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

inference for mixtures of finite polya tree models mixtures of polya tree models provide a flexible alternative when a parametric model may only hold approximately i provide computational strategies for obtaining full semiparametric inference for mixtures of finite polya tree models given a standard parameterization including models that would be troublesome to fit using dirichlet process mixtures recommendations are put forth on choosing the level of a finite polya tree and model comparison is discussed several examples demonstrate the utility of finite polya tree modeling including data fit to generalized linear mixed models and several survival models

model comparison of generalized linear mixed models generalized linear mixed models glmms have been widely appreciated in biological and medical research maximum likelihood estimation has received a great deal of attention comparatively not much has been done on model comparison or hypotheses testing in this article we propose a path sampling procedure to compute the observed data log likelihood function so that the bayesian information criterion bic can be applied to model comparison or hypothesis testing advantages of the proposed path sampling procedure are discussed two medical data sets are analysed for providing illustrative examples of the proposed methodology

identifiability improper priors and gibbs sampling for generalized linear models markov chain monte carlo algorithms are widely used in the fitting of generalized linear models glms such model fitting is somewhat of an art form requiring suitable trickery and tuning to obtain results in which one can have confidence a wide range of practical issues arise the focus here is on parameter identifiability and posterior propriety in particular we clarify that nonidentifiability arises for usual glms and discuss its implications for simulation based model fitting because often some part of the prior specification is vague we consider whether the resulting posterior is proper providing rather general and easily checked results for glms we also show that if a gibbs sampler is run with an improper posterior then it may be possible to use the output to obtain meaningful inference for certain model unknowns

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

estimation in generalized mixed models regression models containing fixed and random effects may have a response variable which is not normally distributed the generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures applications in modelling discrete response variables and in survival analysis are discussed

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

mixed effects nonlinear regression for unbalanced repeated measures repeated measures data such as clinical pharmacokinetic data growth data and dose response data are often inherently nonlinear with respect to a given response function and are frequently incomplete and or unbalanced nonlinear random effects models together with a variety of estimation procedures have been proposed for the analysis of such data this paper is concerned with a straightforward procedure for estimating and comparing the parameters of a generalized mixed effects nonlinear regression model the asymptotic properties of the proposed estimators are given and large sample tests of hypothesis provided the results are applied to in vitro data on the water transport kinetics of hemodialyzers used in the treatment of patients with chronic renal failure

a note on the existence of the posterior distribution for a class of mixed models for binomial responses summary necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses the implications of our results are illustrated through an example

non linear models for the analysis of longitudinal data given the importance of longitudinal studies in biomedical research it is not surprising that considerable attention has been given to linear and generalized linear models for the analysis of longitudinal data a great deal of attention has also been given to non linear models for repeated measurements particularly in the field of pharmacokinetics in this article a brief overview of non linear models for the analysis of repeated measures is given particular emphasis is placed on mixed effects non linear models and on various estimation procedures proposed for such models several of these estimation procedures are compared via a simulation study in addition simulation is used to investigate the effects of model misspecification particularly with respect to one s choice of random effects a relatively straightforward measure useful in selecting an appropriate set of random effects is investigated and found to perform reasonably well

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

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

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

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

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

a simple non linear model in incidence prediction a simple model is proposed for incidence prediction the model is non linear in parameters but linear in time following models in environmental cancer epidemiology assuming a poisson distribution for the age and period specific numbers of incident cases approximate confidence and prediction intervals are calculated the major advantage of this model over current models is that age specific predictions can be made with greater accuracy the model also preserves in the period of prediction the age pattern of incidence rates existing in the data it may be fitted with any package which includes an iteratively reweighted least squares algorithm for example glim cancer incidence predictions for the stockholm gotland oncological region in sweden are presented as an example

