marginalized transition models for longitudinal binary data with ignorable and non ignorable drop out we extend the marginalized transition model of heagerty to accommodate non ignorable monotone drop out using a selection model weakly identified drop out parameters are held constant and their effects evaluated through sensitivity analysis for data missing at random mar efficiency of inverse probability of censoring weighted generalized estimating equations ipcw gee is as low as 40 per cent compared to a likelihood based marginalized transition model mtm with comparable modelling burden mtm and ipcw gee regression parameters both display misspecification bias for mar and non ignorable missing data and both reduce bias noticeably by improving model fit

the effect of two stage sampling on ordinary least squares methods abstract we look at the effect of intracluster correlation on standard procedures in linear regression the ordinary least squares estimator of the coefficient vector performs well in most cases but the usual estimator of cov and procedures based on this such as confidence intervals and hypothesis tests can be seriously misleading the size of the effect however tends to be smaller than the corresponding effect on the variance of an estimated mean in two stage sampling provided that the cluster sample sizes are approximately equal

performance of generalized estimating equations in practical situations moment methods for analyzing repeated binary responses have been proposed by liang and zeger 1986 biometrika 73 13 22 and extended by prentice 1988 biometrics 44 1033 1048 in their generalized estimating equations gee both liang and zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses in this paper we discuss one step estimators i e estimators obtained from one step of the generalized estimating equations and compare their performance to that of the fully iterated estimators in small samples in simulations we find the performance of the one step estimator to be qualitatively similar to that of the fully iterated estimator when the sample size is small and the association between binary responses is high we recommend using the one step estimator to circumvent convergence problems associated with the fully iterated gee algorithm furthermore we find the gee methods to be more efficient than ordinary logistic regression with variance correction for estimating the effect of a time varying covariate

on the analysis of very small samples of gaussian repeated measurements an alternative approach the analysis of very small samples of gaussian repeated measurements can be challenging first due to a very small number of independent subjects contributing outcomes over time statistical power can be quite small second nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size however available statistical strategies that ensure valid statistical inference may lack power whereas more powerful methods may have the potential for inflated test sizes therefore we explore an alternative approach to the analysis of very small samples of gaussian repeated measurements with the goal of maintaining valid inference while also improving statistical power relative to other valid methods this approach uses generalized estimating equations with a bias corrected empirical covariance matrix that accounts for all small sample aspects of nuisance correlation parameter estimation in order to maintain valid inference furthermore the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power in our study we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation this method can improve power relative to existing methods that yield valid inference copyright 2017 john wiley sons ltd

working correlation structure misspecification estimation and covariate design implications for generalised estimating equations performance the method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations we investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods the asymptotic relative efficiency depends on three features of the analysis namely i the discrepancy between the working correlation structure and the unobservable true correlation structure ii the method by which the correlation parameters are estimated and iii the design by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes analytical and numerical studies of realistic data analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a gaussian estimation pseudolikelihood procedure is used with an ar 1 structure

improving power in small sample longitudinal studies when using generalized estimating equations generalized estimating equations gee are often used for the marginal analysis of longitudinal data although much work has been performed to improve the validity of gee for the analysis of data arising from small sample studies little attention has been given to power in such settings therefore we propose a valid gee approach to improve power in small sample longitudinal study settings in which the temporal spacing of outcomes is the same for each subject specifically we use a modified empirical sandwich covariance matrix estimator within correlation structure selection criteria and test statistics use of this estimator can improve the accuracy of selection criteria and increase the degrees of freedom to be used for inference the resulting impacts on power are demonstrated via a simulation study and application example copyright 2016 john wiley sons ltd

a caveat concerning independence estimating equations with multivariate binary data clustered binary data occur commonly in both the biomedical and health sciences in this paper we consider logistic regression models for multivariate binary responses where the association between the responses is largely regarded as a nuisance characteristic of the data in particular we consider the estimator based on independence estimating equations iee which assumes that the responses are independent this estimator has been shown to be nearly efficient when compared with maximum likelihood ml and generalized estimating equations gee in a variety of settings the purpose of this paper is to highlight a circumstance where assuming independence can lead to quite substantial losses of efficiency in particular when the covariate design includes within cluster covariates assuming independence can lead to a considerable loss of efficiency in estimating the regression parameters associated with those covariates

application of generalized estimating equations to a study of in vitro radiation sensitivity we describe an application of the generalized estimating equation gee method liang and zeger 1986 biometrika 73 13 22 for regression analysis of correlated poisson data from a split plot design with a small number of experimental units as an alternative to the use of an arbitrarily chosen working correlation matrix we demonstrate the use of gee with a reasonable model for the true covariance structure among repeated observations within individuals we show that under such a split plot design with large clusters the asymptotic relative efficiency of gee with simple independence or exchangeable working correlation matrices is rather low we conclude by summarizing issues and needs for further work concerning efficiency of the gee parameter estimates in practice

