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

on stable numerical differentiation based on a regularized volterra equation two different approaches for numeri cal differentiation are considered the first approach consists of solving a regularized volterra equation while the second approach is based on solving a disretized version of the regularized volterra equation numerical experiments show that these methods are efficient and compete fa vorably with the variational regularization method for stable calculating the derivatives of noisy functions

a cosine maximization method for the priority vector derivation in ahp abstract the derivation of a priority vector from a pair wise comparison matrix pcm is an important issue in the analytic hierarchy process ahp the existing methods for the priority vector derivation from pcm include eigenvector method ev weighted least squares method wls additive normalization method an logarithmic least squares method lls etc the derived priority vector should be as similar to each column vector of the pcm as possible if a pair wise comparison matrix pcm is not perfectly consistent therefore a cosine maximization method cm based on similarity measure is proposed which maximizes the sum of the cosine of the angle between the priority vector and each column vector of a pcm an optimization model for the cm is proposed to derive the reliable priority vector using three numerical examples the cm is compared with the other prioritization methods based on two performance evaluation criteria euclidean distance and minimum violation the results show that the cm is flexible and efficient

the mathematical equivalence of the spanning tree and row geometric mean preference vectors and its implications for preference analysis abstract pairwise comparison is a widely used approach to elicit comparative judgements from a decision maker dm and there are a number of methods that can be used to then subsequently derive a consistent preference vector from the dm s judgements while the most widely used method is the eigenvector method the row geometric mean approach has gained popularity due to its mathematical properties and its ease of implementation in this paper we discuss a spanning tree method and prove the mathematical equivalence of its preference vector to that of the row geometric mean approach this is an important finding due to the fact that it identifies an approach for generating a preference vector which has the mathematical properties of the row geometric mean preference vector and yet in its entirety the spanning tree method has more to offer than the row geometric mean method in that it is inherently applicable to incomplete sets of pairwise comparison judgements and also facilitates the use of statistical and visual techniques to gain insights into inconsistency in the dm s judgements

a mixed effects model for multivariate ordinal response data including correlated discrete failure times with ordinal responses the mixed effects model for binary responses due to conaway 1990 a random effects model for binary data is extended to accommodate ordinal responses in general and discrete time survival data with ordinal responses in particular given a multinomial likelihood cumulative complementary log log link function and log gamma random effects distribution the resulting marginal likelihood has a closed form as a result a newton raphson estimation procedure is feasible without resorting to numerical approximation based or monte carlo integration techniques the parameters in the model have a proportional hazards interpretation in terms of multivariate discrete time data with ordinal responses using data from a psychological example the proposed method is compared with other mixed effects approaches as well as population averaged models

a random effects model for binary data summary this paper presents a method based on maximizing the marginal likelihood for analyzing binary data with random effects with the assumption of a parametric family that allows for a wide variety of shapes for the distribution of the random effects the marginal likelihood can be computed without numerical integrations the method uses local independence models as well as those that incorporate additional dependence among the responses two examples a panel study with binary responses and an analysis of item response data will be used to illustrate the method

eigenvector ranking method as a measuring tool formulas for errors abstract the eigenvector method em is well known to derive information from pairwise comparison matrices in decision making processes however this method is logically incomplete since its actual numerical error is unknown and its reliability is doubted by such phenomena as right left asymmetry rank reversal and reversal of order of intensity of preference in this paper we associate em with some standard measuring procedure analyze this procedure from the viewpoint of measurement theory and find the actual em error we show that the above phenomena have the same cause and are eliminated when the em errors are taken into account the full decision support tool which has all components of a standard measuring tool is composed of pairwise comparisons as an initial measuring procedure em as a data processor and the obtained formulas for em errors as an error indicator we consider two versions of this tool based on the right and the left principal eigenvectors of a pairwise comparison matrix both versions are equally suitable to measure and rank any comparable elements with positive numerical values and have the same mean relative errors equal to the square root of the double saaty s consistency index using the mean relative error we find the simple upper estimate for maximum permissible errors not impeding the reliable ranking this estimate imposes tight restrictions on inconsistency of expert judgements in decision making processes with a large number of alternatives these restrictions are much stronger than previously thought