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

modelling longitudinal and spatially correlated data methods applications and future directions generalized linear models linear models vector spaces and residual likelihood an assessment of approximate maximum likelihood estimators in generalized linear models scaled link functions for heterogeneous ordinal response data longitudinal data analysis software design for longitudinal data analysis asymptotic properties of nonlinear mized effects models structured antedependence models for longitudinal data effect of confounding and other misspecification in models for longitudinal data the linear mixed model a critical investigation in the context of longitudinal data modelling the order of disability events in activities of daily living using discrete longitudinal data estimation of subject means in fixed and mixed models with application to longitudinal data modeling toxicological multivariate mortality data a bayesian perspective comparison of methods for general nonlinear mixed effects models repeated measures analysis using mixed models some simulation results spatial data analysis object identification using markov random field segmentation models at multiple resolutions of a rectangular lattice comparison of some sampling designs for spatially clustered populations using geostatistical techniques to map the distribution of tree species from ground inventory data global analysis of ozone data based on spherical splines bounded influence estimation in a spatial linear mixed model spatial correlation models as applied to evolutionary biology rainfall modelling using a latent guassian variable estimation of individual exposure following a chemical spill in superior wisconsin flexible response surface methods via spatial regression and eblups robust semivariogram estimation in the presence of influential spatial data values modelling spatio temporal processes elephant seal movements dive types and their sequences models for continuous stationary space time processes a comparison of two spatio temporal semivariograms with use in agriculture structuring correlation within hierarchical spatio temporal models for disease rates modelling messy data generalized linear mixed measurement error models calculating the appropriate information matrix for log linear models when data are missing at random nonparametric regression in the presence of correlated errors exploratory modelling of multiple non stationary time series latent process structure and decompositions modelling correlations between diagnostic tests in efficacy studies with an imperfect reference test special topics and future directions combining standard block analyses with spatial analyses under a random effects model spatial and longitudinal data analysis two histories with a common future

an em algorithm for nonlinear random effects models the pharmaceutical industry is currently interested in the population approach and population models also known as mixed effects models and random effects models depending on the precise form population models are useful in that they can account for both withinand between individual sources of variability and serial correlation within individual observations when analyzing unbalanced repeated measures data the modelling of population pharmacodynamic or pharmacokinetic profiles typically involves nonlinear random effects models each individual s observations are modelled by identical up to unknown parameter values nonlinear regression models with the distribution of the observations or a transformation of the observations about expected responses taken to be normal with the degree of variability described by a variance model between individual variability is modelled by a population distribution for the individual regression parameter values random effects in a parametric analysis the population distribution is taken to be normal the parameters of which along with the parameters of the variance model are known as the population parameters maximum likelihood estimation of the population parameters for nonlinear random effects models was pioneered by beal and sheiner 1979 and since then a number of algorithms have appeared for approximate maximum likelihood including steimer et al 1984 lindstrom and bates 1990 beal and sheiner 1992 and mentre and gomeni 1995 all of these algorithms are approximate in some way for a summary see beal and sheiner 1992 wolfinger 1993 pinheiro and bates 1994 and davidian and giltinan 1995 in this paper an em algorithm for exact maximum likelihood estimation is introduced an em algorithm obtaining maximum likelihood estimates for linear random effects models was introduced by dempster laird and rubin 1977 laird and ware 1982 lindstrom and bates 1988 jennrich and schluchter 1986 and liu and rubin 1994 all describe hybrid em algorithms for the linear random effects model a true em algorithm for the linear model is described by jamshidian and jennrich 1993 mentre and gomeni 1995 describe an approximate em algorithm for nonlinear random effects models and from the algorithm given in this paper it can be seen clearly how their approximations arise the present algorithm uses monte carlo methods to perform the e step a strategy previously adopted in an altogether different model by guo and thompson 1994 guo and thompson require a gibbs sampler that is a markov chain monte carlo method for their e step but the present algorithm uses independent samples in section 2 of this paper the nonlinear random effects model is described section 3 gives the em algorithm without random effect covariates while section 4 gives the modified algorithm in the

the effect of improper priors on gibbs sampling in hierarchical linear mixed models abstract often either from a lack of prior information or simply for convenience variance components are modeled with improper priors in hierarchical linear mixed models although the posterior distributions for these models are rarely available in closed form the usual conjugate structure of the prior specification allows for painless calculation of the gibbs conditionals thus the gibbs sampler may be used to explore the posterior distribution without ever having established propriety of the posterior an example is given showing that the output from a gibbs chain corresponding to an improper posterior may appear perfectly reasonable thus one cannot expect the gibbs output to provide a red flag informing the user that the posterior is improper the user must demonstrate propriety before a markov chain monte carlo technique is used a theorem is given that classifies improper priors according to the propriety of the resulting posteriors applications concerning bayesian analysis of animal breeding