marginal mark regression analysis of recurrent marked point process data summary longitudinal studies typically collect information on the timing of key clinical events and on specific characteristics that describe those events random variables that measure qualitative or quantitative aspects associated with the occurrence of an event are known as marks recurrent marked point process data consist of possibly recurrent events with the mark and possibly exposure measured if and only if an event occurs analysis choices depend on which aspect of the data is of primary scientific interest first factors that influence the occurrence or timing of the event may be characterized using recurrent event analysis methods second if there is more than one event per subject then the association between exposure and the mark may be quantified using repeated measures regression methods we detail assumptions required of any time dependent exposure process and the event time process to ensure that linear or generalized linear mixed models and generalized estimating equations provide valid estimates we provide theoretical and empirical evidence that if these conditions are not satisfied then an independence estimating equation should be used for consistent estimation of association we conclude with the recommendation that analysts carefully explore both the exposure and event time processes prior to implementing a repeated measures analysis of recurrent marked point process data

longitudinal studies of binary response data following case control and stratified case control sampling design and analysis we discuss design and analysis of longitudinal studies after case control sampling wherein interest is in the relationship between a longitudinal binary response that is related to the sampling case control variable and a set of covariates we propose a semiparametric modeling framework based on a marginal longitudinal binary response model and an ancillary model for subjects case control status in this approach the analyst must posit the population prevalence of being a case which is then used to compute an offset term in the ancillary model parameter estimates from this model are used to compute offsets for the longitudinal response model examining the impact of population prevalence and ancillary model misspecification we show that time invariant covariate parameter estimates other than the intercept are reasonably robust but intercept and time varying covariate parameter estimates can be sensitive to such misspecification we study design and analysis issues impacting study efficiency namely choice of sampling variable and the strength of its relationship to the response sample stratification choice of working covariance weighting and degree of flexibility of the ancillary model the research is motivated by a longitudinal study following case control sampling of the time course of attention deficit hyperactivity disorder adhd symptoms

estimating logistic regression parameters for bivariate binary data summary consider bivariate binary data with possibly different covariates for each marginal binary observation suppose that the correlation between paired observations is a nuisance and the interest lies in estimating logistic regression parameters associated with the covariates we consider the estimator obtained by using the independence estimating equation with corrected variance this estimator can be very efficient and robust compared with maximum likelihood or the estimator of liang and zeger some comments are made concerning higher dimensional multivariate data

analysis of clustered data a combined estimating equations approach summary examples of clustered data include data from longitudinal studies and data sampled within groups this paper proposes a regression analysis method for clustered data that optimally weights and combines contrasts of the data through a combination of estimating equations examples of combining between cluster within cluster and longitudinal data contrasts are presented the method results in increased estimation efficiency relative to generalised estimating equations with standard working correlation structures the proposed method also simplifies modelling decisions regarding the true correlation structure of the data and avoids correlation parameter estimation

dissimilarity based ensembles for multiple instance learning in multiple instance learning objects are sets bags of feature vectors instances rather than individual feature vectors in this paper we address the problem of how these bags can best be represented two standard approaches are to use dis similarities between bags and prototype bags or between bags and prototype instances the first approach results in a relatively low dimensional representation determined by the number of training bags whereas the second approach results in a relatively high dimensional representation determined by the total number of instances in the training set however an advantage of the latter representation is that the informativeness of the prototype instances can be inferred in this paper a third intermediate approach is proposed which links the two approaches and combines their strengths our classifier is inspired by a random subspace ensemble and considers subspaces of the dissimilarity space defined by subsets of instances as prototypes we provide insight into the structure of some popular multiple instance problems and show state of the art performances on these data sets

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

violations of the independent increment assumption when using generalized estimating equation in longitudinal group sequential trials in phase 3 clinical trials ethical and financial concerns motivate sequential analyses in which the data are analyzed prior to completion of the entire planned study existing group sequential software accounts for the effects of these interim analyses on the sampling density by assuming that the contribution of subsequent increments is independent of the contribution from previous data this independent increment assumption is satisfied in many common circumstances including when using the efficient estimator however certain circumstances may dictate using an inefficient estimator and the independent increment assumption may then be violated consequences of assuming independent increments in a setting where the assumption does not hold have not been previously explored one important setting in which independent increments may not hold is the setting of longitudinal clinical trials this paper considers dependent increments that arise because of heteroscedastic and correlated data in the context of longitudinal clinical trials that use a generalized estimating equation gee approach both heteroscedasticity over time and correlation of observations within subjects may lead to departures from the independent increment assumption when using gee we characterize situations leading to greater departures in this paper despite violations of the independent increment assumption simulation results suggest that operating characteristics of sequential designs are largely maintained for typically observed patterns of accrual correlation and heteroscedasticity even when using analyses that use standard software that depends on an independent increment structure more extreme scenarios may require greater care to avoid departures from the nominal type i error rate and power copyright 2014 john wiley sons ltd

