are treated as responses of interest we propose a novel two stage random effects logistic regression framework for the ease of interpretation of regression effects both the marginal probability of presence absence of a component as well as the conditional probability of disease status of a present component preserve the approximate logistic regression forms we present a maximum likelihood method of estimation implementable using standard statistical software we compare our models and the physical interpretation of regression effects with competing methods from literature we also present a simulation study to assess the robustness of our procedure to wrong specification of the random effects distribution and to compare finite sample performances of estimates with existing methods the methodology is illustrated via analyzing a study of the periodontal health status in a diabetic gullah population

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

a c0ipg method and its error estimates for the helmholtz transmission eigenvalue problem abstract the interior penalty methods using c 0 lagrange elements c 0 ipg developed in the last decade for the fourth order problems are an interesting topic in academia at present in this paper we apply the methods to the helmholtz transmission eigenvalue problem which is quadratic and non self adjoint and has important applications in the inverse scattering theory we propose a discrete scheme present a complete error analysis and first prove the c 0 ipg method can capture smooth eigenpairs efficiently using the argument in this paper we can prove that the c 0 ipg methods for the fourth order eigenvalue problems in the existing literature can also capture smooth eigenpairs efficiently numerical examples confirm our theoretical analysis

marginal analyses of clustered data when cluster size is informative we propose a new approach to fitting marginal models to clustered data when cluster size is informative this approach uses a generalized estimating equation gee that is weighted inversely with the cluster size we show that our approach is asymptotically equivalent to within cluster resampling hoffman sen and weinberg 2001 biometrika 73 13 22 a computationally intensive approach in which replicate data sets containing a randomly selected observation from each cluster are analyzed and the resulting estimates averaged using simulated data and an example involving dental health we show the superior performance of our approach compared to unweighted gee the equivalence of our approach with wcr for large sample sizes and the superior performance of our approach compared with wcr when sample sizes are small

marginal analyses of longitudinal data with an informative pattern of observations we consider solutions to generalized estimating equations with singular working correlation matrices of which the estimator of diggle et al 2007 is a special case we give explicit conditions for consistent estimation when the pattern of observations may be informative in such cases simulations reveal reduced bias and reduced mean squared error compared with existing alternatives a study of peritoneal dialysis is used to illustrate the methodology

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

two sample tests for comparing intra individual genetic sequence diversity between populations gilbert rossini and shankarappa 2005 biometrics 61 106 117 present four u statistic based tests to compare genetic diversity between different samples the proposed tests improved upon previously used methods by accounting for the correlations in the data we find however that the same correlations introduce an unacceptable bias in the sample estimators used for the variance and covariance of the inter sequence genetic distances for modest sample sizes here we compute unbiased estimators for these and test the resulting improvement using simulated data we also show that contrary to the claims in gilbert et al it is not always possible to apply the welch satterthwaite approximate t test and we provide explicit formulas for the degrees of freedom to be used when on the other hand such approximation is indeed possible

regression analysis of clustered interval censored data with informative cluster size interval censored data are commonly found in studies of diseases that progress without symptoms which require clinical evaluation for detection several techniques have been suggested with independent assumption however the assumption will not be valid if observations come from clusters furthermore when the cluster size relates to response variables commonly used methods can bring biased results for example in a study on lymphatic filariasis a parasitic disease where worms make several nests in the infected person s lymphatic vessels and reside until adulthood the response variable of interest is the nest extinction times as the extinction times of nests are checked by repeated ultrasound examinations exact extinction times are not observed instead data are composed of two examination points the last examination time with living worms and the first examination time with dead worms furthermore as williamson et al statistics in medicine 2008 27 543 555 pointed out larger nests show a tendency for low clearance rates this association has been denoted as an informative cluster size to analyze the relationship between the numbers of nests and interval censored nest extinction times this study proposes a joint model for the relationship between cluster size and clustered interval censored failure data a proportional hazard model with random effect and a mixed ordinal regression model are applied to failure times and cluster size respectively the joint model approach addresses both the association among failure times from the same cluster and the dependency of failure times on cluster size simulation studies are performed to assess the finite sample properties of the estimators and lymphatic filariasis data are analyzed as an illustration

