decoding cyclic codes up to a new bound on the minimum distance a new lower bound on the minimum distance of q ary cyclic codes is proposed this bound improves upon the bose chaudhuri hocquenghem bound and for some codes upon the hartmann tzeng bound several boston bounds are special cases of our bound for some classes of codes the bound on the minimum distance is refined furthermore a quadratic time decoding algorithm up to this new bound is developed the determination of the error locations is based on the euclidean algorithm and a modified chien search the error evaluation is done by solving a generalization of forney s formula

long nonbinary codes exceeding the gilbert varshamov bound for any fixed distance let a q n d denote the maximum size of a q ary code of length n and distance d we study the minimum asymptotic redundancy as n grows while q and d are fixed for any d and q spl ges d 1 long algebraic codes are designed that improve on the bose chaudhuri hocquenghem bch codes and have the lowest asymptotic redundancy known to date prior to this work codes of fixed distance that asymptotically surpass bch codes and the gilbert varshamov bound were designed only for distances 4 5 and 6

a discrete time event history approach to informative drop out in mixed latent markov models with covariates summary mixed latent markov mlm models represent an important tool of analysis of longitudinal data when response variables are affected by time fixed and time varying unobserved heterogeneity in which the latter is accounted for by a hidden markov chain in order to avoid bias when using a model of this type in the presence of informative drop out we propose an event history eh extension of the latent markov approach that may be used with multivariate longitudinal data in which one or more outcomes of a different nature are observed at each time occasion the eh component of the resulting model is referred to the interval censored drop out and bias in mlm modeling is avoided by correlated random effects included in the different model components which follow common latent distributions in order to perform maximum likelihood estimation of the proposed model by the expectation maximization algorithm we extend the usual forward backward recursions of baum and welch the algorithm has the same complexity as the one adopted in cases of non informative drop out we illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest one continuous and the other binary

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

an approximate generalized linear model with random effects for informative missing data this paper develops a class of models to deal with missing data from longitudinal studies we assume that separate models for the primary response and missingness e g number of missed visits are linked by a common random parameter such models have been developed in the econometrics heckman 1979 econometrica 47 153 161 and biostatistics wu and carroll 1988 biometrics 44 175 188 literature for a gaussian primary response we allow the primary response conditional on the random parameter to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness the resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects an example is given to illustrate the approximate approach and simulations are performed to critique the adequacy of the approximation for repeated binary data

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

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

on a class of primitive bch codes the author introduces a special class of primitive bch codes the minimal bch mb codes it is proved that an mb code has as minimum distance its designed distance using the roos bound the author proposes a lower bound sometimes tight for the minimum distance of the dual of an mb code he describes the subclass of weakly self dual extended mb codes and then characterizes some weakly self dual extended bch codes similarly he proves that the nontrivial extended mb code over gf 4 is the smallest extended bch code which is not an even code he points out that extended mb codes are principal ideals of a modular algebra

analysis of smoking trends with incomplete longitudinal binary responses abstract the generalized estimating equations procedure gee widely applied in the analysis of correlated binary data requires that missing data depend only on remote covariates or that they be missing completely at random mcar otherwise gee regression parameter estimates are biased a weighted generalized estimating equations wgee approach that accounts for dropouts under the less stringent assumption of missing at random mar through dependence on observed responses gives unbiased estimation of parameters in the model for the marginal means if the dropout mechanism is specified correctly wgees are applied in the estimation of 7 year trends in cigarette smoking in the united states from a cohort of 5 078 black and white young adults analysis using wgee suggests that there was a general decline in cigarette smoking only among white females whereas the only other subgroup for which smoking declined was white males of the older birth cohort 1955 1962 with college degrees the results of wgee are

a new bound for the minimum distance of a cyclic code from its defining set a new lower bound for the distance of cyclic codes is proposed this bound depends on the defining set of the code like several other bounds the proposed bound improves upon the bose chaudhuri hocquehghen bch bound and for some codes improves upon the hartmann tzeng bound and the roos bound as well

