on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

a mixed effects regression model for longitudinal multivariate ordinal data summary a mixed effects item response theory model that allows for three level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies this model allows for the estimation of different item factor loadings item discrimination parameters for the multiple outcomes the covariates in the model do not have to follow the proportional odds assumption and can be at any level assuming either a probit or logistic response function maximum marginal likelihood estimation is proposed utilizing multidimensional gauss hermite quadrature for integration of the random effects an iterative fisher scoring solution which provides standard errors for all model parameters is used an analysis of a longitudinal substance use data set where four items of substance use behavior cigarette use alcohol use marijuana use and getting drunk or high are repeatedly measured over time is used to illustrate application of the proposed model

comparison of statistical methods for analysis of clustered binary observations when correlated observations are obtained in a randomized controlled trial the assumption of independence among observations within cluster likely will not hold because the observations share the same cluster e g clinic physician or subject further the outcome measurements of interest are often binary the objective of this paper is to compare the performance of four statistical methods for analysis of clustered binary observations namely 1 full likelihood method 2 penalized quasi likelihood method 3 generalized estimating equation method 4 fixed effects logistic regression method the first three methods take correlations into account in inferential processes whereas the last method does not type i error rate power bias and standard error are compared across the four statistical methods through computer simulations under varying effect sizes intraclass correlation coefficients number of clusters and number of observations per cluster including large numbers 20 and 100 of observations per cluster the results show that the performance of the full likelihood and the penalized quasi likelihood methods is superior for analysis of clustered binary observations and is not necessarily inferior to that of the fixed effects logistic regression fit even when within cluster correlations are zero

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

modeling conception as an aggregated bernoulli outcome with latent variables via the em algorithm we describe a general method for analyzing aggregated bernoulli outcomes the research is motivated by an epidemiological reproductive study where the outcome was whether pregnancy was detected in a woman s particular menstrual cycle and the bernoulli trials corresponded to days with intercourse during the cycle each cycle is either viable or not i e is or is not susceptible to conception we develop an em algorithm approach to maximizing the observed data pseudo likelihood based on a set of unobservable latent outcomes linked to the specific days with intercourse this method is flexible in that it allows one to model effect of covariates on the susceptibility factor and on the latent outcomes application of the method to fertility studies enables one to investigate covariates with a long term or transient effect on the daily conception probability a complication is that most couples contribute more than one cycle in a prospective study a generalized estimating equation approach adjusts for the dependency among outcomes within individual couples the method can be applied in any setting where dependency among bernoulli trials is induced by a susceptibility factor and the trial outcomes are only observable in the aggregate

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

predicting longitudinal trajectories of health probabilities with random effects multinomial logit regression researchers often encounter longitudinal health data characterized with three or more ordinal or nominal categories random effects multinomial logit models are generally applied to account for potential lack of independence inherent in such clustered data when parameter estimates are used to describe longitudinal processes however random effects both between and within individuals need to be retransformed for correctly predicting outcome probabilities this study attempts to go beyond existing work by developing a retransformation method that derives longitudinal growth trajectories of unbiased health probabilities variances of the predicted probabilities are estimated by using the delta method additionally the covariates regression coefficients on the multinomial logit function not substantively meaningful are transformed to the conditional effects on the predicted probabilities the empirical illustration uses the longitudinal data from the asset and health dynamics among the oldest old ahead our analysis compares three sets of the predicted probabilities of three health states at six time points obtained from respectively the retransformation method the blup and the fixed effects approach the results demonstrate that neglect of retransforming random errors in the random effects multinomial logit model results in severely biased longitudinal trajectories of health probabilities as well as overestimated effects of covariates on the probabilities

the analysis of longitudinal polytomous data generalized estimating equations and connections with weighted least squares in recent years methods have been developed for modelling repeated observations of a categorical response obtained over time on the same individual although situations in which the repeated response is binary or poisson have been studied extensively relatively little attention has been given to polytomous categorical response variable in this paper we extend the estimating equations initially developed for clustered discrete data by liang and zeger 1986 biometrika 73 13 22 and subsequently extended by prentice 1988 biometrics 44 1033 1048 to polytomous response variables under certain assumptions we illustrate that these estimating equations simplify to the weighted least squares wls equations formalized by koch et al 1977 biometrics 33 133 158 this connection provides a formal framework for obtaining iterated weighted least squares model parameter estimates cumulative logit models are developed and applied to a representative longitudinal data set simulation results comparing wls an iterative form of wls and independence estimating equations using a robust estimate of the variance are presented