on assessing the strength of dependency between failure time variates summary the correlation p between cumulative hazard variates is considered as a measure of dependence between pairs of failure time variates such correlation is readily estimated in the absence of censorship but modelling assumptions are required for its estimation in the presence of independent right censorship a semiparametric class of bivariate failure time models in which a dependence parameter 0 is in one to one correspondence with the cumulative hazard variate correlation p is considered for this purpose a simple estimating function consisting of a weighted sum over the grid formed by the observed failure times of differences between nonparametric and model restricted estimates of covariance rates is proposed for estimation and corresponding asymptotic distribution theory is given this estimation procedure is shown to lack robustness under conditions of moderate to heavy censorship motivating consideration of dependency measures that can be defined on the support of the observed failure times two such measures the correlation between marginal martingales and a cumulative cross ratio statistic are discussed and corresponding nonparametric estimators are proposed

marginal analysis of correlated failure time data with informative cluster sizes we consider modeling correlated survival data when cluster sizes may be informative to the outcome of interest based on a within cluster resampling wcr approach and a weighted score function wsf method we derive the large sample properties for the wcr estimators under the cox proportional hazards model we establish consistency and asymptotic normality of the regression coefficient estimators and the weak convergence property of the estimated baseline cumulative hazard function the wsf method is to incorporate the inverse of cluster sizes as weights in the score function we conduct simulation studies to assess and compare the finite sample behaviors of the estimators and apply the proposed methods to a dental study as an illustration

a log rank test for clustered data with informative within cluster group size the log rank test is a popular nonparametric test for comparing survival distributions among groups when data are organized in clusters of potentially correlated observations adjustments can be made to account for within cluster dependencies among observations eg tests derived from frailty models tests for clustered data can be further biased when the number of observations within each cluster and the distribution of groups within cluster are correlated with survival times phenomena known as informative cluster size and informative within cluster group size in this manuscript we develop a log rank test for clustered data that adjusts for the potentially biasing effect of informative cluster size and within cluster group size we provide the results of a simulation study demonstrating that our proposed test remains unbiased under cluster based informativeness while other candidate tests not accounting for the clustering structure do not properly maintain size furthermore our test exhibits power advantages under scenarios in which traditional tests are appropriate we demonstrate an application of our test by comparing time to functional progression between groups defined initial functional status in a spinal cord injury data set

mixed methods for the elastic transmission eigenvalue problem abstract the elastic transmission eigenvalue problem is quadratic in the eigenvalue parameter nonselfadjoint and of fourth order in this paper we apply the ciarlet raviart mixed method to this problem give a mixed variational form and establish two mixed methods using the classical lagrange finite element and the spectral element respectively we deduce the error estimates of the discrete eigenpairs theoretical analysis and numerical experiments show that these two methods are simple and easy to implement and can efficiently compute real and complex elastic transmission eigenvalues

a signed rank test for clustered data we consider the problem of comparing two outcome measures when the pairs are clustered using the general principle of within cluster resampling we obtain a novel signed rank test for clustered paired data we show by a simple informative cluster size simulation model that only our test maintains the correct size under a null hypothesis of marginal symmetry compared to four other existing signed rank tests further our test has adequate power when cluster size is noninformative in general cluster size is informative if the distribution of pair wise differences within a cluster depends on the cluster size an application of our method to testing radiation toxicity trend is presented

