infinite time exact observability of volterra systems in hilbert spaces abstract we study infinite time exact observability of volterra systems in hilbert spaces sufficient conditions are established under which infinite time exact observability of a volterra system follows from that of the corresponding cauchy system without convolution term this is done by combining the composition operator method with a result about bounded below composition operators on the hardy space

robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

exact observability conditions for hilbert space dynamical systems connected with riesz basis of divided differences abstract in the paper we consider the problem of exact observability of a general class of distributed parameter systems in hilbert spaces we show that under some conditions on asymptotic behavior of the spectrum of the differential operator the system is not exact observable in default topologies and find a stronger topology for state observation for which the system becomes exactly observable we illustrate this result with a vibrating clamped free timoshenko beam model

a gamma model for extra binomial variation in dilution assays dilution assays are widely used to estimate the concentration of a particular type of cell called a limiting cell in a population of cells from an animal for each animal the response vector is a set of binomial variables derived at different plating frequencies often extra binomial variation is found when dilution assay data are analysed this paper proposes a mixture model where the animal level effects are assumed to have a gamma distribution this leads to more realistic standard errors for the estimates of the limiting cell concentrations

comparison of the proportions of affected relatives of cases and controls analysis and minimum sample size formula the problem of familial aggregation has frequently been approached by comparing the proportion of affected relatives of index cases with the proportion of affected relatives of index controls this type of study has an analogy with the case control design and is frequently analysed as if it was one it is however an essentially different design which may involve dependent observations we show that conventional tests for comparing proportions of affected subjects are still valid with this design we give a formula for computing the minimum sample size required to detect a given degree of aggregation measured by the intracluster correlation coefficient which can be estimated very simply by the difference in proportions of affected relatives in the two groups

use of odds ratio or relative risk to measure a treatment effect in clinical trials with multiple correlated binary outcomes data from the ninds t pa stroke trial in clinical trials when a single outcome is not sufficient to describe the underlying concept of interest it may be necessary to compare treatment groups on multiple correlated outcomes a global test based on a logit link function provides an estimate of the odds ratio for assessing a common treatment effect among correlated binary outcomes in this paper we extend the use of generalized estimating equations gee to calculate a common relative risk from correlated binary outcomes based on a log link function in the context of global tests we discuss the equivalence and difference between logit and log links and their estimates we also derive a formula for calculating a common risk difference between two treatment groups based on multiple correlated binary outcomes with categorical covariates assuming the asymptotic equivalency between the logit and log linear links we discuss the statistical tools to be used in choosing between the logit and log links when models on different links yield contrasting results examples using data from the ninds t pa stroke trials are provided we conclude in a study of correlated binary outcomes that the choice of the logit or log link could be based on a comparison of goodness of link

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

the foundations of finite sample estimation in stochastic processes generally in the literature on stochastic processes estimation is investigated in terms of asymptotic properties in this paper we establish some finite sample optimal estimation let y1 y2 be a discrete stochastic process since we will be discussing results for samples of finite size n we restrict the process to r in the following the term parameter is used in the same broad sense as by godambe thompson 1984 let y be a class of probability distributions f on r and 0 0 f f e jz be a real parameter let hi be a real function of y 1 yi and 0 be such that

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

spectral properties of non homogeneous timoshenko beam and its rest to rest controllability the controllability of a slowly rotating non homogeneous beam clamped to a disc is considered it is assumed that at the beginning the beam remains at the position of rest and it is supposed to rotate by the given angle and stop the movement is governed by the system of two differential equations with non constant coefficients mass density flexural rigidity and shear stiffness to solve the problem of controllability the spectrum of the operator generating the dynamics of the model is studied then the problem of controllability is reduced to the moment problem that is in turn solved with the use of the asymptotics of the spectrum

likelihood methods for incomplete longitudinal binary responses with incomplete categorical covariates summary we consider longitudinal studies in which the outcome observed over time is binary and the covariates of interest are categorical with no missing responses or covariates one specifies a multinomial model for the responses given the covariates and uses maximum likelihood to estimate the parameters unfortunately incomplete data in the responses and covariates are a common occurrence in longitudinal studies here we assume the missing data are missing at random rubin 1976 biometrika63 581 592 since all of the missing data responses and covariates are categorical a useful technique for obtaining maximum likelihood parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 journal of the american statistical association85 765 769 in using the em algorithm with missing responses and covariates one specifies the joint distribution of the responses and covariates here we consider the parameters of the covariate distribution as a nuisance in data sets where the percentage of missing data is high the estimates of the nuisance parameters can lead to highly unstable estimates of the parameters of interest we propose a conditional model for the covariate distribution that has several modeling advantages for the em algorithm and provides a reduction in the number of nuisance parameters thus providing more stable estimates in finite samples

