a multilevel mixed effects varying coefficient model with multilevel predictors and random effects for modeling hospitalization risk in patients on dialysis for patients on dialysis hospitalizations remain a major risk factor for mortality and morbidity we use data from a large national database united states renal data system to model time varying effects of hospitalization risk factors as functions of time since initiation of dialysis to account for the three level hierarchical structure in the data where hospitalizations are nested in patients and patients are nested in dialysis facilities we propose a multilevel mixed effects varying coefficient model mme vcm where multilevel patient and facility level random effects are used to model the dependence structure of the data the proposed mme vcm also includes multilevel covariates where baseline demographics and comorbidities are among the patient level factors and staffing composition and facility size are among the facility level risk factors to address the challenge of high dimensional integrals due to the hierarchical structure of the random effects we propose a novel two step approximate em algorithm based on the fully exponential laplace approximation inference for the varying coefficient functions and variance components is achieved via derivation of the standard errors using score contributions the finite sample performance of the proposed estimation procedure is studied through 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

marginalized binary mixed effects models with covariate dependent random effects and likelihood inference les modeles marginaux et les modeles a effets mixtes conditionnels sont couramment utilises pour des donnees binaires agregees cependant les parametres de regression et les predictions de modeles non lineaires a effets mixtes n ont pas habituellement une interpretation marginale directe des que la forme fonctionnelle conditionnelle ne peut etre transposee a la marge une approche unifiee est interessante des que l on est interesse a la fois par des inferences marginales et conditionnelles a cette fin nous avons etudie une parametrisation de modeles lineaires generalises mixtes avec une distribution structuree de l intercept aleatoire qui apparie les formes conditionnelles et marginales nous modelisons la distribution des reponses moyennes marginales et selectionnons la distribution des intercept pour realiser l appariement et aussi pour modeliser des effets aleatoires de covariables nous discutons la relation entre cette approche et quelques modeles existant et comparons ces approches sur deux jeux de donnees

estimated estimating equations semiparametric inference for clustered and longitudinal data summary we introduce a flexible marginal modelling approach for statistical inference for clustered and longitudinal data under minimal assumptions this estimated estimating equations approach is semiparametric and the proposed models are fitted by quasi likelihood regression where the unknown marginal means are a function of the fixed effects linear predictor with unknown smooth link and variance covariance is an unknown smooth function of the marginal means we propose to estimate the nonparametric link and variance covariance functions via smoothing methods whereas the regression parameters are obtained via the estimated estimating equations these are score equations that contain nonparametric function estimates the proposed estimated estimating equations approach is motivated by its flexibility and easy implementation moreover if data follow a generalized linear mixed model with either a specified or an unspecified distribution of random effects and link function the model proposed emerges as the corresponding marginal population average version and can be used to obtain inference for the fixed effects in the underlying generalized linear mixed model without the need to specify any other components of this generalized linear mixed model among marginal models the estimated estimating equations approach provides a flexible alternative to modelling with generalized estimating equations applications of estimated estimating equations include diagnostics and link selection the asymptotic distribution of the proposed estimators for the model parameters is derived enabling statistical inference practical illustrations include poisson modelling of repeated epileptic seizure counts and simulations for clustered binomial responses

identifying variables responsible for data not missing at random when data are not missing at random nmar maximum likelihood ml procedure will not generate consistent parameter estimates unless the missing data mechanism is correctly modeled understanding nmar mechanism in a data set would allow one to better use the ml methodology a survey or questionnaire may contain many items certain items may be responsible for nmar values in other items the paper develops statistical procedures to identify the responsible items by comparing ml estimates mle statistics are developed to test whether the mles are changed when excluding items the items that cause a significant change of the mles are responsible for the nmar mechanism normal distribution is used for obtaining the mles a sandwich type covariance matrix is used to account for distribution violations the class of nonnormal distributions within which the procedure is valid is provided both saturated and structural models are considered effect sizes are also defined and studied the results indicate that more missing data in a sample does not necessarily imply more significant test statistics due to smaller effect sizes knowing the true population means and covariances or the parameter values in structural equation models may not make things easier either

a class of markov models for longitudinal ordinal data summary generalized linear models with serial dependence are often used for short longitudinal series heagerty 2002 has proposed marginalized transition models for the analysis of longitudinal binary data in this paper we extend this work to accommodate longitudinal ordinal data fisher scoring algorithms are developed for estimation methods are illustrated on quality of life data from a recent colorectal cancer clinical trial