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

rank sum tests for clustered data the wilcoxon rank sum test is widely used to test the equality of two populations because it makes fewer distributional assumptions than parametric procedures such as the t test however the wilcoxon rank sum test can be used only if data are independent when data are clustered tests based on generalized estimating equations gees that generalize the t test have been proposed here we develop a rank sum test that can be used when data are clustered as an application we use our rank sum test to develop a nonparametric test of association between a genetic marker and a quantitative trait locus we also give a rank sum test for equivalence of three or more populations that generalizes the kruskal wallis test to situations with clustered data unlike previous rank tests for clustered data our proposal is valid when members of the same cluster belong to different groups or when the correlation between cluster members differs across groups

informative cluster sizes for subcluster level covariates and weighted generalized estimating equations williamson et al 2003 s cluster weighted generalized estimating equations cwgee are effective at adjusting for bias due to informative cluster sizes for cluster level covariates we show that cwgee may not perform well however for covariates that can take different values within a cluster if the numbers of observations at each covariate level are informative on the other hand inverse probability of treatment weighting accounts for informative treatment propensity but not for informative cluster size motivated by evaluating the effect of a binary exposure in presence of such types of informativeness we propose several weighted generalized estimating equation estimators with weights related to the size of a cluster as well as the distribution of the binary exposure within the cluster choice of the weights depends on the population of interest and the nature of the exposure through simulation studies we demonstrate the superior performance of the new estimators compared to existing estimators such as from gee cwgee and inverse probability of treatment weighted gee we demonstrate the use of our method using an example examining covariate effects on the risk of dental caries among small children

evaluating prediction rules for t year survivors with censored regression models suppose that we are interested in establishing simple but reliable rules for predicting future t year survivors through censored regression models in this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate sensitivity and specificity and positive and negative predictive values specifically under various working models we derive consistent estimators for the above measures through substitution and cross validation estimation procedures furthermore we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified confidence intervals for example for the difference of the precision measures between two competing rules can then be constructed all of the proposals are illustrated with real examples and their finite sample properties are evaluated through a simulation study

efficient spectral galerkin methods iii polar and cylindrical geometries we present in this paper several extremely efficient and accurate spectral galerkin methods for second and fourth order equations in polar and cylindrical geometries these methods are based on appropriate variational formulations which incorporate naturally the pole condition s in particular the computational complexities of the chebyshev galerkin method in a disk and the chebyshev legendre galerkin method in a disk or a cylinder are quasi optimal optimal up to a logarithmic term as an indication of efficiency the cpu time for the poisson solver on a disk by our chebyshev galerkin method is only about 70 of the corresponding finite difference code in fishpack

within cluster resampling for multilevel models under informative cluster size a within cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster we then estimate the parameters by maximising an average over the bootstrap samples of a suitable composite log likelihood the consistency of the proposed estimator is shown 15 and does not require that the correct model for cluster size is specified we give an estimator of the covariance matrix of the proposed estimator and a test for the non informativeness of the cluster sizes a simulation study shows as in neuhaus mcculloch 2011 that the standard maximum likelihood estimator exhibits little bias for some regression coefficients however for those parameters which exhibit non negligible bias the proposed method is successful in cor 20 recting for this bias

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

on the uniqueness of the shape of a penetrable anisotropic obstacle we consider the scattering of time harmonic waves in an isotropic homogeneous medium which contains a penetrable anisotropic inhomogeneous obstacle after reviewing existence uniqueness and regularity of a variational solution we prove that a knowledge of the scattered near fields for all incident plane waves at a fixed wave number uniquely determines the obstacle provided the matrix characterizing the anisotropic medium satisfies a suitable condition to this end we examine the corresponding interior transmission problem and prove that it is a compact perturbation of an interior transmission problem which is well posed

hierarchical conforming finite element methods for the biharmonic equation the paper deals with hierarchical bases in spaces of conforming c 1 elements in connection with the approximate solution of the biharmonic equation delta 2 u f quad text in omega qquad u frac partial u partial n 0 quad text on partial omega on a plane polygonal domain omega two different composite finite elements are studied piecewise quadratic powell sabin elements and piecewise cubic elements of clough tocher type the main result are estimates for the condition numbers of the corresponding discretization matrices that show that a conjugate gradient method applied to the hierarchical discretization the so called hierarchical multilevel method will yield suboptimal convergence rates in comparison with standard multigrid schemes