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

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

a marginal model for analyzing discrete outcomes from longitudinal surveys with outcomes subject to multiple cause nonresponse techniques for analyzing categorical outcomes obtained from longitudinal survey samples with outcomes subject to multiple cause nonresponse are developed within the framework of weighted generalized estimating equations development of these techniques was motivated by disability data obtained from the longitudinal study of aging lsoa a longitudinal survey sample containing missing follow up for many elderly participants we posit a model that combines different multivariate link functions to permit fitting markov models to an outcome with categories represented by a mixture of ordinal success states and multiple failure states extending the missing data approach of robins rotnitzky and zhao to longitudinal survey sample settings we use multiple logit models to model the probability of multiple reasons for missing success or failure outcomes given the assumption that the probability of nonresponse depends only on observed responses and covariates specified in the missing data model weighted est

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

pattern mixture models for multivariate incomplete data consider a random sample on variables x1 xv with some values of xv missing selection models specify the distribution of x1 xv over respondents and nonrespondents to xv and the conditional distribution that xv is missing given x1 xv in contrast pattern mixture models specify the conditional distribution of x 1 xv given that xv is observed or missing respectively and the marginal distribution of the binary indicator for whether or not xv is missing for multivariate data with a general pattern of missing values the literature has tended to adopt the selection modeling approach see for example little and rubin here pattern mixture models are proposed for this more general problem pattern mixture models are chronically underidentified in particular for the case of univariate nonresponse mentioned above there are no data on the distribution of xv given x1 xv 1 in the stratum with xv missing thus the models require restrictions or prior information to identify the paramet

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

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

effect of initial conditions on the speed of reaction diffusion fronts the effect of initial conditions on the speed of propagating fronts in reaction diffusion equations is examined in the framework of the hamilton jacobi theory we study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

analysing ordinal longitudinal survey data generalised estimating equations approach summary longitudinal survey data may comprise ordinal polytomous repeated observations and a set of multidimensional covariates for a large number of individuals one of the main goals of the longitudinal survey is then to describe the marginal expectation of the ordinal polytomous outcome variable as a function of the covariates while accounting for the structural as well as longitudinal correlations the structural correlations come from the polytomous nature of the response variable and the longitudinal correlations from the repetition of the polytomous responses over time in this paper we develop a generalised estimating equations approach based on autocorrelation structure to deal with multivariate polytomous longitudinal survey data the univariate and bivariate analyses being special cases the regression estimators are shown to be consistent for the corresponding regression parameters the methods are illustrated by using the survey of labour and income dynamics data from statistics canada

projected partial likelihood and its application to longitudinal data summary an estimating equation which we call the projected partial score is introduced for longitudinal data analysis the estimating equation is obtained by projecting the partial likelihood score function onto the vector space spanned by a class of conditionally linear estimating equations we demonstrate that removing certain terms from the projection of the full likelihood score does not alter important inferential properties of the estimating equation and doing so is advantageous in handling missing data and time varying covariates within a prequential frame of reference it is shown that the estimating equation is optimal among the largest collection of estimating equations determined by the conditional moments furthermore the method possesses similar properties to generalised estimating equations in particular the correct conditional variance specification is necessary for efficiency but not for asymptotic consistency and distribution theory

the analysis of binomial data by a generalized linear mixed model summary methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution the method estimates the parameters directly on the underlying scale for a balanced one way random effects model the variance estimator simplifies to the usual analysis of variance one the estimation of variances and the prediction of random effects for binomial traits is required by animal breeders the predictors given are analogous to best linear unbiased predictors henderson 1973 but differ from those presented by harville mee 1984