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

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

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

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

paperfolding morphisms planefilling curves and fractal tiles an interesting class of automatic sequences emerges from iterated paperfolding the sequences generate curves in the plane with an almost periodic structure we generalize the results obtained by davis and knuth on the self avoiding and planefilling properties of these curves giving simple geometric criteria for a complete classification finally we show how the automatic structure of the sequences leads to self similarity of the curves which turns the planefilling curves in a scaling limit into fractal tiles for some of these tiles we give a particularly simple formula for the hausdorff dimension of their boundary

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

morphic words beatty sequences and integer images of the fibonacci language abstract morphic words are letter to letter images of fixed points x of morphisms on finite alphabets there are situations where these letter to letter maps do not occur naturally but have to be replaced by a morphism we call this a decoration of x theoretically decorations of morphic words are again morphic words but in several problems the idea of decorating the fixed point of a morphism is useful we present two of such problems the first considers the so called aa sequences where is a quadratic irrational a is the beatty sequence defined by a n n and aa is the sequence a a n the second example considers homomorphic embeddings of the fibonacci language into the integers which turns out to lead to generalized beatty sequences with terms of the form v n p n q n r where p q and r are integers

maximum likelihood estimation of multilevel structural equation models with random slopes for latent covariates a maximum likelihood estimation routine for two level structural equation models with random slopes for latent covariates is presented because the likelihood function does not typically have a closed form solution numerical integration over the random effects is required the routine relies upon a method proposed by du toit and cudeck psychometrika 74 1 65 82 2009 for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically reducing the computational burden of high dimensional numerical integration the method is demonstrated and assessed using a small scale simulation study and an empirical example

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

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

conditional second order generalized estimating equations for generalized linear and nonlinear mixed effects models generalized linear and nonlinear mixed effects models are used extensively in health care research including applications in pharmacokinetics clinical trials and epidemiology because the underlying model may be nonlinear in the random effects there will generally be no closed form expression for the marginal likelihood or indeed for the marginal moments consequently estimation is often carried out either using numerical integration techniques or by approximating the marginal likelihood and or marginal moments using first order expansion methods an advantage of the first order methods is that they do not necessarily require specification of a conditional like lihood to estimate the regression parameters of interest however in many cases they may not take full advantage of the fact that the conditional variance depends on both fixed and random effects in this article we propose using conditional second order generalized estimating equations cgee2 to estimate both fixed and random effects param

latent curve analysis as a method for representing development latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth maximum likelihood parameter estimates and associated asymptotic tests follow directly these procedures may be viewed as an alternative to standard repeated measures anova and to first order auto regressive methods as formulated the model encompasses cohort sequential designs and allow for period or practice effects a numerical illustration using data initially collected by nesselroade and baltes is presented

an appraisal of methods for the analysis of longitudinal categorical data with mar drop outs a number of methods for analysing longitudinal ordinal categorical data with missing at random drop outs are considered two are maximum likelihood methods maxlik which employ marginal global odds ratios to model associations the remainder use weighted or unweighted generalized estimating equations gee two of the gee use cholesky decomposed standardized residuals to model the association structure while another three extend methods developed for longitudinal binary data in which the association structures are modelled using either gaussian estimation multivariate normal estimating equations or conditional residuals simulated data sets were used to discover differences among the methods in terms of biases variances and convergence rates when the association structure is misspecified the methods were also applied to a real medical data set two of the gee methods referred to as cond and ml norm in this paper and by their originators were found to have relatively good convergence rates and mean squared errors for all sample sizes 80 120 300 considered and one more referred to as mgee in this paper and by its originators worked fairly well for all but the smallest sample size 80

mixed effects logistic regression models for longitudinal binary response data with informative drop out a shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop out the model consists of observed longitudinal and missing response components that share random effects parameters to our knowledge this is the first presentation of such a model for longitudinal binary response data comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations the naive mixed effects logit model that does not account for informative drop out is also compared the simulation based differences among the models with respect to coverage of confidence intervals bias and mean squared error mse depend on at least two factors whether an effect is a between or within subject effect and the amount of between subject variation as exhibited by variance components of the random effects distributions when the shared parameter model holds the approximate conditional model provides confidence intervals with good coverage for within cluster factors but not for between cluster factors the converse is true for the naive model under a different drop out mechanism when the probability of drop out is dependent only on the current unobserved observation all three models behave similarly by providing between subject confidence intervals with good coverage and comparable mse and bias but poor within subject confidence intervals mse and bias the naive model does more poorly with respect to the within subject effects than do the shared parameter and approximate conditional models the data analysis which entails a comparison of two pain relievers and a placebo with respect to pain relief conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome driven drop out process this comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data