efficient estimation for rank based regression with clustered data rank based inference is widely used because of its robustness this article provides optimal rank based estimating functions in analysis of clustered data with random cluster effects the extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations the performance of the proposed method is satisfactory even when the correlation structure is misspecified or when heteroscedasticity in variance is present finally a real dataset is analyzed for illustration

cox regression analysis of multivariate failure time data the marginal approach multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated in this paper i present a general methodology for analysing such data which is analogous to that of liang and zeger for longitudinal data analysis this approach formulates the marginal distributions of multivariate failure times with the familiar cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified the baseline hazard functions for the marginal models may be identical or different simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators and robust variance covarinace estimators are constructed to account for the intra class correlation simulation results demonstrate that the large sample approximations are adequate for practical use and that ignoring the intra class correlation could yield rather misleading variance estimators the proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches detailed illustrations with data from four clinical or epidemiologic studies are provided

rank based inference for covariate and group effects in clustered data in presence of informative intra cluster group size there have been numerous attempts to extend the wilcoxon rank sum test to clustered data recently one such rank sum test dutta datta 2016 biometrics 72 432 440 was developed to compare the group specific marginal distributions of outcomes in clustered data where the conditional distributions of outcomes depend on the number of observations from that group in a given cluster a phenomenon referred to as informative intra cluster group icg size however comparison of group specific marginal distributions may not be sufficient in presence of some potentially useful covariables that are observed in the study in addition not accounting for the effect of these covariates can lead to biased and misleading inference for the group comparisons thus the purpose of this article is twofold first we develop a method to estimate the covariate effects using rank based weighted estimating equations that are appropriate when the icg size is informative second we construct an aligned rank sum test based on the covariate adjusted outcomes asymptotic distributions of the r estimators and the test statistic are provided through simulation studies we show the importance of selecting proper weights in constructing the estimating equations when informativeness is present through the cluster or icg sizes we also demonstrate the superiority and the robustness of our method in comparison to regular parametric linear mixed models in clustered data we apply our method to analyze different real life data sets including a data on birthweights of rat pups in different litters and a dental data on tooth attachment loss

a covariate specific time dependent receiver operating characteristic curve for correlated survival data several studies for the clinical validity of circulating tumor cells ctcs in metastatic breast cancer were conducted showing that it is a prognostic biomarker of overall survival in this work we consider an individual patient data meta analysis for nonmetastatic breast cancer to assess the discrimination of ctcs regarding the risk of death data are collected in several centers and present correlated failure times for subjects of the same center however although the covariate specific time dependent receiver operating characteristic roc curve has been widely used for assessing the performance of a biomarker there is no methodology yet that can handle this specific setting with clustered censored failure times we propose an estimator for the covariate specific time dependent roc curves and area under the roc curve when clustered failure times are detected we discuss the assumptions under which the estimators are consistent and their interpretations we assume a shared frailty model for modeling the effect of the covariates and the biomarker on the outcome in order to account for the cluster effect a simulation study was conducted and it shows negligible bias for the proposed estimator and a nonparametric one based on inverse probability censoring weighting while a semiparametric estimator ignoring the clustering is markedly biased finally in our application to breast cancer data the estimation of the covariate specific area under the curves illustrates that the ctcs discriminate better patients with inflammatory tumor than patients with noninflammatory tumor with respect to their risk of death

bayesian modeling of multivariate spatial binary data with applications to dental caries dental research gives rise to data with potentially complex correlation structure assessments of dental caries yield a binary outcome indicating the presence or absence of caries experience for each surface of each tooth in a subject s mouth in addition to this nesting caries outcome exhibit spatial structure among neighboring teeth we develop a bayesian multivariate model for spatial binary data using random effects autologistic regression that controls for the correlation within tooth surfaces and spatial correlation among neighboring teeth using a sample from a clinical study conducted at the medical university of south carolina we compare this autologistic model with covariates to alternative models to demonstrate the improvement in predictions and also to assess the effects of covariates on caries experience