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

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

a random effects ordinal regression model for multilevel analysis a random effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data this model is developed for both the probit and logistic response functions the threshold concept is used in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects a maximum marginal likelihood mml solution is described using gauss hermite quadrature to numerically integrate over the distribution of random effects an analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random effects analysis of clustered ordinal data while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random effects approach for longitudinal ordinal data

estimation of covariance matrix of multivariate longitudinal data using modified choleksky and hypersphere decompositions linear models are typically used to analyze multivariate longitudinal data with these models estimating the covariance matrix is not easy because the covariance matrix should account for complex correlated structures the correlation between responses at each time point the correlation within separate responses over time and the cross correlation between different responses at different times in addition the estimated covariance matrix should satisfy the positive definiteness condition and it may be heteroscedastic however in practice the structure of the covariance matrix is assumed to be homoscedastic and highly parsimonious such as exchangeable or autoregressive with order one these assumptions are too strong and result in inefficient estimates of the effects of covariates several studies have been conducted to solve these restrictions using modified cholesky decomposition mcd and linear covariance models however modeling the correlation between responses at each time point is not easy because there is no natural ordering of the responses in this paper we use mcd and hypersphere decomposition to model the complex correlation structures for multivariate longitudinal data we observe that the estimated covariance matrix using the decompositions is positive definite and can be heteroscedastic and that it is also interpretable the proposed methods are illustrated using data from a nonalcoholic fatty liver disease study

marginal modeling of correlated ordinal data using a multivariate plackett distribution abstract an extension of the bivariate model suggested by dale is proposed for the analysis of dependent ordinal categorical data the so called multivariate dale model is constructed by first generalizing the bivariate plackett distribution to any dimensions because the approach is likelihood based it satisfies properties that are not fulfilled by other popular methods such as the generalized estimating equations approach the proposed method models both the marginal and the association structure in a flexible way the attractiveness of the multivariate dale model is illustrated in three key examples covering areas such as crossover trials longitudinal studies with patients dropping out from the study and discriminant analysis applications the differences and similarities with the generalized estimating approach are highlighted

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

an approximate marginal logistic distribution for the analysis of longitudinal ordinal data subject specific and marginal models have been developed for the analysis of longitudinal ordinal data subject specific models often lack a population average interpretation of the model parameters due to the conditional formulation of random intercepts and slopes marginal models frequently lack an underlying distribution for ordinal data in particular when generalized estimating equations are applied to overcome these issues latent variable models underneath the ordinal outcomes with a multivariate logistic distribution can be applied in this article we extend the work of o brien and dunson 2004 who studied the multivariate t distribution with marginal logistic distributions we use maximum likelihood instead of a bayesian approach and incorporated covariates in the correlation structure in addition to the mean model we compared our method with gee and demonstrated that it performs better than gee with respect to the fixed effect parameter estimation when the latent variables have an approximately elliptical distribution and at least as good as gee for other types of latent variable distributions

local versus global association for bivariate ordered responses summary local and global parameters modelling association are examined for contingency tables with both margins ordered responses local association parameters are crossratios of 2 x 2 subtables of adjacent cell probabilities global association parameters are cross ratios of quadrant probabilities the interpretation and various properties of these measures of association are compared and illustrated

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

tabu search for dna sequencing with false negatives and false positives abstract the paper deals with the problem of dna deoxyribonucleic acid sequencing by hybridization a computational phase of this approach i e a construction of a dna sequence from oligonucleotides is np hard in the strong sense in case of errors thus since the last problem does not admit a polynomial time solution a need arises to construct efficient heuristics solving the problem in the paper such a heuristic algorithm based on tabu search is proposed computational tests have proved its low complexity and high accuracy for both types of errors false negatives and false positives

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

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

a bivariate cumulative probit regression model for ordered categorical data this paper proposes a latent variable regression model for bivariate ordered categorical data and develops the necessary numerical procedure for parameter estimation the proposed model is an extension of the standard bivariate probit model for dichotomous data to ordered categorical data with more than two categories for each margin in addition the proposed model allows for different covariates for the margins which is characteristic of data from typical ophthalmological studies it utilizes the stochastic ordering implicit in the data and the correlation coefficient of the bivariate normal distribution in expressing intra subject dependency illustration of the proposed model uses data from the wisconsin epidemiologic study of diabetic retinopathy for identifying risk factors for diabetic retinopathy among younger onset diabetics the proposed regression model also applies to other clinical or epidemiological studies that involve paired organs