estimation of the nonlinear random coefficient model when some random effects are separable a method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters this is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects the resulting distribution then requires an integral equation that is of dimension equal to the number of nonlinear terms for nonlinear functions that have linear coefficients the improvement in computational speed and accuracy using the new algorithm can be dramatic an illustration of the method with repeated measures data from a learning experiment is presented

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

inference for covariates that accounts for ascertainment and random genetic effects in family studies summary family studies to identify disease related genes often collect families with multiple cases if environmental exposures or other measured covariates are also important they should be incorporated into these genetic analyses to control for confounding and increase statistical power we propose a two level mixed effects model that allows us to estimate environmental effects while accounting for varying genetic correlations among family members and adjusting for ascertainment by conditioning on the number of cases in the family we describe a conditional maximum likelihood analysis based on this model when genetic effects are negligible this conditional likelihood reduces to standard conditional logistic regression we show that the simpler conditional logistic regression typically yields biased estimators of exposure effects and we describe conditions under which the conditional logistic approach has little or no bias

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

latent variables measurement error and methods for analysing longitudinal binary and ordinal data we explore structural equations with latent variables for modelling between individual variability and measurement error in the analysis of longitudinal binary and ordinal data the structural equation formulation provides insight into the assumptions and differences in interpretation of methods that are popular for longitudinal data analysis introducing the concept of continuous latent variables makes it clear that marginal and cluster specific models differ because their predicted variables are scaled to different standard deviations and that adjustment for measurement error in the outcome involves a change in scale as well we apply both structural equation modelling and common longitudinal modelling approaches to data from a study of sleep disorders in the process we compare results from marginal modelling using an sas gee routine karim and zeger 1988 qu s gauss program qu 1992 for generalized mixed models using gee the mixor package for cluster specific mixed effects models hedeker and gibbons 1994 and liscomp for structural models muthen 1988

the analysis of ring recovery data using random effects we show how random terms describing both yearly variation and overdispersion can easily be incorporated into models for mark recovery data through the use of bayesian methods for recovery data on lapwings we show that the incorporation of the random terms greatly improves the goodness of fit omitting the random terms can lead to overestimation of the significance of weather on survival and overoptimistic prediction intervals in simulations of future population behavior random effects models provide a natural way of modeling overdispersion which is more satisfactory than the standard classical approach of scaling up all standard errors by a uniform inflation factor we compare models by means of bayesian p values and the deviance information criterion dic

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

mixtures of marginal models summary in this paper we adapt a mixture model originally developed for regression models with independent data for the more general case of correlated outcome data which includes longitudinal data as a special case the estimation is performed by a generalisation of the em algorithm which we call the expectation solution es algorithm in this es algorithm the m step of the em algorithm is replaced by a step requiring the solution of a series of generalised estimating equations the es algorithm a general algorithm for solving generalised estimating equations with incomplete data is then applied to the present problem of mixtures of marginal models in addition to allowing for correlation inherent in correlated outcome data the systematic component of this mixture of marginal models is more flexible than the conventional linear function the methodology is applied in the contexts of normal and poisson response data some theory regarding the es algorithm is presented

on bayesian analysis of generalized linear models using jeffreys s prior abstract generalized linear models glm s have proved suitable for modeling various kinds of data consisting of exponential family response variables with covariates bayesian analysis of such data requires specification of a prior for the regression parameters in the model used uniform priors are very commonly used as conventional noninformative priors we show however that uniform priors for glm s can lead to improper posterior distributions thus making them undesirable alternative reference priors may be constructed from jeffreys s rule in this article we give two theorems that support the use of jeffreys s priors for glm s with intrinsically fixed or known scale parameters these theorems provide i sufficient and ii necessary and sufficient conditions for the propriety of the i posterior and ii prior distributions as well as for the existence of moments implications of these theorems for some commonly used glm s are discussed finally an illustrative example is given for the binomial