matching conditional and marginal shapes in binary random intercept models using a bridge distribution function summary random effects logistic regression models are often used to model clustered binary response data regression parameters in these models have a conditional subject specific interpretation in that they quantify regression effects for each cluster very often the logistic functional shape conditional on the random effects does not carry over to the marginal scale thus parameters in these models usually do not have an explicit marginal population averaged interpretation we study a bridge distribution function for the random effect in the random intercept logistic regression model under this distributional assumption the marginal functional shape is still of logistic form and thus regression parameters have an explicit marginal interpretation the main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework the generality of the results and some properties of the bridge distribution functions are discussed an example is used for illustration

robustness of the latent variable model for correlated binary data the marginal regression model offers a useful alternative to conditional approaches to analyzing binary data liang zeger and qaqish 1992 journal of the royal statistical society series b 54 3 40 instead of modelling the binary data directly as do liang and zeger 1986 biometrika 73 13 22 the parametric marginal regression model developed by qu et al 1992 biometrics 48 1095 1102 assumes that there is an underlying multivariate normal vector that gives rise to the observed correlated binary outcomes although this parametric approach provides a flexible way to model different within cluster correlation structures and does not restrict the parameter space it is of interest to know how robust the parameter estimates are with respect to choices of the latent distribution we first extend the latent modelling to include multivariate t distributed latent vectors and assess the robustness in this class of distributions then we show through a simulation that the parameter estimates are robust with respect to the latent distribution even if latent distribution is skewed in addtion to this empirical evidence for robustness we show through the iterative algorithm that the robustness of the regression coefficents with respect to misspecifications of covariance structure in liang and zeger s model in fact indicates robustness with respect to underlying distributional assumptions of the latent vector in the latent variable model

the complexity of approximating a nonlinear program we consider the problem of finding the maximum of a multivariate polynomial inside a convex polytope we show that there is no polynomial time approximation algorithm for this problem even one with a very poor guarantee unless p np we show that even when the polynomial is quadratic i e quadratic programming there is no polynomial time approximation unless np is contained in quasi polynomial time

conditional estimation for generalized linear models when covariates are subject specific parameters in a mixed model for longitudinal measurements the relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest and a relevant framework is that of a generalized linear model with covariates that are subject specific random effects in a linear mixed model for the longitudinal measurements naive implementation by imputing subject specific effects from individual regression fits yields biased inference and several methods for reducing this bias have been proposed these require a parametric normality assumption on the random effects which may be unrealistic adapting a strategy of stefanski and carroll 1987 biometrika74 703 716 we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution the methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause

the effects of mixture distribution misspecification when fitting mixed effects logistic models summary mixed effects logistic models are often used to analyze binary response data which have been gathered in clusters or groups responses are assumed to follow a logistic model within clusters with an intercept which varies across clusters according to a specified probability distribution g in this paper we examine the performance of mixed effects logistic regression analysis when a main component of the model the mixture distribution is misspecified we show that when the mixture distribution is misspecified estimates of model parameters including the effects of covariates typically are asymptotically biased i e inconsistent however we present some approximations which suggest that the magnitude of the bias in the estimated covariate effects is typically small these findings are corroborated by a set of simulations which also suggest that valid variance estimates of estimated covariate effects can be obtained when the mixture distribution is misspecified

rejoinder to a note on type ii error under random effects misspecification in generalized linear mixed models summary in this rejoinder we discuss the impact of misspecifying the random effects distribution on inferences obtained from generalized linear mixed models glmms special attention is paid to the power of the tests for the fixed effect parameters to study this misspecification researchers often use simulation designs in which several choices for the true underlying random effects distribution are considered while the assumed distribution is kept fixed neuhaus mcculloch and boylan 2010 biometrics 00 000 000 argue that a logically correct approach should consist of varying the assumed fitted distribution while holding the true fixed we argue that both simulation designs can bring valuable insights into the impact of the misspecification furthermore using both designs we illustrate that the power associated with the tests for the fixed effect parameters in glmm may be affected by misspecifying the random effects distribution