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

a generalization of the berlekamp massey algorithm for multisequence shift register synthesis with applications to decoding cyclic codes a generalization of the berlekamp massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences a more general problem is first considered that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field which includes the multisequence problem as a special case a simple iterative algorithm the fundamental iterative algorithm fia is presented for solving this problem the generalized algorithm is then derived through a refinement of the fia application of this generalized algorithm to decoding cyclic codes up to the hartmann tzeng ht bound and roos bound making use of multiple syndrome sequences is considered conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error locator polynomial are determined with respect to decoding up to the ht bound and special cases of the roos bound

multivariate logistic models for incomplete binary responses abstract in this article we describe a likelihood based regression model appropriate for analyzing incomplete multivariate binary responses we focus on marginal models that is models where the marginal mean or expectation of the binary response is related to a set of covariates the association between the binary responses is modeled in terms of conditional log odds ratios when the nonresponse mechanism is ignorable it is not necessary to specify a nonresponse model and valid inferences can be obtained provided that the likelihood for the responses has been correctly specified but when the nonresponse mechanism is nonignorable valid inferences can only be obtained by incorporating a model for nonresponse an unresolved issue with nonignorable models concerns the identifiability of the parameters so far no general and practically useful necessary and sufficient conditions for identifiability are available here we suggest some simple procedures for examining the identifiability status of nonign

every missingness not at random model has a missingness at random counterpart with equal fit over the last decade a variety of models to analyse incomplete multivariate and longitudinal data have been proposed many of which allowing for the missingness to be not at random in the sense that the unobserved measurements influence the process governing missingness in addition to influences coming from observed measurements and or covariates the fundamental problems that are implied by such models to which we refer as sensitivity to unverifiable modelling assumptions has in turn sparked off various strands of research in what is now termed sensitivity analysis the nature of sensitivity originates from the fact that a missingness not at random mnar model is not fully verifiable from the data rendering the empirical distinction between mnar and missingness at random mar where only covariates and observed outcomes influence missingness difficult or even impossible unless we are willing to accept the posited mnar model in an unquestioning way we show that the empirical distinction between mar and mnar is not possible in the sense that each mnar model fit to a set of observed data can be reproduced exactly by an mar counterpart of course such a pair of models will produce different predictions of the unobserved outcomes given the observed outcomes theoretical considerations are supplemented with an illustration that is based on the slovenian public opinion survey which has been analysed before in the context of sensitivity analysis

a new lower bound for the minimum distance of a cyclic code a new lower bound for the minimum distance of a linear code is derived when applied to cyclic codes both the bose chaudhuri hocquenghem bch bound and the hartmann tzeng ht bound are obtained as corollaries examples for which the new bound is superior to these two bounds as well as to the carlitz uchiyama bound are given

codes for symbol pair read channels a new coding framework is established for channels whose outputs are overlapping pairs of symbols such channels are motivated by storage applications in which the spatial resolution of the reader may be insufficient to isolate adjacent symbols reading symbols as pairs changes the coding theoretic error model from the standard bounded number of symbol errors to a bounded number of pair errors starting from the most basic coding theoretic questions the paper studies codes that protect against pair errors it provides answers on pair error correctability conditions code construction and decoding and lower and upper bounds on code sizes asymptotic analysis of pair error correction shows that there exist pair error codes with rates that are strictly higher than the best known codes in the hamming metric

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

analysis of change in the presence of informative censoring application to a longitudinal clinical trial of progressive renal disease the rate of change in a continuous variable measured serially over time is often used as an outcome in longitudinal studies or clinical trials when patients terminate the study before the scheduled end of the study there is a potential for bias in estimation of rate of change using standard methods which ignore the missing data mechanism these methods include the use of unweighted generalized estimating equations methods and likelihood based methods assuming an ignorable missing data mechanism we present a model for analysis of informatively censored data based on an extension of the two stage linear random effects model where each subject s random intercept and slope are allowed to be associated with an underlying time to event the joint distribution of the continuous responses and the time to event variable are then estimated via maximum likelihood using the em algorithm and using the bootstrap to calculate standard errors we illustrate this methodology and compare it to simpler approaches and usual maximum likelihood using data from a multi centre study of the effects of diet and blood pressure control on progression of renal disease the modification of diet in renal disease mdrd study sensitivity analyses and simulations are used to evaluate the performance of this methodology in the context of the mdrd data under various scenarios where the drop out mechanism is ignorable as well as non ignorable