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

analyzing bivariate ordinal data using a global odds ratio abstract a moment method is proposed for regression analysis of bivariate ordered categorical data using the global odds ratio as the measure of association for modeling the margins this method utilizes the stochastic ordering implicit in the data this method allows for covariate effects in modeling the association between responses an application of the proposed model is illustrated using the ophthalmological data from the wisconsin epidemiologic study of diabetic retinopathy for identifying risk factors among younger onset diabetics this model is also extended to a longitudinal data setting with more than two repeated measures

latent variable models for longitudinal data with bivariate ordinal outcomes we use the concept of latent variables to derive the joint distribution of bivariate ordinal outcomes and then extend the model to allow for longitudinal data specifically we relate the observed ordinal outcomes using threshold values to a bivariate latent variable which is then modelled as a linear mixed model random effects terms are used to tie all together repeated observations from the same subject the cross sectional association between the two outcomes is modelled through the correlation coefficient of the bivariate latent variable conditional on random effects assuming conditional independence given random effects the marginal likelihood under the missing data at random assumption is approximated using an adaptive gaussian quadrature for numerical integration the model provides fixed effects parameters that are subject specific but retain the population averaged interpretation when properly scaled this is particularly well suited for the situation in which population comparisons and individual level contrasts are of equal importance data from a psychiatric trial the fluvoxamine an antidepressant drug study are used to illustrate the methodology

testing proportionality in the proportional odds model fitted with gee generalized estimating equations gee methodology as proposed by liang and zeger has received widespread use in the analysis of correlated binary data miller et al and lipsitz et al extended gee to correlated nominal and ordinal categorical data in particular they used gee for fitting mccullagh s proportional odds model in this paper we consider robust that is empirically corrected and model based versions of both a score test and a wald test for assessing the assumption of proportional odds in the proportional odds model fitted with gee the wald test is based on fitting separate multiple logistic regression models for each dichotomization of the response variable whereas the score test requires fitting just the proportional odds model we evaluate the proposed tests in small to moderate samples by simulating data from a series of simple models we illustrate the use of the tests on three data sets from medical studies

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

simultaneous confidence intervals using ordinal effect measures for ordered categorical outcomes when outcomes are ordered categorical a model using an ordinal effect size measure is a good alternative of the cumulative logit model to compare several independent group differences we present a method of constructing simultaneous confidence intervals for the ordinal effect size measures using the studentized range distribution with the score test statistic a simulation study shows that the proposed method performs well in terms of coverage probability and it seems better than the method using a bonferroni correction for wald type statistics and methods that account for the dependencies among pairwise ordinal effect size measures using the multivariate normal distribution or the multivariate t distribution for small samples

marginalized transition models and likelihood inference for longitudinal categorical data summary marginal generalized linear models are now frequently used for the analysis of longitudinal data semiparametric inference for marginal models was introduced by liang and zeger 1986 biometrics73 13 22 this article develops a general parametric class of serial dependence models that permits likelihood based marginal regression analysis of binary response data the methods naturally extend the first order markov models of azzalini 1994 biometrika81 767 775 and prove computationally feasible for long series

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

the simplified partial digest problem approximation and a graph theoretic model the goal of the simplified partial digest problem spdp is motivated by the reconstruction of the linear structure of a dna chain with respect to a given nucleotide pattern based on the multiset of distances between the adjacent patterns interpoint distances and the multiset of distances between each pattern and the two unlabeled endpoints of the dna chain end distances we consider optimization versions of the problem called spdp min and spdp max the aim of spdp min spdp max is to find a dna linear structure with the same multiset of end distances and the minimum maximum number of incorrect correct interpoint distances results are presented on the worst case efficiency of approximation algorithms for these problems we suggest a graph theoretic model for spdp min and spdp max which can be used to reduce the search space for an optimal solution in either of these problems we also present heuristic polynomial time algorithms based on this model in computational experiments with randomly generated and real life input data our best algorithm delivered an optimal solution in 100 of the instances for a number of restriction sites not greater than 50