exact controllability for the semilinear mindlin timoshenko system abstract we consider the dynamical one dimensional mindlin timoshenko system for beams we obtain a global exact controllability result for this semilinear system with superlinear nonlinearities for this purpose we establish an observability estimate for the linearized system with bounded potentials moreover we obtain an explicit estimate of the observability constant in terms of the norms of the potentials such an estimate is obtained by a combination of a pointwise estimate a global carleman estimate for hyperbolic differential operators and an analysis of the regularity of solutions of a auxiliary optimal control problem the controllability of the semilinear system is proved using the hilbert uniqueness method hum and a fixed point technique

exact observability and controllability for linear neutral type systems the problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach the duality with the exact controllabil ity problem is the main tool it is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system a nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator the characterization of the duality between controllability and observability is deduced and then observability conditions are obtained

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

likelihood inference for exchangeable binary data with varying cluster sizes ce papier etudie l estimation au maximum de vraisemblance dans des modeles satures et insatures pour des donnees binaires correlees echangeables lorsqu on dispose d un echantillon de clusters independants de tailles variables nous discutons plusieurs parametrisations de ces modeles et nous proposons l utilisation de l algorithme em pour obtenir des estimations du maximum de vraisemblance la methodologie est illustree par des applications a une etude d agregation familiale de maladie et a la construction d un essai randomise par groupe pour la prevention du cancer

information ratio test for model misspecification in quasi likelihood inference in this article we focus on the circumstances in quasi likelihood inference that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment but the estimation efficiency could be diminished due to misspecification of the second moment we propose an information ratio ir statistic to test for model misspecification of the variance covariance structure through a comparison between two forms of information matrix the negative sensitivity matrix and the variability matrix we establish asymptotic distributions of the proposed ir test statistics we also suggest an approximation to the asymptotic distribution of the ir statistic via a perturbation resampling method moreover we propose a selection criterion based on the ir test to select the best fitting variance covariance structure from a class of candidates through simulation studies it is shown that the ir statistic provides a powerful statistical tool to detect different scenarios of misspecific

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

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

on linear and quadratic estimating functions summary in some cases maximum quasi likelihood estimation which is at the core of glim can fail to give reasonable results a more general class of estimating functions is investigated which avoids such failure and also is not restricted to the particular forms of mean and variance function of glim

a note on implementation of decaying product correlation structures for quasi least squares this note implements an unstructured decaying product matrix via the quasi least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations the structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix it is straightforward to show that the quasi least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure furthermore subject to conditions that are easily checked the quasi least squares estimators are valid for longitudinal bernoulli data we demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable

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

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

logistic regression for dependent binary observations summary the likelihood of a set of binary dependent outcomes with or without explanatory variables is expressed as a product of conditional probabilities each of which is assumed to be logistic the models are called regressive logistic models they provide a simple but relatively unknown parametrization of the multivariate distribution they have the theoretical and practical advantage that they can be analyzed and fitted as in logistic regression for independent outcomes and with the same computer programs the paper is largely expository and is intended to motivate the development and usage of the regressive logistic models the discussion includes serially dependent outcomes equally predictive outcomes more specialized patterns of dependence multidimensional tables and three examples this paper seeks to promote the development and usage of a simple but relatively unknown approach to the specification of models for dependent binary outcomes that are useful in situations where it is apt to describe the dependence in terms of conditional probabilities the joint probability is decomposed into a product of successive conditional probabilities each of which is assumed to be univariate logistic since the probability of an observation is conditioned on all preceding observations the models will be referred to as regressive logistic models two broad situations are distinguished in this paper the first concerning sequences of binary outcomes possibly with measures on associated explanatory variables can usually be supported by simple patterns of dependence these will be discussed in sections 2 5 the second broad situation concerns dependent binary outcomes crossclassified into multidimensional tables that admit a fuller parametrization this is discussed in section 6 for all the regressive logistic models discussed here the parametrization is such that jointly dependent binary observations with or without explanatory variables can be fitted with existing computer programs for the standard logistic regression for independent observations some of the possibilities of the approach are illustrated with real data in section 8

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

galilei covariance and quasi free representations of fermi fields some quasi free irreducible representations of the car algebra of a non relativistic free fermi field are constructed which are covariant under certain subgroups of the extended galilei group the construction of fully covariant but reducible representations as direct integrals of partially covariant ones is described this method is also applicable to arbitrary c algebras and other covariance groups