detecting case control expression quantitative trait loci using locally most powerful or maximin robust rank tests in testing genome wide gene expression quantitative trait loci efficiency robust statistical methods and their computational convenience are most relevant for this purpose we propose to use a modified locally most powerful rank test for the analysis of case control expression data this modified rank test statistic is computationally simple robust for non normally distributed expression data and asymptotically locally most powerful it depends on the specification of a location distribution form for data but is not sensitive to misspecifications when such a location distribution form cannot be specified we apply gastwirth s maximin efficiency robust rank test to gene expression data to maximize the worst pitman asymptotic relative efficiency among a family of location distributions we conduct simulation studies to assess their performance and use an application to real data for illustration copyright 2011 john wiley sons ltd

efficiency of regression estimates for clustered data statistical methods for clustered data such as generalized estimating equations gee and generalized least squares gls require selecting a correlation or convariance structure to specify the dependence between observations within a cluster valid regression estimates can be obtained that do not depend on correct specification of the true correlation but inappropriate specifications can result in a loss of efficiency we derive general expressions for the asymptotic relative efficiency of gee and gls estimators under nested correlation structures efficiency is shown to depend on the covariate distribution the cluster sizes the response variable correlation and the regression parameters the results demonstrate that efficiency is quite sensitive to the between and within cluster variation of the covariates and provide useful characterizations of models for which upper and lower efficiency bounds are attained efficiency losses for simple working correlation matrices such as independence can be large even for small to moderate correlations and cluster sizes

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

classical and quantum kinetic equations with exact conservation laws stationary and dynamic properties of reduced density matrices can be determined from formal or approximate closures of an infinite hierarchy of equations the local macroscopic conservation laws place weak but important constraints on the reduced density matrices which should be respected by any closure for pairwise additive forces conditions on the closure of the one and two particle equations are obtained that preserve the exact functional dependence of the conserved densities and their fluxes on the reduced density matrices to illustrate the nature of these conditions a closure approximation suitable for a quantum gas is given yielding an extension of the time dependent hartree fock equations for the dynamics of a nuclear fluid to include collisions

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

cluster adjusted regression for displaced subject data cards marginal inference under potentially informative temporal cluster size profiles ignorance of the mechanisms responsible for the availability of information presents an unusual problem for analysts it is often the case that the availability of information is dependent on the outcome in the analysis of cluster data we say that a condition for informative cluster size ics exists when the inference drawn from analysis of hypothetical balanced data varies from that of inference drawn on observed data much work has been done in order to address the analysis of clustered data with informative cluster size examples include inverse probability weighting ipw cluster weighted generalized estimating equations cwgee and doubly weighted generalized estimating equations dwgee when cluster size changes with time i e the data set possess temporally varying cluster sizes tvcs these methods may produce biased inference for the underlying marginal distribution of interest we propose a new marginalization that may be appropriate for addressing clustered longitudinal data with tvcs the principal motivation for our present work is to analyze the periodontal data collected by beck et al 1997 journal of periodontal research 6 497 505 longitudinal periodontal data often exhibits both ics and tvcs as the number of teeth possessed by participants at the onset of study is not constant and teeth as well as individuals may be displaced throughout the study