on the minimum distance of ternary cyclic codes there are many ways to find lower bounds for the minimum distance of a cyclic code based on investigation of the defining set some new theorems are derived these and earlier techniques are applied to find lower bounds for the minimum distance of ternary cyclic codes furthermore the exact minimum distance of ternary cyclic codes of length less than 40 is computed numerically a table is given containing all ternary cyclic codes of length less than 40 and having a minimum distance exceeding the bch bound it seems that almost all lower bounds are equal to the minimum distance especially shifting which is also done by computer seems to be very powerful for length 40

on the minimum distance of cyclic codes the main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds i e bch bound ht bound roos bound this bound is related to a second method for bounding the minimum distance of a cyclic code which we call shifting this method can be even stronger than the first one for all binary cyclic codes of length with two exceptions we show that our methods yield the true minimum distance the two exceptions at the end of our list are a code and its even weight subcode we treat several examples of cyclic codes of length geq 63

a multistate markov chain model for longitudinal categorical quality of life data subject to non ignorable missingness summary quality of life qol is an important outcome in clinical research particularly in cancer clinical trials typically data are collected longitudinally from patients during treatment and subsequent follow up missing data are a common problem and missingness may arise in a non ignorable fashion in particular the probability that a patient misses an assessment may depend on the patient s qol at the time of the scheduled assessment we propose a markov chain model for the analysis of categorical outcomes derived from qol measures our model assumes that transitions between qol states depend on covariates through generalized logit models or proportional odds models to account for non ignorable missingness we incorporate logistic regression models for the conditional probabilities of observing measurements given their actual values the model can accommodate time dependent covariates estimation is by maximum likelihood summing over all possible values of the missing measurements we

mixed effects logistic regression models for longitudinal ordinal functional response data with multiple cause drop out from the longitudinal study of aging summary in the context of analyzing ordinal functional limitation responses from the longitudinal study of aging we investigate the association between current functional limitation and previous year s limitation and its modification by physical activity and multiple causes of drop out we accommodate the longitudinal nature of the multiple causes of informative drop out death and unknown loss to follow up with a mixed effects logistic model under the proposed model with a random intercept and slope the ordinal functional outcome and multiple discrete time survival profiles share a common random effect structure this shared parameter selection model assumes that the multiple causes of drop out are conditionally independent of the functional limitation outcome given the underlying random effect representing an individual s trajectory of general health status across time although it is not possible to fully assess the adequacy of this assumption we assess the robustness of the approach by varying the assumptions underlying the proposed model such as the random effects distribution and the drop out component it appears that between subject differences in initial functional limitation are strongly associated with future functional limitation and that this association is stronger for those who do not have physical activity regardless of the random effects and informative dropout specifications in contrast the association between current functional limitation and previous trajectory of functional status within an individual is weaker and more sensitive to changes in the random effects and drop out assumptions

a latent class mixture model for incomplete longitudinal gaussian data in the analyses of incomplete longitudinal clinical trial data there has been a shift away from simple methods that are valid only if the data are missing completely at random to more principled ignorable analyses which are valid under the less restrictive missing at random assumption the availability of the necessary standard statistical software nowadays allows for such analyses in practice while the possibility of data missing not at random mnar cannot be ruled out it is argued that analyses valid under mnar are not well suited for the primary analysis in clinical trials rather than either forgetting about or blindly shifting to an mnar framework the optimal place for mnar analyses is within a sensitivity analysis context one such route for sensitivity analysis is to consider next to selection models pattern mixture models or shared parameter models the latter can also be extended to a latent class mixture model the approach taken in this article the performance of the so obtained flexible model is assessed through simulations and the model is applied to data from a depression trial