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

joint models for a primary endpoint and multiple longitudinal covariate processes summary joint models are formulated to investigate the association between a primary endpoint and features of multiple longitudinal processes in particular the subject specific random effects in a multivariate linear random effects model for multiple longitudinal processes are predictors in a generalized linear model for primary endpoints li zhang and davidian 2004 biometrics60 1 7 proposed an estimation procedure that makes no distributional assumption on the random effects but assumes independent within subject measurement errors in the longitudinal covariate process based on an asymptotic bias analysis we found that their estimators can be biased when random effects do not fully explain the within subject correlations among longitudinal covariate measurements specifically the existing procedure is fairly sensitive to the independent measurement error assumption to overcome this limitation we propose new estimation procedures that require neither a distributional or covariance structural assumption on covariate random effects nor an independence assumption on within subject measurement errors these new procedures are more flexible readily cover scenarios that have multivariate longitudinal covariate processes and can be implemented using available software through simulations and an analysis of data from a hypertension study we evaluate and illustrate the numerical performances of the new estimators

marginalized models for moderate to long series of longitudinal binary response data marginalized models heagerty 1999 biometrics 55 688 698 permit likelihood based inference when interest lies in marginal regression models for longitudinal binary response data two such models are the marginalized transition and marginalized latent variable models the former captures within subject serial dependence among repeated measurements with transition model terms while the latter assumes exchangeable or nondiminishing response dependence using random intercepts in this article we extend the class of marginalized models by proposing a single unifying model that describes both serial and long range dependence this model will be particularly useful in longitudinal analyses with a moderate to large number of repeated measurements per subject where both serial and exchangeable forms of response correlation can be identified we describe maximum likelihood and bayesian approaches toward parameter estimation and inference and we study the large sample operating characteristics under two types of dependence model misspecification data from the madras longitudinal schizophrenia study thara et al 1994 acta psychiatrica scandinavica 90 329 336 are analyzed

estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes generalized linear mixed models with random intercepts and slopes provide useful analyses of clustered and longitudinal data and typically require the specification of the distribution of the random effects previous work for models with only random intercepts has shown that misspecifying the shape of this distribution may bias estimates of the intercept but typically leads to little bias in estimates of covariate effects very few papers have examined the effects of misspecifying the joint distribution of random intercepts and slopes however simulation results in a recent paper suggest that misspecifying the shape of the random slope distribution can yield severely biased estimates of all model parameters using analytic results simulation studies and fits to example data this paper examines the bias in parameter estimates due to misspecification of the shape of the joint distribution of random intercepts and slopes consistent with results for models with only random intercepts and contrary to the claims of severe bias in a recent paper we show that misspecification of the joint distribution typically yields little bias in estimates of covariate effects and is restricted to covariates associated with the misspecified random effects distributions we also show that misspecification of the distribution of random effects has little effect on confidence interval performance coverage rates based on the model based standard errors from fitted likelihoods were generally quite close to nominal

a diagnostic test for the mixing distribution in a generalised linear mixed model summary we introduce a diagnostic test for the mixing distribution in a generalised linear mixed model the test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimators of a subset of the fixed effects in the model we derive the asymptotic variance of this difference and propose a test statistic that has a limiting chi squared distribution under the null hypothesis that the mixing distribution is correctly specified this strategy uses an idea presented by hausman 1978 who considered analogous tests for the linear mixed model an important advantage of the methods outlined here is that the resulting diagnostic test is easily implemented in commercial software we illustrate the method by applying it to data from a clinical trial investigating the effect of hormonal contraceptives in women

misspecified maximum likelihood estimates and generalised linear mixed models summary we investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model specifically we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects we compare the impact of model violation for two parameterisations of the regression model substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depends on measured covariates or there are autoregressive random effects a marginally specified regression structure that is estimated using maximum likelihood is much less susceptible to bias resulting from random effects model misspecification

the impact of a misspecified random effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models estimation in generalized linear mixed models glmms is often based on maximum likelihood theory assuming that the underlying probability model is correctly specified however the validity of this assumption is sometimes difficult to verify in this paper we study through simulations the impact of misspecifying the random effects distribution on the estimation and hypothesis testing in glmms it is shown that the maximum likelihood estimators are inconsistent in the presence of misspecification the bias induced in the mean structure parameters is generally small as far as the variability of the underlying random effects distribution is small as well however the estimates of this variability are always severely biased given that the variance components are the only tool to study the variability of the true distribution it is difficult to assess whether problems in the estimation of the mean structure occur the type i error rate and the power of the commonly used inferential procedures are also severely affected the situation is aggravated if more than one random effect is included in the model further we propose to deal with possible misspecification by way of sensitivity analysis considering several random effects distributions all the results are illustrated using data from a clinical trial in schizophrenia