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

deriving weights from pairwise comparison ratio matrices an axiomatic approach abstract this paper examines the problem of extracting object or attribute weights from a pairwise comparison ratio matrix this problem is approached from the point of view of a distance measure on the space of all such matrices a set of axioms is presented which such a distance measure should satisfy and the uniqueness of the measure is proven the problem of weight derivation is then shown to be equivalent to that of finding a totally transitive matrix which is a minimum distance from the given matrix this problem reduces to a goal programming model finally it is shown that the problem of weight derivation is related to that of ranking players in a round robin tournament the space of all binary tournament matrices is proven to be isometric to a subset of the space of ratio matrices

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

estimation and comparison of changes in the presence of information right censoring by modeling the censoring process abstract in estimating and comparing the rates of change of a continuous variable between two groups the unweighted averages of individual simple least squares estimates from each group are often used under a linear random effects model when all individuals have completed observations at identical time points these statistics are maximum likelihood estimates for the expected rates of change however with censored of missing data these estimates are no longer efficient when compared to generalized least squares estimates when in addition the right censoring process is dependent upon the individual rates of change i e informative right censoring the generalized least squares estimates will be biased likelihood ratio test for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right censoring process are developed under a linear random effect models with a probit model for the right censoring process in realistic situations we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group difference could be substantial when strong dependency of the right censoring process on individual rates of change is ignored author

a regularization parameter for nonsmooth tikhonov regularization in this paper we develop a novel rule for choosing regularization parameters in nonsmooth tikhonov functionals it is solely based on the value function and applicable to a broad range of nonsmooth models and it extends one known criterion a posteriori error estimates of the approximations are derived an efficient numerical algorithm for computing the minimizer is developed and its convergence properties are discussed numerical results for several common nonsmooth models are presented including deblurring natural images the numerical results indicate the rule can yield results comparable with those achieved with the discrepancy principle and the optimal choice and the algorithm merits a fast and steady convergence

a two part joint model for the analysis of survival and longitudinal binary data with excess zeros many longitudinal studies generate both the time to some event of interest and repeated measures data this article is motivated by a study on patients with a renal allograft in which interest lies in the association between longitudinal proteinuria a dichotomous variable measurements and the time to renal graft failure an interesting feature of the sample at hand is that nearly half of the patients were never tested positive for proteinuria 1g day during follow up which introduces a degenerate part in the random effects density for the longitudinal process in this article we propose a two part shared parameter model framework that effectively takes this feature into account and we investigate sensitivity to the various dependence structures used to describe the association between the longitudinal measurements of proteinuria and the time to renal graft failure

numerical differentiation from a viewpoint of regularization theory in this paper we discuss the classical ill posed problem of numerical differentiation assuming that the smoothness of the function to be differentiated is unknown using recent results on adaptive regularization of general ill posed problems we propose new rules for the choice of the stepsize in the finite difference methods and for the regularization parameter choice in numerical differentiation regularized by the iterated tikhonov method these methods are shown to be effective for the differentiation of noisy functions and the order optimal convergence results for them are proved

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

a regularization parameter in discrete ill posed problems the tikhonov regularization method for discrete ill posed problems is considered for the practical choice of the regularization parameter alpha some authors use a plot of the norm of the regularized solution versus the norm of the residual vector for all alpha considered this paper contains an analysis of the shape of this plot and gives a theoretical justification for choosing the regularization parameter so it is related to the l corner of the plot considered in the logarithmic scale moreover a new criterion for choosing alpha is introduced independent of the shape of the plot which gives a new interpretation of the corner criterion mentioned above the existence of l corner is discussed