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

sample size considerations for gee analyses of three level cluster randomized trials cluster randomized trials in health care may involve three instead of two levels for instance in trials where different interventions to improve quality of care are compared in such trials the intervention is implemented in health care units clusters and aims at changing the behavior of health care professionals working in this unit subjects while the effects are measured at the patient level evaluations within the generalized estimating equations approach we derive a sample size formula that accounts for two levels of clustering that of subjects within clusters and that of evaluations within subjects the formula reveals that sample size is inflated relative to a design with completely independent evaluations by a multiplicative term that can be expressed as a product of two variance inflation factors one that quantifies the impact of within subject correlation of evaluations on the variance of subject level means and the other that quantifies the impact of the correlation between subject level means on the variance of the cluster means power levels as predicted by the sample size formula agreed well with the simulated power for more than 10 clusters in total when data were analyzed using bias corrected estimating equations for the correlation parameters in combination with the model based covariance estimator or the sandwich estimator with a finite sample correction

model for the analysis of binary longitudinal pain data subject to informative dropout through remedication abstract we address the problem of accounting for informative dropout in the form of rescue medication when comparing pain relievers with respect to longitudinal binary pain relief outcomes we present a selection model approach for binary longitudinal data that accommodates informative dropout the relationship between dropout or remedication and the binary pain relief response is assumed to be characterized by a random effect that is conditional on this random effect response and dropout are independent unlike previous approaches to this problem which rely on numerical or approximation methods we obtain a closed form expression for the marginal log likelihood of response and dropout by specifying a complementary log log link function for both components and a conjugate log gamma random effect distribution a data analysis supported by simulation results suggest that the model fits reasonably well results are compared to those obtained from conventional but somewhat inappropriate analyses

variance component models with binary response interviewer variability summary interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non normal family the maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire this raises some interesting questions about the use of unbalanced ano va methods with these data two interviewers asking the same question of the same respondent can obtain different responses such interviewer effects create problems in the design and analysis of survey questionnaires collins 1980 gives a review of these problems together with a variety of partial remedies these include pilot studies and careful design to eliminate difficulties with wording of questions and instructions on the questionnaires in spite of these precautions interviewer effects remain questionnaire items are usually categorical and occasionally binary but usually for analysis the questionnaire item is reduced to a binary response it is the variability of the population of interviewers that is of interest and not just the individual interviewers thus this variability is best modelled as a random effect rather than a fixed effect the number of interviews completed by each interviewer varies so that the design is unbalanced thus we have an unbalanced variance component model with a categorical or binary response the intraclass correlation the ratio of the interviewer variance to the sum of all variances in the model is of great interest as a measure of interviewer variability in estimating the variance components the categorical or binary nature of the response is usually ignored and the analysis carried out using analysis of variance this is not maximum likelihood but analysis of variance does have some desirable properties when the error variables are non normal the rule of thumb generally applied is that the analysis of variance is reasonably accurate as long as the proportions in each of the categories of the response are between 0 1 and 0 9 scheffe 1959 p 343 discusses the effects of non normality in a one way balanced model very little theoretical work has been

practical issues in using generalized estimating equations for inference on transitions in longitudinal data what is being estimated generalized estimating equations gees are commonly used to estimate transition models when the markov assumption does not hold but first order transition probabilities are still of interest the transition inference is sensitive to the choice of working correlation in this paper we consider a random process transition model as the true underlying data generating mechanism which characterizes subject heterogeneity and complex dependence structure of the outcome process in a very flexible way we formally define two types of transition probabilities at the population level naive transition probabilities that average across all the transitions and population average transition probabilities that average the subject specific transition probabilities through asymptotic bias calculations and finite sample simulations we demonstrate that the unstructured working correlation provides unbiased estimators of the population average transition probabilities while the independence working correlation provides unbiased estimators of the naive transition probabilities for population average transition estimation we demonstrate that the sandwich estimator fails for unstructured gee and recommend the use of either jackknife or bootstrap variance estimates the proposed method is motivated by and applied to the next generation health study where the interest is in estimating the population average transition probabilities of alcohol use in adolescents

a mixture of transition models for heterogeneous longitudinal ordinal data with applications to longitudinal bacterial vaginosis data markov models used to analyze transition patterns in discrete longitudinal data are based on the limiting assumption that individuals follow the common underlying transition process however when one is interested in diseases with different disease or severity subtypes explicitly modeling subpopulation specific transition patterns may be appropriate we propose a model which captures heterogeneity in the transition process through a finite mixture model formulation and provides a framework for identifying subpopulations at different risks we apply the procedure to longitudinal bacterial vaginosis bv study data and demonstrate that the model fits the data well further we show that under the mixture model formulation we can make the important distinction between how covariates affect transition patterns unique to each of the subpopulations and how they affect which subgroup a participant will belong to practically covariate effects on subpopulation specific transition behavior and those on subpopulation membership can be interpreted as effects on short term and long term transition behavior we further investigate models with higher order subpopulation specific transition dependence