estimating equations inference with missing data there is a large and growing body of literature on estimating equation ee as an estimation approach one basic property of ee that has been universally adopted in practice is that of unbiasedness and there are deep conceptual reasons why unbiasedness is a desirable ee characteristic this article deals with inference from ees when data are missing at random the investigation is motivated by the observation that direct imputation of missing data in ees generally leads to ees that are biased and thus violates a basic assumption of the ee approach the main contribution of this article is that it goes beyond existing imputation methods and proposes a procedure whereby one mitigates the effects of missing data through a reformulation of ees imputed through a kernel regression method these modified ees then constitute a basis for inference by the generalized method of moments gmm and empirical likelihood el asymptotic properties of the gmm and el estimators of the unknown parameters are derived a

on the existence of maximum likelihood estimators for the binomial response models summary necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response this includes logit and probit models the question of existence of maximum likelihood estimators mle for logit models arose in an analysis of the relationship of psychiatric caseness to scores on a psychiatric screening questionnaire tennant 1977 administered the ghq general health questionnaire goldberg 1972 to 120 patients attending a general practitioner s surgery and also gave each one a standardized psychiatric interview from the interview patients were classified as psychiatric case non case in a secondary analysis of tennant s data duncan jones and henderson 1978 fitted a logit regression of caseness on ghq score and obtained a good fit with the model

a finite mixture of nonlinear random coefficient models for continuous repeated measures data nonlinear random coefficient models nrcms for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development or growth over time in measured variables as an extension of this model this study considers the finite mixture of nrcms that combine features of nrcms with the idea of finite mixture or latent class models the efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations thus allowing the simultaneous investigation of intra individual within person variability inter individual between person variability and subpopulation heterogeneity effectiveness of this model to work under real data analytic conditions was examined by executing a monte carlo simulation study the simulation study was carried out using an r routine specifically developed for the purpose of this study the r routine used maximum likelihood with the expectation maximization algorithm the design of the study mimicked the output obtained from running a two class mixture model on task completion data

bayesian analysis for generalized linear models with nonignorably missing covariates we propose bayesian methods for estimating parameters in generalized linear models glms with nonignorably missing covariate data we show that when improper uniform priors are used for the regression coefficients phi of the multinomial selection model for the missing data mechanism the resulting joint posterior will always be improper if i all missing covariates are discrete and an intercept is included in the selection model for the missing data mechanism or ii at least one of the covariates is continuous and unbounded this impropriety will result regardless of whether proper or improper priors are specified for the regression parameters beta of the glm or the parameters alpha of the covariate distribution to overcome this problem we propose a novel class of proper priors for the regression coefficients phi in the selection model for the missing data mechanism these priors are robust and computationally attractive in the sense that inferences about beta are not sensitive to the choice of the hyperparameters of the prior for phi and they facilitate a gibbs sampling scheme that leads to accelerated convergence in addition we extend the model assessment criterion of chen dey and ibrahim 2004a biometrika 91 45 63 called the weighted l measure to glms and missing data problems as well as extend the deviance information criterion dic of spiegelhalter et al 2002 journal of the royal statistical society b 64 583 639 for assessing whether the missing data mechanism is ignorable or nonignorable a novel markov chain monte carlo sampling algorithm is also developed for carrying out posterior computation several simulations are given to investigate the performance of the proposed bayesian criteria as well as the sensitivity of the prior specification real datasets from a melanoma cancer clinical trial and a liver cancer study are presented to further illustrate the proposed methods

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

prior elicitation variable selection and bayesian computation for logistic regression models summary bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models specifying a prior distribution on the model space and computations we address these three issues for the logistic regression model for the first we propose an informative prior distribution for variable selection several theoretical and computational properties of the prior are derived and illustrated with several examples for the second we propose a method for specifying an informative prior on the model space and for the third we propose novel methods for computing the marginal distribution of the data the new computational algorithms only require gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models several properties of the algorithms are also derived the prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction yo for the response vector and a quantity ao quantifying the uncertainty in yo then yo and ao are used to specify a prior for the regression coefficients semi automatically examples using real data are given to demonstrate the methodology