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

iterative methods for transmission eigenvalues transmission eigenvalues have important applications in inverse scattering theory they can be used to obtain useful information of the physical properties such as the index of refraction of the scattering target despite considerable effort devoted to the existence and estimation for the transmission eigenvalues the numerical treatment is limited since the problem is nonstandard classical finite element methods result in non hermitian matrix eigenvalue problems in this paper we focus on the computation of a few lowest transmission eigenvalues which are of practical importance instead of a non hermitian problem we work on a series of generalized hermitian problems we first use a fourth order reformulation of the transmission eigenproblem to construct functions involving an associated generalized eigenvalue problem the roots of these functions are the transmission eigenvalues then we apply iterative methods to compute the transmission eigenvalues we show the convergence of the numerical schemes the effectiveness of the methods is demonstrated using various numerical examples

pearson s chi square test and rank correlation inferences for clustered data pearson s chi square test has been widely used in testing for association between two categorical responses spearman rank correlation and kendall s tau are often used for measuring and testing association between two continuous or ordered categorical responses however the established statistical properties of these tests are only valid when each pair of responses are independent where each sampling unit has only one pair of responses when each sampling unit consists of a cluster of paired responses the assumption of independent pairs is violated in this article we apply the within cluster resampling technique to u statistics to form new tests and rank based correlation estimators for possibly tied clustered data we develop large sample properties of the new proposed tests and estimators and evaluate their performance by simulations the proposed methods are applied to a data set collected from a pet ct imaging study for illustration

analysis of clustered binary outcomes using within cluster paired resampling summary conditional logistic regression clr is useful for analyzing clustered binary outcome data when interest lies in estimating a cluster specific exposure parameter while treating the dependency arising from random cluster effects as a nuisance clr aggregates unmeasured cluster specific factors into a cluster specific baseline risk and is invalid in the presence of unmodeled heterogeneous covariate effects or within cluster dependency we propose an alternative resampling based method for analyzing clustered binary outcome data within cluster paired resampling wcpr which allows for within cluster dependency not solely due to baseline heterogeneity for example dependency may be in part caused by heterogeneity in response to an exposure across clusters due to unmeasured cofactors when both clr and wcpr are valid our simulations suggest that the two methods perform comparably when clr is invalid wcpr continues to have good operating characteristics for illustration we apply both wcpr and clr to a periodontal data set where there is heterogeneity in response to exposure across clusters

spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem we first develop an efficient spectral galerkin method and a rigorous error analysis for the generalized eigenvalue problems associated to a transmission eigenvalue problem then we present an iterative scheme based on computation of the first transmission eigenvalue to estimate the index of refraction of an inhomogeneous medium we present ample numerical results to demonstrate the effectiveness and accuracy of our approach

event weighted proportional hazards modelling for recurrent gap time data the analysis of gap times in recurrent events requires an adjustment to standard marginal models one can perform this adjustment with a modified within cluster resampling technique however this method is computationally intensive in this paper we describe a simple adjustment to the standard cox proportional hazards model analysis that mimics the intent of within cluster resampling and results in similar parameter estimates this method essentially weights the partial likelihood contributions by the inverse of the number of gap times observed within the individual while assuming a working independence correlation matrix we provide an example involving recurrent mammary tumours in female rats to illustrate the methods considered in this paper copyright 2012 john wiley sons ltd

a quantum kinetic equation for nonideal gases in the three particle collision approximation a quantum mechanical version of a kinetic equation is derived which accounts for three particle collisions it is shown that the total energy is conserved in the binary collision approximation

solving constrained quadratic inverse eigenvalue problem via conjugate direction method abstract inverse eigenvalue problems are among the most important problems in numerical linear algebra this paper is concerned with the problem of designing an iterative method for a quadratic inverse eigenvalue problem of the form m x 2 g x k x 0 where m g and k should be partially doubly symmetric under a prescribed submatrix constraint this kind of quadratic inverse eigenvalue problem includes the classical and generalized inverse eigenvalue problems as special cases we propose the conjugate direction cd method for computing the least frobenius norm solutions of this constrained quadratic inverse eigenvalue problem in a finite number of steps in the absence of round off errors the cd method can automatically determine the solvability of this problem finally the overall performance and efficiency of the cd method for computing approximate solutions of the problem are discussed