a functional based distribution diagnostic for a linear model with correlated outcomes in this paper we present an easy to implement graphical distribution diagnostic for linear models with correlated errors houseman et al 2004 constructed quantile quantile plots for the marginal residuals of such models suitably transformed we extend the pointwise asymptotic theory to address the global stochastic behaviour of the corresponding empirical cumulative distribution function and describe a simulation technique that serves as a computationally efficient parametric bootstrap for generating representatives of its stochastic limit thus continuous functionals of the empirical cumulative distribution function may be used to form global tests of normality through the use of projection matrices we generalised our methods to include tests that are directed at assessing the normality of particular components of the error thus tests proposed by lange ryan 1989 follow as a special case our method works well both for models having independent units of sampling and for those in which all observations are correlated

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

diagnosis of random effect model misspecification in generalized linear mixed models for binary response summary generalized linear mixed models glmms are widely used in the analysis of clustered data however the validity of likelihood based inference in such analyses can be greatly affected by the assumed model for the random effects we propose a diagnostic method for random effect model misspecification in glmms for clustered binary response we provide a theoretical justification of the proposed method and investigate its finite sample performance via simulation the proposed method is applied to data from a longitudinal respiratory infection study

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

diagnosing misspecification of the random effects distribution in mixed models it is traditionally assumed that the random effects in mixed models follow a multivariate normal distribution making likelihood based inferences more feasible theoretically and computationally however this assumption does not necessarily hold in practice which may lead to biased and unreliable results we introduce a novel diagnostic test based on the so called gradient function proposed by verbeke and molenberghs 2013 to assess the random effects distribution we establish asymptotic properties of our test and show that under a correctly specified model the proposed test statistic converges to a weighted sum of independent chi squared random variables each with one degree of freedom the weights which are eigenvalues of a square matrix can be easily calculated we also develop a parametric bootstrap algorithm for small samples our strategy can be used to check the adequacy of any distribution for random effects in a wide class of mixed models including linear mixed models generalized linear mixed models and non linear mixed models with univariate as well as multivariate random effects both asymptotic and bootstrap proposals are evaluated via simulations and a real data analysis of a randomized multicenter study on toenail dermatophyte onychomycosis

modelling sparse generalized longitudinal observations with latent gaussian processes summary in longitudinal data analysis one frequently encounters non gaussian data that are repeatedly collected for a sample of individuals over time the repeated observations could be binomial poisson or of another discrete type or could be continuous the timings of the repeated measurements are often sparse and irregular we introduce a latent gaussian process model for such data establishing a connection to functional data analysis the functional methods proposed are non parametric and computationally straightforward as they do not involve a likelihood we develop functional principal components analysis for this situation and demonstrate the prediction of individual trajectories from sparse observations this method can handle missing data and leads to predictions of the functional principal component scores which serve as random effects in this model these scores can then be used for further statistical analysis such as inference regression discriminant analysis or clustering we illustrate these non parametric methods with longitudinal data on primary biliary cirrhosis and show in simulations that they are competitive in comparisons with generalized estimating equations and generalized linear mixed models

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

a comparison of mixed effects logistic regression models for binary response data with two nested levels of clustering we compare mixed effects logistic regression models for binary response data with two nested levels of clustering the comparison of these models occurs in the context of developmental toxicity data sets for which multiple types of outcomes first level are measured on each rat pup second level nested within a litter third level because the nested nature of such data is occasionally accommodated by ignoring one level of clustering we consider three models i a three level model adjusting for clustering due to both pup and litter m1 ii a two level model adjusting for just pup m2 and iii another two level model adjusting for just litter m3 the three types of effects of interest are i differences among malformation types first level effects ii differences among groups of pups for example sex of pup second level effects and iii differences among groups of litters for example dose third level effects simulations and data analyses suggest that the m3 model leads to more bias than the m1 or m2 models for all three types of effects in terms of coverage of confidence intervals for fixed effects log odds ratio parameters the m1 model achieves nominal coverage whereas the m2 model reduces coverage for the third level effects and the m3 model obtains poor coverage for both first and second level effects these reductions in coverage for certain model parameter combinations worsen as baseline risk increases the data analyses support these simulation based conclusions to some extent copyright 1999 john wiley sons ltd