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

a multicriteria evaluation of methods for obtaining weights from ratio scale matrices abstract ratio scale matrices are commonly used as a vehicle to distinguish among competing alternatives or conflicting criteria the issue of extracting weights out of such matrices has attracted increasing attention in recent years and resulted in the development of several scaling methods this paper presents an attempt to evaluate some of the more known techniques in this area the evaluation procedure includes random generation of a large number of representative matrices which are used to evaluate the various scaling methods according to the specified criteria the performance of the different techniques is analyzed with respect to the proposed criteria and conclusions are drawn

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

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 progression of cd4 lymphocyte count and its relationship to survival time the purpose of this article is to model the progression of cd4 lymphocyte count and the relationship between different features of this progression and survival time the complicating factors in this analysis are that the cd4 lymphocyte count is observed only at certain fixed times and with a high degree of measurement error and that the length of the vector of observations is determined in part by the length of survival if probability of death depends on the true unobserved cd4 lymphocyte count then the survival process must be modelled wu and carroll 1988 biometrics 44 175 188 proposed a random effects model for two sample longitudinal data in the presence of informative censoring in which the individual effects included only slopes and intercepts we propose methods for fitting a broad class of models of this type in which both the repeated cd4 lymphocyte counts and the survival time are modelled using random effects these methods permit us to estimate parameters describing the progression of cd4 lymphocyte count as well as the effect of differences in the cd4 trajectory on survival we apply these methods to results of aids clinical trials

the geometric consistency index approximated thresholds abstract crawford and williams journal of mathematical psychology 29 1985 387 suggested for the row geometric mean method rgmm one of the most extended ahp s priorization procedure a measure of the inconsistency based on stochastic properties of a subjacent model in this paper we formalize this inconsistency measure hereafter called the geometric consistency index gci and provide the thresholds associated with it these thresholds allow us an interpretation of the inconsistency tolerance level analogous to that proposed by saaty multicriteria decision making the analytic hierarchy process new york 1980 for the consistency ratio cr used with the right eigenvector method in conventional ahp

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

on computing first and second order derivative spectra enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis first and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing but high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data an algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed the algorithm is formalized in the framework of an inverse problem where based on the fundamental theorem of calculus a matrix equation is formed using a volterra type integral equation of first kind a regularization technique where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra the higher order derivative spectra are obtained while using the algorithm in sequel the algorithm is tested successfully with synthetically generated spectral data contaminated with additive white gaussian noise and also with real absorbance and reflectance spectral data for fresh and sea water respectively robust and efficient algorithm of computing first and second orders derivative spectra is designed the algorithm is based on the premise of inverse problem where a robust solution is achieved via regularization it couples discrepancy and balancing principles to determine regularization parameter and implement stopping rule respectively numerical experiments on noisy data suggest superiority of the method over finite difference and fourier transform based techniques the proposed method is applied on absorbance and reflectance spectral data for fresh and sea water

sensitivity analysis of longitudinal binary quality of life data with drop out an example using the eortc qlq c30 analysing quality of life data qol may be complicated for several reasons quality of life data not only involves repeated measures but is also usually collected on ordered categorical responses in addition it is evident that not all patients provide the same number of assessments due to attrition caused by death or other medical reasons in the recent statistical literature increasing attention is given to methods which can handle non continuous outcomes in the presence of missing data the aim of this paper is to investigate the effect on statistical conclusions of applying different modelling techniques to qol data generated from an eortc phase iii trial treatment effects and treatment differences are of major concern first a random effects model is fitted relating a binary longitudinal response derived from the physical functioning scale of the qlq c30 to several covariates in a second approach marginal models are fitted retaining the response variable and the mean structure used before the fitted marginal models only differ with respect to the considered estimation procedure generalized estimating equations gee weighted generalized estimating equations wgee and maximum likelihood ml copyright c 2001 john wiley sons ltd

a random pattern mixture model for ordinal outcomes with informative dropouts we extend a random pattern mixture joint model for longitudinal ordinal outcomes and informative dropouts the patients are generalized to pattern groups based on known covariates that are potential surrogated for the severity of the underlying condition the random pattern effects are defined as the latent effects linking the dropout process and the ordinal longitudinal outcome conditional on the random pattern effects the longitudinal outcome and the dropout times are assumed independent estimates are obtained via the em algorithm we applied the model to the end stage renal disease esrd data anemia was found to be significantly affected by baseline iron treatment when the dropout information was adjusted via the study model as opposed to an independent or shared parameter model simulations were performed to evaluate the performance of the random pattern mixture model under various assumptions