marginal association measures for clustered data the use of correlation coefficients in measuring the association between two continuous variables is common but regular methods of calculating correlations have not been extended to the clustered data framework for clustered data in which observations within a cluster may be correlated regular inferential procedures for calculating marginal association between two variables can be biased this is particularly true for data in which the number of observations in a given cluster is informative for the association being measured in this paper we apply the principle of inverse cluster size reweighting to develop estimators of marginal correlation that remain valid in the clustered data framework when cluster size is informative for the correlation being measured these correlations are derived as analogs to regular correlation estimators for continuous independent data namely pearson s and kendall s we present the results of a simple simulation study demonstrating the appropriateness of our proposed estimators and the inherent bias of other inferential procedures for clustered data we illustrate their use through an application to data from patients with incomplete spinal cord injury in the usa

nonequilibrium real time green s functions and the condition of weakening of initial correlation a new method is given to calculate real time green s functions in nonequilibrium from the hierarchy of equations of motion in connection with the boundary condition of weakening of initial correlations the way of deriving a generalized quantum boltzmann equation is shown

a rank sum test for clustered data when the number of subjects in a group within a cluster is informative the wilcoxon rank sum test is a popular nonparametric test for comparing two independent populations groups in recent years there have been renewed attempts in extending the wilcoxon rank sum test for clustered data one of which datta and satten 2005 journal of the american statistical association 100 908 915 addresses the issue of informative cluster size i e when the outcomes and the cluster size are correlated we are faced with a situation where the group specific marginal distribution in a cluster depends on the number of observations in that group i e the intra cluster group size we develop a novel extension of the rank sum test for handling this situation we compare the performance of our test with the datta satten test as well as the naive wilcoxon rank sum test using a naturally occurring simulation model of informative intra cluster group size we show that only our test maintains the correct size we also compare our test with a classical signed rank test based on averages of the outcome values in each group paired by the cluster membership while this test maintains the size it has lower power than our test extensions to multiple group comparisons and the case of clusters not having samples from all groups are also discussed we apply our test to determine whether there are differences in the attachment loss between the upper and lower teeth and between mesial and buccal sites of periodontal patients

a high accuracy spectral method based on min max principle for biharmonic eigenvalue problems on a spherical domain abstract in this study we develop a high accuracy spectral method based on the min max principle for biharmonic eigenvalue problems in the spherical domain by analyzing the orthogonal spherical harmonic and approximation and using the min max principle we first deduce the error estimates of approximate eigenvalues then we construct an appropriate set of orthogonal spherical functions contained in h 0 2 and establish the matrix formulations for the discrete variational form whose mass matrix and stiff matrix are all sparse so that we can solve the numerical solutions efficiently finally we provide some numerical experiments to validate that the theoretical results are correct

analysis of failure time data with multilevel clustering with application to the child vitamin a intervention trial in nepal we consider the problem of estimating covariate effects in the marginal cox proportional hazard model and multilevel associations for child mortality data collected from a vitamin a supplementation trial in nepal where the data are clustered within households and villages for this purpose a class of multivariate survival models that can be represented by a functional of marginal survival functions and accounts for hierarchical structure of clustering is exploited based on this class of models an estimation strategy involving a within cluster resampling procedure is proposed and a model assessment approach is presented the asymptotic theory for the proposed estimators and lack of fit test is established the simulation study shows that the estimates are approximately unbiased and the proposed test statistic is conservative under extremely heavy censoring but approaches the size otherwise the analysis of the nepal study data shows that the association of mortality is much greater within households than within villages

marginal regression models for multivariate failure time data abstract in this article we propose a general cox type regression model to formulate the marginal distributions of multivariate failure time data this model has a nested structure in that it allows different baseline hazard functions among distinct failure types and imposes a common baseline hazard function on the failure times of the same type we prove that the maximum quasi partial likelihood estimator for the vector of regression parameters under the independence working assumption is consistent and asymptotically normal with a covariance matrix for which a consistent estimator is provided furthermore we establish the uniform consistency and joint weak convergence of the aalen breslow type estimators for the cumulative baseline hazard functions and develop a resampling technique to approximate the joint distribution of these processes which enables one to make simultaneous inference about the survival functions over the time axis and across failure types finally we assess the small sample pro