analysis of repeated categorical data using generalized estimating equations moment methods for analysing repeated binary responses have been proposed by liang and zeger and extended by prentice and zhao and prentice in these estimating equations models are proposed for the correlation between the repeated binary responses we extend liang and zeger s method to models for the correlation between repeated nominal or ordinal categorical responses in particular when the repeated responses are binary our methods reduce to liang and zeger s method our method is illustrated with two datasets one dataset contains repeated observations of self assessment of arthritis an ordered variable with three categories collected during a randomized comparative study of alternative treatments of patients with rheumatoid arthritis the second dataset is a longitudinal study of the health effects of air pollution in which the repeated ordered multinomial response is the wheezing status no wheeze wheeze with cold wheeze apart from cold of a child at ages 9 10 11 and 12 years

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

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

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

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

generalization of the mantel haenszel estimating function for sparse clustered binary data we extend the mantel haenszel estimating function to estimate both the intra cluster pairwise correlation and the main effects for sparse clustered binary data we propose both a composite likelihood approach and an estimating function approach for the analysis of such data the proposed estimators are consistent and asymptotically normally distributed simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency however the estimating equation approach is computationally simpler analysis of the georgia high blood pressure survey is used for illustration

dna sequencing by hybridization via genetic search an innovative approach to dna sequencing by hybridization utilizes isothermic oligonucleotide libraries in this paper we demonstrate the utility of a genetic algorithm for the combinatorial portion of this new approach by incorporating characteristics of dna sequencing by hybridization in addition to isothermic oligonucleotide libraries specialized crossover and mutation operators were developed for this purpose after initial experiments for parameter adjustment the performance of the genetic algorithm approach was evaluated with respect to previous methods in the literature the results indicate that the proposed new approach is superior to previous approaches the proposed new crossover operator that inherits some features of the structured weighted combinations might also be of value for some other combinatorial problems including the traveling salesman problem

asymptotic linearization of the fisher equation for a class of initial conditions we present a novel method of linearizing the fisher equation asymptotically in time i e we use a nonlinear transformation to convert the initial value problem for the fisher equation into an initial value problem for the diffusion equation for a class of initial conditions the analytic result we obtain is in excellent agreement with numerical simulations our method easily generalizes to other reaction diffusion equations also

regression models for nonstationary categorical time series asymptotic estimation theory for the analysis of nonstationary categorical time series a parsimonious and flexible class of models is proposed these models are generalizations of regression models for stochastically independent categorical observations consistency asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements some models for binary time series are discussed in detail to demonstrate asymptotic properties a theorem is given addressing maximum likelihood estimation for general stochastic processes then it is shown that the assumptions of this theorem are consequences of the requirements for categorical time series for this proof some lemmas are used which may be of interest in similar cases

tree structured logistic model for over dispersed binomial data with application to modeling developmental effects this article proposes tree structured logistic regression modeling for over dispersed binomial data recursive partitioning is performed using a combination of statistical tests and residual analysis the splitting criterion in cross validation is based on the deviance function a nested grid algorithm to estimate the bootstrap parameters is developed the regression tree procedure provides a new approach for exploring in detail the relationship between the binomial response and explanatory variables the proposed procedure is used to model the relationship between the incidence of malformation and dose and fetal weight using data from a developmental experiment conducted at the national center for toxicological research a conditional gaussian chain model is used to account for the effect of fetal weight by dose

complexity of dna sequencing by hybridization in the paper the question of the complexity of the combinatorial part of the dna sequencing by hybridization is analyzed subproblems of the general problem depending on the type of error positive negative are distinguished since decision versions of the subproblems assuming only one type of error are trivial complexities of the search counterparts are studied both search subproblems are proved to be strongly np hard as well as their uniquely promised versions