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

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

a characterization of the logarithmic least squares method abstract we provide an axiomatic characterization of the logarithmic least squares method sometimes called row geometric mean used for deriving a preference vector from a pairwise comparison matrix this procedure is shown to be the only one satisfying two properties correctness in the consistent case which requires the reproduction of the inducing vector for any consistent matrix and invariance to a specific transformation on a triad that is the weight vector is not influenced by an arbitrary multiplication of matrix elements along a 3 cycle by a positive scalar

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

interpreting potential field anomaly of an isolated source of regular geometry revisited abstracti have developed an improved practical method for interpreting a symmetrical shaped potential field anomaly due to an isolated source body of regular geometric configuration the method uses the first order horizontal derivative of the logarithmically transformed absolute value of the anomaly in estimating the source body parameters such as the location depth of burial and shape factor to tackle noise in data a regularization technique is designed which ensures a robust estimate of the first order derivative of logarithmically transformed data the regularization technique uses an optimal value of regularization parameter that although noise dependent requires no a priori knowledge of the noise level in the data a graphical method is designed to determine an optimal value of the regularization parameter from the position of the local minimum of a specially defined functional with respect to the regularization parameters numerical tests have been conducted on the noise contaminated synthe

incomplete pairwise comparison and consistency optimization this paper proposes a new method for calculating the missing elements of an incomplete matrix of pairwise comparison values for a decision problem the matrix is completed by minimizing a measure of global inconsistency thus obtaining a matrix which is optimal from the point of view of consistency with respect to the available judgements the optimal values are obtained by solving a linear system and unicity of the solution is proved under general assumptions some other methods proposed in the literature are discussed and a numerical example is presented

a revised framework for deriving preference values from pairwise comparison matrices in a recent study choo and wedley proposed a framework to categorize and conduct simulations to compare methods for deriving preference values from pairwise comparison matrices this study demonstrates that some pairs in the examined methods are identical and some methods can be solved in better ways additionally the simulations of choo and wedley are somewhat idealized thus this study provides additional simulations the simulation results lead to different method ranking and conclusions from those of choo and wedley

a transformation approach in linear mixed effects models with informative missing responses we consider a linear mixed effects model in which the response panel vector has missing components and the missing data mechanism depends on observed data as well as missing responses through unobserved random effects using a transformation of the data that eliminates the random effects we derive asymptotically unbiased and normally distributed estimators of certain model parameters estimators of model parameters that cannot be estimated using the transformed data are also constructed and their asymptotic unbiasedness and normality are established simulation results are presented to examine the finite sample performance of the proposed estimators and a real data example is discussed

a correlated random effects model for normal longitudinal data with nonignorable missingness the missing data problem is common in longitudinal or hierarchical structure studies in this paper we propose a correlated random effects model to fit normal longitudinal or cluster data when the missingness mechanism is nonignorable computational challenges arise in the model fitting due to intractable numerical integrations we obtain the estimates of the parameters based on an accurate approximation of the log likelihood which has higher order accuracy but with less computational burden than the existing approximation we apply the proposed method it to a real data set arising from an autism study