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 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 commutative algebra approach to linear codes abstract recently some methods have been proposed to find the distance and weight distribution of cyclic codes using grobner bases we identify a class of codes for which these methods can be generalized we show that this class contains all interesting linear codes and we provide variants and improvements this approach sometimes reveals an unexpected algebraic structure in the code we also investigate the decoding for a subclass proving the existence of general error locator polynomials

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

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

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

error locating pairs for cyclic codes a general decoding method for linear codes is investigated for cyclic codes the decoding consists of solving two systems of linear equations all but four binary cyclic codes of length less than 63 can so be decoded up to their actual distance a new family of codes is given for which the decoding needs only o n sup 2 operations

estimation and comparison of changes in the presence of informative right censoring conditional linear model a general linear regression model for the usual least squares estimated rate of change slope on censoring time is described as an approximation to account for informative right censoring in estimating and comparing changes of a continuous variable in two groups two noniterative estimators for the group slope means the linear minimum variance unbiased lmvub estimator and the linear minimum mean squared error lmmse estimator are proposed under this conditional model in realistic situations we illustrate that the lmvub and lmmse estimators derived under a simple linear regression model are quite competitive compared to the pseudo maximum likelihood estimator pmle derived by modeling the censoring probabilities generalizations to polynomial response curves and general linear models are also described

estimation and testing for multiple regulation of multivariate mixed outcomes considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies either to capture the multidimensionality of complex disorders or to understand shared etiology of related disorders we seek to identify multiple regulators or predictors that are associated with multiple outcomes when these outcomes may be measured on very different scales or composed of a mixture of continuous binary and not fully observed elements we first propose an estimation technique to put all effects on similar scales and we induce sparsity on the estimated effects we provide standard asymptotic results for this estimator and show that resampling can be used to quantify uncertainty in finite samples we finally provide a multiple testing procedure which can be geared specifically to the types of multiple regulators of interest and we establish that under standard regularity conditions the familywise error rate will approach 0 as sample size diverges simulation results indicate that our approach can improve over unregularized methods both in reducing bias in estimation and improving power for testing

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

statistical inference for familial disease clusters in many epidemiologic studies the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units the concept of clustering is contrasted with incidence we assume that all individuals are exchangeable except for their disease status this assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease conditional on the number of diseased cases and the distribution of the sizes of the various family units new parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering we consider models and an example that takes covariates into account ascertainment bias is described and the appropriate sampling distribution is demonstrated four numerical examples with real data illustrate these methods

decoding cyclic and bch codes up to actual minimum distance using nonrecurrent syndrome dependence relations the decoding capabilities of algebraic algorithms mainly the berlekamp massey algorithm the euclidean algorithm and the authors 1989 generalizations of these algorithms are basically constrained by the minimum distance bounds of the codes the authors introduce a more general procedure which breaks away from this restriction and which can determine the error locations from nonrecurrent dependence relations among the syndromes it can decode many cyclic and bch codes up to their actual minimum distance and is seen to be a generalization of the procedure introduced by w w peterson and e j weldon 1972

the minimum distance of the 38 19 ternary extended qr code is 11 corresp the method of mykkeltveit lam and mceliece for finding weight enumerators of binary qr codes is used to prove that the minimum distance of the 38 19 ternary extended qr code is 11