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

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

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

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

bivariate categorical data analysis using normal linear conditional multinomial probability model bivariate multinomial data such as the left and right eyes retinopathy status data are analyzed either by using a joint bivariate probability model or by exploiting certain odds ratio based association models however the joint bivariate probability model yields marginal probabilities which are complicated functions of marginal and association parameters for both variables and the odds ratio based association model treats the odds ratios involved in the joint probabilities as working parameters which are consequently estimated through certain arbitrary working regression models also this later odds ratio based model does not provide any easy interpretations of the correlations between two categorical variables on the basis of pre specified marginal probabilities in this paper we develop a bivariate normal type linear conditional multinomial probability model to understand the correlations between two categorical variables the parameters involved in the model are consistently estimated using the optimal likelihood and generalized quasi likelihood approaches the proposed model and the inferences are illustrated through an intensive simulation study as well as an analysis of the well known wisconsin diabetic retinopathy status data copyright 2014 john wiley sons ltd

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

a note on gauss hermite quadrature summary for gauss hermite quadrature we consider a systematic method for transforming the variable of integration so that the integrand is sampled in an appropriate region the effectiveness of the quadrature then depends on the ratio of the integrand to some gaussian density being a smooth function well approximated by a low order polynomial it is pointed out that in this approach order one gauss hermite quadrature becomes the laplace approximation thus the quadrature as implemented here can be thought of as a higher order laplace approximation

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

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

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

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

trend in correlated proportions a random effects probit model is developed for the case in which the same units are sampled repeatedly at each level of an independent variable because the observed proportions may be correlated under these conditions estimating their trend with respect to the independent variable is no longer a standard problem for probit logit or loglinear analysis using a qualitative analogue of a random regressions model we employ instead marginal maximum likelihood to estimate the average latent trend line likelihood ratio tests of the hypothesis of no trend in the average line and the hypothesis of no differences in average trend lines between experimental treatments are proposed we illustrate the model both with simulated data and with observed data from a clinical experiment in which psychiatric patients on two drug therapies are rated on five occasions for the presence or absence of symptoms

perturbative linearization of reaction diffusion equations we develop perturbative expansions to obtain solutions for the initial value problems of two important reaction diffusion systems namely the fisher equation and the time dependent ginzburg landau equation the starting point of our expansion is the corresponding singular perturbation solution this approach transforms the solution of nonlinear reaction diffusion equations into the solution of a hierarchy of linear equations our numerical results demonstrate that this hierarchy rapidly converges to the exact solution

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

random effects probit and logistic regression models for three level data in analysis of binary data from clustered and longitudinal studies random effect models have been recently developed to accommodate two level problems such as subjects nested within clusters or repeated classifications within subjects unfortunately these models cannot be applied to three level problems that occur frequently in practice for example multicenter longitudinal clinical trials involve repeated assessments within individuals and individuals are nested within study centers this combination of clustered and longitudinal data represents the classic three level problem in biometry similarly in prevention studies various educational programs designed to minimize risk taking behavior e g smoking prevention and cessation may be compared where randomization to various design conditions is at the level of the school and the intervention is performed at the level of the classroom previous statistical approaches to the three level problem for binary response data have either ignored one level of nesting treated it as a fixed effect or used first and second order taylor series expansions of the logarithm of the conditional likelihood to linearize these models and estimate model parameters using more conventional procedures for measurement data recent studies indicate that these approximate solutions exhibit considerable bias and provide little advantage over use of traditional logistic regression analysis ignoring the hierarchical structure in this paper we generalize earlier results for two level random effects probit and logistic regression models to the three level case parameter estimation is based on full information maximum marginal likelihood estimation mmle using numerical quadrature to approximate the multiple random effects the model is illustrated using data from 135 classrooms from 28 schools on the effects of two smoking cessation interventions

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

gee for multinomial responses using a local odds ratios parameterization in this article we propose a generalized estimating equations gee approach for correlated ordinal or nominal multinomial responses using a local odds ratios parameterization our motivation lies upon observing that i modeling the dependence between correlated multinomial responses via the local odds ratios is meaningful both for ordinal and nominal response scales and ii ordinary gee methods might not ensure the joint existence of the estimates of the marginal regression parameters and of the dependence structure to avoid ii we treat the so called working association vector as a nuisance parameter vector that defines the local odds ratios structure at the marginalized contingency tables after tabulating the responses without a covariate adjustment at each time pair to estimate and simultaneously approximate adequately possible underlying dependence structures we employ the family of association models proposed by goodman in simulations the parameter estimators with the proposed gee method for a marginal cumulative probit model appear to be less biased and more efficient than those with the independence working model especially for studies having time varying covariates and strong correlation

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

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