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

a semi parametric shared parameter model to handle nonmonotone nonignorable missingness longitudinal studies often generate incomplete response patterns according to a missing not at random mechanism shared parameter models provide an appealing framework for the joint modelling of the measurement and missingness processes especially in the nonmonotone missingness case and assume a set of random effects to induce the interdependence parametric assumptions are typically made for the random effects distribution violation of which leads to model misspecification with a potential effect on the parameter estimates and standard errors in this article we avoid any parametric assumption for the random effects distribution and leave it completely unspecified the estimation of the model is then made using a semi parametric maximum likelihood method our proposal is illustrated on a randomized longitudinal study on patients with rheumatoid arthritis exhibiting nonmonotone missingness

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

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

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

a scheme for stable numerical differentiation a method for stable numerical differentiation of noisy data is proposed the method requires solving a volterra integral equation of the second kind this equation is solved analytically in the examples considered its solution is computed analytically some numerical results of its application are presented these examples show that the proposed method for stable numerical differentiation is numerically more efficient than some other methods in particular than variational regularization

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

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

a mixed effects model for the analysis of ordinal longitudinal pain data subject to informative drop out we extend the model of pulkstenis et al that models binary longitudinal data subject to informative drop out through remedication to the ordinal response case we present a selection model shared parameter approach that specifies mixed models for both ordinal response and discrete survival time to remedication in this fashion the random parameter present in both models completely characterizes the relationship between response and time to remedication inducing their conditional independence with a log log link function for both response and study survival as well as specification of a log gamma distribution for the random effect we obtain a closed form expression for the marginal log likelihood of response and time to remedication that does not require approximation or numerical integration techniques a data analysis is performed and simulation results presented which support the consistency of parameter and standard error estimates

a random effects model for ordered categorical data abstract this article presents a random effects model for multivariate and grouped univariate ordered categorical data the assumed family of distributions for the random effects adopts a wide variety of forms and shapes the model s likelihood has a closed expression and can be computed without recourse to numerical integration or gaussian quadrature a bivariate and a grouped univariate example are used to illustrate the proposed model

contribution of individual judgments toward inconsistency in pairwise comparisons pairwise comparison pc is a well established method to assist decision makers in estimating their preferences in pcs the acquired judgments are used to construct a pc matrix pcm that is used to check whether the inconsistency in judgments is acceptable or requires revision the use of consistency ratio cr a widely used measure for inconsistency has been widely debated and the literature survey has identified a need for a more appropriate measure considering this need a new measure termed congruence is proposed in this paper the measure is shown to be useful in finding the contribution of individual judgments toward overall inconsistency of a pcm and therefore can be used to detect and correct cardinally inconsistent judgments the proposed measure is applicable to incomplete sets of pc judgments without modification unlike cr which requires a complete set of pc judgments to address ordinal inconsistency another measure termed dissonance is proposed as a supplement to the congruence measure the two measures appear useful in detecting both outliers and the phenomenon of consistency deadlock where all judgments equally contribute toward the overall inconsistency

representing the strengths and directions of pairwise comparisons we consider the problem of finding weights that well represent a set of pairwise multiplicative comparisons of a set of objects as in the ahp and other methods our main contribution is a method for deriving such weights that takes into consideration not only the strengths of the pairwise comparisons but also their directions for example if the comparison directions satisfy transitivity then the weights produced by our method also satisfy transitivity this is not always true for other methods we also present a set of reasonable axioms for which our method is the essentially unique solution our method and axioms are closely related to those of cook and kress eur j oper res 37 1988 335 our method like theirs reduces to solving a linear program hence it is different from the approach used in the ahp for the special case that the comparison directions satisfy transitivity our method is quite simple and reduces to performing a forward pass as in the critical path method

on robust estimation of discrete hilbert transform of noisy data abstractwe developed a novel technique of robust estimation of the discrete hilbert transform dht of noisy geophysical data the technique used the sinc method in which the data were transformed via conformal mapping and the sinc bases were determined by solving a linear matrix equation a transformation rule was presented for selecting a suitable conformal mapping function that would transform the class of geophysical data set in an appropriate interval range a novel regularization technique was designed to obtain a robust solution of sinc bases when the data contained noise in which an optimal regularization parameter was obtained in an automated way using a 1d optimization scheme the technique of selecting the optimal value of the regularization parameter required no a priori knowledge about the level of noise contamination in the data numerical experiments were conducted on synthetically generated and published field data sets with a varying level of noise contamination to test the performance