an efficient spectral galerkin approximation based on dimension reduction scheme for transmission eigenvalues in polar geometries abstract in this paper we put forward an efficient spectral galerkin approximation in view of dimension reduction scheme for transmission eigenvalue problem in polar geometries firstly we turn the original problem into an equivalent fourth order nonlinear eigenvalue problem then the fourth order nonlinear eigenvalue problem is transformed into a coupled fourth order linear eigenvalue system by introducing an auxiliary poisson equation secondly based on polar coordinate transformation we further reduce the coupled fourth order linear eigenvalue system to a series of equivalent one dimensional eigenvalue systems thirdly we derive the essential polar condition and introduce the appropriate weighted sobolev space according to the polar condition and establish the weak form and the corresponding discrete form in addition by utilizing spectral theory of compact operators we prove the error estimates of approximation eigenvalues and eigenvectors for each one dimensional eigenvalue system finally we provide ample numerical experiments and the numerical results show the effectiveness of the algorithm and the correctness of the theoretical results

within cluster resampling within cluster resampling is proposed as a new method for analysing clustered data although the focus of this paper is clustered binary data the within cluster resampling asymptotic theory is general for many types of clustered data within cluster resampling is a simple but computationally intensive estimation method its main advantage over other marginal analysis methods such as generalised estimating equations liang zeger 1986 zeger liang 1986 is that it remains valid when the risk for the outcome of interest is related to the cluster size which we term nonignorable cluster size we present theory for the asymptotic normality and provide a consistent variance estimator for the within cluster resampling estimator simulations and an example are developed that assess the finite sample behaviour of the new method and show that when both methods are valid its performance is similar to that of generalised estimating equations

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

model selection for semiparametric marginal mean regression accounting for within cluster subsampling variability and informative cluster size we propose a model selection criterion for semiparametric marginal mean regression based on generalized estimating equations the work is motivated by a longitudinal study on the physical frailty outcome in the elderly where the cluster size that is the number of the observed outcomes in each subject is informative in the sense that it is related to the frailty outcome itself the new proposal called resampling cluster information criterion rcic is based on the resampling idea utilized in the within cluster resampling method hoffman sen and weinberg 2001 biometrika 88 1121 1134 and accommodates informative cluster size the implementation of rcic however is free of performing actual resampling of the data and hence is computationally convenient compared with the existing model selection methods for marginal mean regression the rcic method incorporates an additional component accounting for variability of the model over within cluster subsampling and leads to remarkable improvements in selecting the correct model regardless of whether the cluster size is informative or not applying the rcic method to the longitudinal frailty study we identify being female old age low income and life satisfaction and chronic health conditions as significant risk factors for physical frailty in the elderly

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations

marginal analysis of ordinal clustered longitudinal data with informative cluster size the issue of informative cluster size ics often arises in the analysis of dental data ics describes a situation where the outcome of interest is related to cluster size much of the work on modeling marginal inference in longitudinal studies with potential ics has focused on continuous outcomes however periodontal disease outcomes including clinical attachment loss are often assessed using ordinal scoring systems in addition participants may lose teeth over the course of the study due to advancing disease status here we develop longitudinal cluster weighted generalized estimating equations cwgee to model the association of ordinal clustered longitudinal outcomes with participant level health related covariates including metabolic syndrome and smoking status and potentially decreasing cluster size due to tooth loss by fitting a proportional odds logistic regression model the within teeth correlation coefficient over time is estimated using the two stage quasi least squares method the motivation for our work stems from the department of veterans affairs dental longitudinal study in which participants regularly received general and oral health examinations in an extensive simulation study we compare results obtained from cwgee with various working correlation structures to those obtained from conventional gee which does not account for ics our proposed method yields results with very low bias and excellent coverage probability in contrast to a conventional generalized estimating equations approach