a note on the bias of estimators with missing data it is well known that many standard analyses including maximum likelihood estimation and the generalized estimating equation approach liang and zeger 1986 biometrika 73 13 22 can result in biased estimation when there are missing observations in such cases it is of interest to calculate the magnitude of the bias incurred under specific assumptions about the process generating the full data and the nonresponse mechanism in this paper we give a condition that identifies the limit in probability of estimators that are solutions of estimating equations computed from the incomplete data with discrete data this condition suggests a simple algorithm to compute the asymptotic bias of these estimators that can be easily implemented with existing statistical software we illustrate our approach with asthma prevalence data in children

marginalized models for longitudinal ordinal data with application to quality of life studies random effects are often used in generalized linear models to explain the serial dependence for longitudinal categorical data marginalized random effects models mrems for the analysis of longitudinal binary data have been proposed to permit likelihood based estimation of marginal regression parameters in this paper we introduce an extension of the mrem to accommodate longitudinal ordinal data maximum marginal likelihood estimation is implemented utilizing quasi newton algorithms with monte carlo integration of the random effects our approach is applied to analyze the quality of life data from a recent colorectal cancer clinical trial dropout occurs at a high rate and is often due to tumor progression or death to deal with progression death we use a mixture model for the joint distribution of longitudinal measures and progression death times and principal stratification to draw causal inferences about survivors

variances are not always nuisance parameters summary in classical problems e g comparing two populations fitting a regression surface etc variability is a nuisance parameter the term nuisance parameter is meant here in both the technical and the practical sense however there are many instances where understanding the structure of variability is just as central as understanding the mean structure the purpose of this article is to review a few of these problems i focus in particular on two issues a the determination of the validity of an assay and b the issue of the power for detecting health effects from nutrient intakes when the latter are measured by food frequency questionnaires i will also briefly mention the problems of variance structure in generalized linear mixed models robust parameter design in quality technology and the signal in microarrays in these and other problems treating variance structure as a nuisance instead of a central part of the modeling effort not only leads to inefficient estimation of means but also to misleading conclusions

semiparametric estimation in general repeated measures problems summary the paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function special cases in our approach include marginal models for longitudinal or clustered data conditional logistic regression for matched case control studies multivariate measurement error models generalized linear mixed models with a semiparametric component and many others we propose profile kernel and backfitting estimation methods for these problems derive their asymptotic distributions and show that in likelihood problems the methods are semiparametric efficient although generally not true it transpires that with our methods profiling and backfitting are asymptotically equivalent we also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm the methods proposed are evaluated by using simulation studies and applied to the kenya haemoglobin data

modeling the random effects covariance matrix for longitudinal data with covariates measurement error longitudinal data occur frequently in practice such as medical studies and life sciences generalized linear mixed models glmms are commonly used to analyze such data it is typically assumed that the random effects covariance matrix is constant among subjects in these models in many situations however the correlation structure may differ among subjects and ignoring this heterogeneity can lead to biases in model parameters estimate recently lee et al developed a heterogeneous random effects covariance matrix for glmms for error free covariates covariates measured with error also happen frequently in the longitudinal data set up eg blood pressure and cholesterol level ignoring this issue in the data may produce bias in model parameters estimate and lead to wrong conclusions in this paper we propose an approach to properly model the random effects covariance matrix based on covariates in the class of glmms where we also have covariates measured with error the resulting parameters from the decomposition of random effects covariance matrix have a sensible interpretation and can be easily modeled without the concern of positive definiteness of the resulting estimator the performance of the proposed approach is evaluated through simulation studies which show that the proposed method performs very well in terms of bias mean squared error and coverage rate an application of the proposed method is also provided using a longitudinal data from manitoba follow up study