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

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

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

the equivalence of two models for ordinal data summary the equivalence of the grouped continuous and continuation ratio models for ordinal data when the complementary log log link is used is demonstrated recent experience using two regression models for ordinal data gave essentially identical results when the complementary log log transform was used for the probabilities pregibon 1980 implies that these models are the same the present note makes the equivalence explicit suppose that y is an ordinal response variable whose values are labelled 1 k let 7rj x pr y j i x for an observation with covariate vector x and yj x 1 x rj x pr y k j i x and set bj x pr y ij y j x 7tj x i yj l x j 1 k 1 grouped continuous models fit a linear predictor to some monotonic function f of the cumulative probabilities yj x namely f 7j x oj oc x continuation ratio models use the probabilities bj x instead of the yj s that is

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

preference elicitation from inconsistent judgments using multi objective optimization abstract several decision making techniques involve pairwise comparisons to elicit the preferences of a decision maker dm this paper proposes a new approach for prioritization from pairwise comparisons using the concept of indirect judgments no method exists that simultaneously minimizes deviations from both direct and indirect judgments in order to estimate preferences it is sensible to consider both the acquired judgments and the other judgments latent in the dm s mind hence a technique is developed here to minimize the deviations from both types of judgments estimated preferences are generally evaluated based on two criteria their deviation from the provided judgments and the number of judgments that have been ordinally violated here it is proposed to optimize three objectives simultaneously the deviations from both direct and indirect judgments and the number of judgments violated a prototype application has been developed to generate all non dominated solutions using a multiple objective evolutionary algorithm the new approach is shown to offer users greater flexibility than all other tested methods

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

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

a critical analysis of the eigenvalue method used to derive priorities in ahp abstract a lot of research has been devoted to the critical analysis of the analytic hierarchy process ahp from various perspectives however as far as we know no one has addressed a fundamental problem discussed in this paper concerning the meaning of the priority vector derived from the principal eigenvalue method used in ahp the role of ahp s consistency ratio is also analysed

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

the analysis of longitudinal ordinal data with nonrandom drop out a model is proposed for longitudinal ordinal data with nonrandom drop out which combines the multivariate dale model for longitudinal ordinal data with a logistic regression model for drop out since response and drop out are modelled as conditionally independent given complete data the resulting likelihood can be maximised relatively simply using the em algorithm which with acceleration is acceptably fast and with appropriate additions can produce estimates of precision the approach is illustrated with an example such modelling of nonrandom drop out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense and the conclusions cannot be regarded as necessarily robust the main role of such modelling may be as a component of a sensitivity analysis

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

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

efficient weight vectors from pairwise comparison matrices abstract pairwise comparison matrices are frequently applied in multi criteria decision making a weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix and strictly better in at least one position a weight vector is weakly efficient if the pairwise ratios cannot be improved in all non diagonal positions we show that the principal eigenvector is always weakly efficient but numerical examples show that it can be inefficient the linear programs proposed test whether a given weight vector is weakly efficient and in case of strong inefficiency an efficient strongly dominating weight vector is calculated the proposed algorithms are implemented in pairwise comparison matrix calculator available at pcmc online

bayesian quantile regression for longitudinal studies with nonignorable missing data summary we study quantile regression qr for longitudinal measurements with nonignorable intermittent missing data and dropout compared to conventional mean regression quantile regression can characterize the entire conditional distribution of the outcome variable and is more robust to outliers and misspecification of the error distribution we account for the within subject correlation by introducing a l2 penalty in the usual qr check function to shrink the subject specific intercepts and slopes toward the common population values the informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects we assess the performance of the proposed method using simulation studies and illustrate it with data from a pediatric aids clinical trial

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