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

robust estimation in mixed linear models with non monotone missingness we introduce a model to account for abrupt changes among repeated measures with non monotone missingness development of likelihood inferences for such models is hard because it involves intractable integration to obtain the marginal likelihood we use hierarchical likelihood to overcome such difficulty abrupt changes among repeated measures can be well described by introducing random effects in the dispersion a simulation study shows that the resulting estimator is efficient robust against misspecification of fatness of tails for illustration we use a schizophrenic behaviour data presented by rubin and wu

an empirical bayes model for markov dependent binary sequences with randomly missing observations abstract we develop an improved empirical bayes estimation methodology for the analysis of two state markov chains observed from heterogeneous individuals first the two transition probabilities corresponding to each chain are assumed to be drawn from a common bivariate distribution that has beta marginals second randomly missing observations are incorporated into the likelihood for the hyperparameters by efficiently summing over all possible values for the missing observations a likelihood ratio test is used to test for dependence between the transition probabilities posterior distributions for the transition probabilities are also derived as is an approximation for the equilibrium probabilities the proposed procedures are illustrated in a numerical example and in an analysis of longitudinal store display data

birkhoff periodic orbits for small perturbations of completely integrable hamiltonian systems with convex hamiltonians pour des systemes a n degres de liberte on montre l existence d au moins n orbites periodiques distinctes avec un vecteur frequence rationnel admissible proche du tore correspondant du systeme non perturbe sous l hypothese que le hamiltonien du systeme non perturbe a des surfaces d energie convexes pour les variables action angle

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

from ds bounds for cyclic codes to true minimum distance for abelian codes in this paper we develop a technique to extend any bound for the minimum distance of cyclic codes constructed from its defining sets ds bounds to abelian or multivariate codes through the notion of mathbb b apparent distance we also study conditions for an abelian code to verify that its mathbb b apparent distance reaches its true minimum distance then we construct some codes as an application

application of empirical bayes inference to estimation of rate of change in the presence of informative right censoring we apply parametric empirical bayes inference of morris7 to the estimation of rate of change from incomplete longitudinal studies where the right censoring process is considered informative that is the length of time the subjects participate in the study is associated with level of the study variable ignoring such an association can result in a biased estimate of rate of change the proposed method provides estimates of rate of change for individual subjects as well as for the entire group adjusted for informative right censoring the method is considered more robust than those based on a specific parametric model for the censoring distribution under non informative right censoring these estimators of slopes are equivalent to the bayes estimators derived by fearn 11 we illustrate the method with an example involving renal transplant data we evaluate the method s performance through a simulation study

empirical bayes estimation of random effects parameters in mixed effects logistic regression models we extend an approach for estimating random effects parameters under a random intercept and slope logistic regression model to include standard errors thereby including confidence intervals the procedure entails numerical integration to yield posterior empirical bayes eb estimates of random effects parameters and their corresponding posterior standard errors we incorporate an adjustment of the standard error due to kass and steffey ks 1989 journal of the american statistical association 84 717 726 to account for the variability in estimating the variance component of the random effects distribution in assessing health care providers with respect to adult pneumonia mortality comparisons are made with the penalized quasi likelihood pql approximation approach of breslow and clayton 1993 journal of the american statistical association 88 9 25 and a bayesian approach to make comparisons with an eb method previously reported in the literature we apply these approaches to crossover trials data previously analyzed with the estimating equations eb approach of waclawiw and liang 1994 statistics in medicine 13 541 551 we also perform simulations to compare the proposed ks and pql approaches these two approaches lead to eb estimates of random effects parameters with similar asymptotic bias however for many clusters with small cluster size the proposed ks approach does better than the pql procedures in terms of coverage of nominal 95 confidence intervals for random effects estimates for large cluster sizes and a few clusters the pql approach performs better than the ks adjustment these simulation results agree somewhat with those of the data analyses

a simulation study of estimators for rates of change in longitudinal studies with attrition many longitudinal studies and clinical trials are designed to compare rates of change over time in one or more outcome variables in several groups most such studies have incomplete data because some patients drop out before completing the study the missing data may induce bias and inefficiency in naive estimates of important parameters this paper uses monte carlo methods to compare the bias and efficiency of several two stage estimators of the effect of treatment on the mean rate of change when the missing data arise from one of four processes we also study the validity of confidence intervals and the power of hypothesis tests based on these estimates and their standard errors in general the weighted least squares estimator does relatively well as does an analysis of covariance type estimator proposed by wu et al the best estimates of variance components are based on complete cases or maximum likelihood

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