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

polynomial regression and estimating functions in the presence of multiplicative measurement error we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor two general methods are considered with the methods differing in their assumptions about the distributions of the predictor and the measurement errors consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory diagnostics are presented for distinguishing additive and multiplicative measurement error data from a nutrition study are analysed by using the methods the results from a simulation study are presented and the performances of the methods are compared

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

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

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

comparison of methods for the analysis of longitudinal interval count data longitudinal studies are often concerned with estimating the recurrence rate of a non fatal event in many cases only the total number of events occurring during successive time intervals is known we compared a mixed poisson gamma regression method proposed by thall and a quasi likelihood method proposed by zeger and liang for the analysis of such data in the case where the mean was correctly specified using simulation techniques with large samples both methods produced similar standard errors in most situations except in the case of time dependent covariates with non poisson gamma data where they were seriously underestimated by the thall method a simple method for discriminating between the variance forms of the two methods is described the findings are applied to the analyses of clinical trials of non melanoma skin cancer and familial polyposis this study extends the findings of breslow concerning variance misspecification in overdispersed poisson and quasi likelihood models to the longitudinal setting

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

the frobenius problem for homomorphic embeddings of languages into the integers abstract let s be a map from a language l to the integers satisfying s v w s v s w for all v w l the classical frobenius problem asks whether the complement of s l in the natural numbers will be infinite or finite and in the latter case the value of the largest element in this complement this is also known as the coin problem and l is the full language consisting of all words over a finite alphabet we solve the frobenius problem for the golden mean language any sturmian language and the thue morse language we also consider two dimensional embeddings

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

a two part random effects model for semicontinuous longitudinal data a semicontinuous variable has a portion of responses equal to a single value typically 0 and a continuous often skewed distribution among the remaining values in cross sectional analyses variables of this type may be described by a pair of regression models for example a logistic model for the probability of nonzero response and a conditional linear model for the mean response given that it is nonzero we extend this two part regression approach to longitudinal settings by introducing random coefficients into both the logistic and the linear stages fitting a two part random effects model poses computational challenges similar to those found with generalized linear mixed models we obtain maximum likelihood estimates for the fixed coefficients and variance components by an approximate fisher scoring procedure based on high order laplace approximations to illustrate we apply the technique to data from the adolescent alcohol prevention trial examining reported recent alcohol use for students in g

computing abelian complexity of binary uniform morphic words although a lot of research has been done on the factor complexity also called subword complexity of morphic words obtained as fixed points of iterated morphisms there has been little development in exploring algorithms that can efficiently compute their abelian complexity the factor complexity counts the number of factors of a given length n while the abelian complexity counts that number up to letter permutation we propose and analyze a simple o n algorithm for quickly computing the exact abelian complexities for all indices from 1 up to n when considering binary uniform morphisms using our algorithm we also analyze the structure in the abelian complexity for that class of morphisms our main result implies in particular that the infinite word over the alphabet 1 0 1 constructed from the consecutive forward differences of the abelian complexity of a fixed point of a binary uniform morphism is in fact an automatic sequence with the same morphic length since the proof produces morphisms that typically contain many redundant letters we present an efficient algorithm to eliminate them in order to simplify the morphisms and to see the patterns produced more clearly

maximum likelihood methods for cure rate models with missing covariates we propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction in which the covariates are allowed to be missing we allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions we propose a novel em algorithm for maximum likelihood estimation and derive standard errors by using louis s formula louis 1982 journal of the royal statistical society series b 44 226 233 computational techniques using the monte carlo em algorithm are discussed and implemented a real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

propriety of the posterior distribution and existence of the mle for regression models with covariates missing at random characterizing model identifiability in the presence of missing covariate data is a very important issue in missing data problems in this article we characterize the propriety of the posterior distribution of the regression coefficients for some general classes of regression models including the class of generalized linear models glm s and parametric survival models with right censored data toward this goal we derive some very general and easy to check conditions for the matrix of covariates we also derive sufficient conditions for the existence of the maximum likelihood estimates and establish novel results for checking propriety of the posterior when the sample size is large several theorems are given to establish propriety of the posterior and the existence of the maximum likelihood estimator the conditions reduce to solving a system of linear equations which can be carried out using software such as maple imsl or sas we assume that the missing covariates are missing at random and assume

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