imputation approaches for estimating diagnostic accuracy for multiple tests from partially verified designs interest often focuses on estimating sensitivity and specificity of a group of raters or a set of new diagnostic tests in situations in which gold standard evaluation is expensive or invasive various authors have proposed semilatent class modeling approaches for estimating diagnostic accuracy in this situation this article presents imputation approaches for this problem i show how imputation provides a simpler way of performing diagnostic accuracy and prevalence estimation than the use of semilatent modeling furthermore the imputation approach is more robust to modeling assumptions and in general there is only a moderate efficiency loss relative to a correctly specified semilatent class model i apply imputation to a study designed to estimate the diagnostic accuracy of digital radiography for gastric cancer the feasibility and robustness of imputation is illustrated with analysis asymptotic results and simulations

type i and type ii error under random effects misspecification in generalized linear mixed models generalized linear mixed models glmms have become a frequently used tool for the analysis of non gaussian longitudinal data estimation is based on maximum likelihood theory which assumes that the underlying probability model is correctly specified recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based in the present work we have used simulations with a logistic random intercept model to study the impact of misspecifying the random effects distribution on the type i and ii errors of the tests for the mean structure in glmms we found that the misspecification can either increase or decrease the power of the tests depending on the shape of the underlying random effects distribution and it can considerably inflate the type i error rate additionally we have found a theoretical result which states that whenever a subset of fixed effects parameters not included in the random effects structure equals zero the corresponding maximum likelihood estimator will consistently estimate zero this implies that under certain conditions a significant effect could be considered as a reliable result even if the random effects distribution is misspecified

modelling the random effects covariance matrix in longitudinal data a common class of models for longitudinal data are random effects mixed models in these models the random effects covariance matrix is typically assumed constant across subject however in many situations this matrix may differ by measured covariates in this paper we propose an approach to model the random effects covariance matrix by using a special cholesky decomposition of the matrix in particular we will allow the parameters that result from this decomposition to depend on subject specific covariates and also explore ways to parsimoniously model these parameters an advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix in addition the parameters resulting from this decomposition have a sensible interpretation we propose fully bayesian modelling for which a simple gibbs sampler can be implemented to sample from the posterior distribution of the parameters we illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects

new methods for the computer assisted 3 d reconstruction of neurons from confocal image stacks exact geometrical reconstructions of neuronal architecture are indispensable for the investigation of neuronal function neuronal shape is important for the wiring of networks and dendritic architecture strongly affects neuronal integration and firing properties as demonstrated by modeling approaches confocal microscopy allows to scan neurons with submicron resolution however it is still a tedious task to reconstruct complex dendritic trees with fine structures just above voxel resolution we present a framework assisting the reconstruction user time investment is strongly reduced by automatic methods which fit a skeleton and a surface to the data while the user can interact and thus keeps full control to ensure a high quality reconstruction the reconstruction process composes a successive gain of metric parameters first a structural description of the neuron is built including the topology and the exact dendritic lengths and diameters we use generalized cylinders with circular cross sections the user provides a rough initialization by marking the branching points the axes and radii are fitted to the data by minimizing an energy functional which is regularized by a smoothness constraint the investigation of proximity to other structures throughout dendritic trees requires a precise surface reconstruction in order to achieve accuracy of 0 1 microm and below we additionally implemented a segmentation algorithm based on geodesic active contours that allow for arbitrary cross sections and uses locally adapted thresholds in summary this new reconstruction tool saves time and increases quality as compared to other methods which have previously been applied to real neurons

tweedie family of generalized linear models with distribution free random effects for skewed longitudinal data generalized linear mixed models have played an important role in the analysis of longitudinal data however traditional approaches have limited flexibility in accommodating skewness and complex correlation structures in addition the existing estimation approaches generally rely heavily on the specifications of random effects distributions therefore the corresponding inferences are sometimes sensitive to the choice of random effect distributions under certain circumstance in this paper we incorporate serially dependent distribution free random effects into tweedie generalized linear models to accommodate a wide range of skewness and covariance structures for discrete and continuous longitudinal data an optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects our approach unifies population averaged and subject specific inferences our method is illustrated through the analyses of patient controlled analgesia data and framingham cholesterol data

a cautionary note on the robustness of latent class models for estimating diagnostic error without a gold standard modeling diagnostic error without a gold standard has been an active area of biostatistical research in a majority of the approaches model based estimates of sensitivity specificity and prevalence are derived from a latent class model in which the latent variable represents an individual s true unobserved disease status for simplicity initial approaches assumed that the diagnostic test results on the same subject were independent given the true disease status i e the conditional independence assumption more recently various authors have proposed approaches for modeling the dependence structure between test results given true disease status this note discusses a potential problem with these approaches namely we show that when the conditional dependence between tests is misspecified estimators of sensitivity specificity and prevalence can be biased importantly we demonstrate that with small numbers of tests likelihood comparisons and other model diagnostics may not be able to distinguish between models with different dependence structures we present asymptotic results that show the generality of the problem further data analysis and simulations demonstrate the practical implications of model misspecification finally we present some guidelines about the use of these models for practitioners