familial associations of lipid profiles a generalized estimating equations approach elevated plasma levels of apolipoproteins a1 apoa1 and b apob are important protective factors and risk factors respectively for atherosclerosis and coronary heart disease it is well known that both apoa1 and apob reveal strong familial aggregation our goal was to investigate whether exogenous variables influence these associations we used marginal regression models for the mean and association structure generalized estimating equations 2 gee2 to analyse data from 1435 family members within 469 families of different sizes included in the donolo tel aviv three generation offspring study the usual robust variance matrix was approximated by extensions of jack knife estimators of variance to gee2 models estimation of standard errors in models with quite complex correlation structures was possible using this approach all analyses were easily carried out using a menu driven stand alone software tool for marginal regression modelling we demonstrate that a variety of hypotheses can be tested using wald statistics by modelling regression matrices for the association structure we show that correlation for apob between parent offspring pairs increased with decreasing age difference and that pairs with individuals of the same gender had more similar apoa1 levels than individuals of different gender associations between different relative pairs did not all agree with those expected from differences in kinship coefficients the analysis using gee2 models revealed structures that would not have been detected by other models and should therefore be used in addition to traditional approaches of analysing family data gee2 should be considered a standard method for the investigation of familial aggregation

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

estimation efficiency and tests of covariate effects with clustered binary data several approaches have been proposed to analyze clustered binary data which arise in fields such as teratology and ophthalmology these methods include mixed effects and quasi likelihood approaches as well as models that use cluster responses as covariates the three approaches measure different effects of covariates on binary responses but simple approximations relate the magnitudes of their parameters in this article we present approximations to relate the standard errors of model parameters and wald tests for covariate effects obtained from the different approaches these approximations show that wald tests involving cluster level covariates will be approximately equivalent using the different approaches however approaches that model intracluster correlation such as the mixed effects model provide more powerful tests of within cluster covariates than those that do not model the correlation simulations and example data illustrate these findings

optimal combination of estimating equations in the analysis of multilevel nested correlated data multilevel nested correlated data often arise in biomedical research examples include teeth nested within quadrants in a mouth or students nested within classrooms in schools in some settings cluster sizes may be large relative to the number of independent clusters and the degree of correlation may vary across clusters when cluster sizes are large fitting marginal regression models using generalized estimating equations with flexible correlation structures that reflect the nested structure may fail to converge and result in unstable covariance estimates also the use of patterned nested working correlation structures may not be efficient when correlation varies across clusters this paper describes a flexible marginal regression modeling approach based on an optimal combination of estimating equations particular within cluster and between cluster data contrasts are used without specification of the working covariance structure and without estimation of covariance parameters the method involves estimation of the covariance matrix only for the vector of component estimating equations which is typically of small dimension rather than the covariance matrix of the observations within a cluster which may be of large dimension in settings where the number of clusters is large relative to the cluster size the method is stable and is highly efficient while maintaining appropriate coverage levels performance of the method is investigated with simulation studies and an application to a periodontal study

combined convex technique on delay dependent stability for delayed neural networks in this brief by employing an improved lyapunov krasovskii functional lkf and combining the reciprocal convex technique with the convex one a new sufficient condition is derived to guarantee a class of delayed neural networks dnns to be globally asymptotically stable since some previously ignored terms can be considered during the estimation of the derivative of lkf a less conservative stability criterion is derived in the forms of linear matrix inequalities whose solvability heavily depends on the information of addressed dnns finally we demonstrate by two numerical examples that our results reduce the conservatism more efficiently than some currently used methods

analysis of pregnancy and other factors on detection of human papilloma virus hpv infection using weighted estimating equations for follow up data generalized estimating equations have been well established to draw inference for the marginal mean from follow up data many studies suffer from missing data that may result in biased parameter estimates if the data are not missing completely at random robins and co workers proposed using weighted estimating equations wee in estimating the mean structure if drop out occurs missing at random we illustrate the differences between the wee and the commonly applied available case analysis in a simulation study we apply the wee and reanalyse data of a longitudinal study of pregnancy and human papilloma virus hpv infection we estimate the response probabilities and demonstrate that the data are not missing completely at random upon use of the wee we are able to show that pregnant women have an increased odds for an hpv infection compared with non pregnant women after delivery p 0 027 we conclude that the wee are useful for dealing with monotone missing data due to drop outs in follow up data

sample size calculations for randomised trials including both independent and paired data randomised trials including a mixture of independent and paired data arise in many areas of health research yet methods for determining the sample size for such trials are lacking we derive design effects algebraically assuming clustering because of paired data will be taken into account in the analysis using generalised estimating equations with either an independence or exchangeable working correlation structure continuous and binary outcomes are considered along with three different methods of randomisation cluster randomisation individual randomisation and randomisation to opposite treatment groups the design effect is shown to depend on the intracluster correlation coefficient proportion of observations belonging to a pair working correlation structure type of outcome and method of randomisation the derived design effects are validated through simulation and example calculations are presented to illustrate their use in sample size planning these design effects will enable appropriate sample size calculations to be performed for future randomised trials including both independent and paired data copyright 2017 john wiley sons ltd

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

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