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

pseudo and conditional score approach to joint analysis of current count and current status data we develop a joint analysis approach for recurrent and nonrecurrent event processes subject to case i interval censorship which are also known in literature as current count and current status data respectively we use a shared frailty to link the recurrent and nonrecurrent event processes while leaving the distribution of the frailty fully unspecified conditional on the frailty the recurrent event is assumed to follow a nonhomogeneous poisson process and the mean function of the recurrent event and the survival function of the nonrecurrent event are assumed to follow some general form of semiparametric transformation models estimation of the models is based on the pseudo likelihood and the conditional score techniques the resulting estimators for the regression parameters and the unspecified baseline functions are shown to be consistent with rates of square and cubic roots of the sample size respectively asymptotic normality with closed form asymptotic variance is derived for the estimator of the regression parameters we apply the proposed method to a fracture osteoporosis survey data to identify risk factors jointly for fracture and osteoporosis in elders while accounting for association between the two events within a subject

on the use of the quasi likelihood method in teratological experiments this paper concerns the impact of litter effects on the inference of dose response relationships in teratological experiments with binary response kupper et al 1986 biometrics 42 85 98 concluded that when intra litter correlations are dose dependent the use of a common intra litter correlation likelihood based on the beta binomial distribution could lead to severe bias in estimation of the parameter beta which characterizes the dose response relationship we show here that the problems of bias and coverage probability for beta could still be substantial when one uses the likelihood with heterogeneous intra litter correlations we then examine through a simulation study the performance of the quasi likelihood method wedderburn 1974 biometrika 61 439 447 and recommend that this method with a common intra litter correlation parameter be used when the number of litters is small or modest

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

nonignorable models for intermittently missing categorical longitudinal responses a class of nonignorable models is presented for handling nonmonotone missingness in categorical longitudinal responses this class of models includes the traditional selection models and shared parameter models this allows us to perform a broader than usual sensitivity analysis in particular instead of considering variations to a chosen nonignorable model we study sensitivity between different missing data frameworks an appealing feature of the developed class is that parameters with a marginal interpretation are obtained while algebraically simple models are considered specifically marginalized mixed effects models heagerty 1999 biometrics 55 688 698 are used for the longitudinal process that model separately the marginal mean and the correlation structure for the correlation structure random effects are introduced and their distribution is modeled either parametrically or non parametrically to avoid potential misspecifications

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

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

marginally specified generalized linear mixed models a robust approach la modelisation des donnees longitudinales est compliquee par la necessite de prendre en compte correctement la correlation entre les observations faites chez le meme individu en partant d une version anterieure non robuste proposee par heagerty 1999 biometrics 55 688 698 notre modele lineaire generalise mixte robuste marginalement robms glmm fournit methode une methode efficace pour traiter de telles donnees ce modele est un des premiers a permettre a la fois des inferences moyennee sur la population et specifique a l individu de plus il adopte la flexibilite et l interpretation des modeles lineaires generalises mixtes pour introduire la dependance mais construit la structure de regression pour l esperance marginale permettant une application valide avec des covariables dependantes du temps exogenes et independantes du temps ces nouveaux estimateurs sont obtenus comme les solutions d une equation de vraisemblance rendue robuste basee sur la distribution la moins favorable de huber et une collection de poids la distribution la moins favorable de huber produit tics estimations qui sont resistantes a certaines deviations des hypotheses de distribution des effets aleatoires des strategies innovantes de ponderation permettent an robs glmm de bien fonctionner quand on est confronte a des observations eloignees a la fois dans la reponse et les covariables nous illustrons la methodologie avec une analyse d une etude longitudinale prospective de l intubation laryngoscopique endotracheale une methode que de nombreux professionnels de sante doivent acquerir le but principal de notre recherche est d obtenir une inference robuste dans les analyses longitudinales