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

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

marginal modelling of multivariate categorical data this paper describes likelihood methods of analysis for multivariate categorical data the joint distribution is specified in terms of marginal mean functions and pairwise and higher order association measures for the association the emphasis is on global odds ratios the method allows flexible formulation of a broad class of designs such as repeated measurements longitudinal studies interrater agreement and cross over trials the proposed model can be used for parameter estimation and hypothesis testing simple fitting algorithms are proposed the method is illustrated using a data example

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

bivariate binary data analysis with nonignorably missing outcomes one of the objectives in the northern manhattan stroke study is to investigate the impact of stroke subtype on the functional status 2 years after the first ischemic stroke a challenge in this analysis is that the functional status at 2 years after stroke is not completely observed in this paper we propose a method to handle nonignorably missing binary functional status when the baseline value and the covariates are completely observed the proposed method consists of fitting four separate binary regression models for the baseline outcome the outcome 2 years after the stroke the product of the previous two and finally the missingness indicator we then conduct a sensitivity analysis by varying the assumptions about the third and the fourth binary regression models our method belongs to an imputation paradigm and can be an alternative to the weighting method of rotnitzky and robins 1997 statistics in medicine 16 81 102 a jackknife variance estimate is proposed for the variance of the resulting estimate the proposed analysis can be implemented using statistical software such as sas

detectability observability and lyapunov type theorems of linear discrete time varying stochastic systems with multiplicative noise abstractthe objective of this paper is to study detectability observability and related lyapunov type theorems of linear discrete time time varying stochastic systems with multiplicative noise some new concepts such as uniform detectability k exact detectability resp kwft exact detectability kft exact detectability kn exact detectability and k exact observability resp kwft exact detectability kft exact detectability kn exact detectability are introduced respectively and nice properties associated with uniform detectability exact detectability and exact observability are also obtained moreover some lyapunov type theorems associated with generalised lyapunov equations and exponential stability in mean square sense are presented under uniform detectability kn exact observability and kn exact detectability respectively

on the hautus test for exponentially stable c_0 groups for finite dimensional systems the hautus test is a well known and easy checkable condition for observability russell and weiss siam j control optim 32 1994 pp 1 23 suggested an infinite dimensional version of the hautus test which is necessary for exact observability and sufficient for approximate observability of exponentially stable systems in this paper it is shown that this hautus test is sufficient for exact observability of certain exponentially stable systems generated by a c 0 group and it is proved that the hautus test is in general not sufficient for approximate observability of strongly stable systems even if the system is modeled by a contraction semigroup and the observation operator is bounded

some covariant representations of massless fermi fields studies the class of pure quasi free gauge invariant states of the fermion algebra the authors show that the question of g covariance of the corresponding representations i e implementability of some group g of one particle symmetry transformations is related to a cohomology group with values in the hilbert schmidt class in four dimensional space time this cohomology is nontrivial thus leading to g covariant non fock representations when g is taken to be the space time translation group together with rotations or space time translations together with boosts in one direction and rotations about it and the fermion mass is zero in two space time dimensions some new fully poincare covariant representations for free massless fermions are constructed

analysis of serially correlated data using quasi least squares summary quasi least squares qls a marginal statistical approach via generalized estimating equations that is described in the balanced data setting by chaganty 1997 journal of statistical planning and inference 63 39 54 allows for application of a wide range of working correlation structures when analyzing serially correlated data we extend the application of qls to serially correlated unequally spaced and unbalanced data using three useful working correlation models the firstorder autoregressive ar 1 the markov and the generalized markov structure described by nuniez anton and woodworth 1994 biometrics 50 445 456 we compare qls and the original formulation of the generalized estimating equation approach gee for these structures demonstrating that i infeasibility of the gee correlation parameter estimates can be a problem ii it is difficult to obtain consistent moment estimates of the correlation parameters for the generalized markov structure and iii the use of qls can lead to reduced mean square error of the estimate of the regression parameter for small samples of moderately correlated data to choose between alternative correlation models we propose a criterion that is based on the principle of generalized least squares finally data for which the generalized markov structure is appropriate are analyzed to demonstrate the use of qls in selecting a suitable working correlation structure and identifying in this paper we apply a statistical method based on the generalized estimating equation approach of liang and zeger 1986 to the analysis of longitudinal data that may be difficult to analyze using other established methods we consider repeated measures data collected by taking measurements of an outcome variable and associated covariates on each of a group of independent subjects our primary data analysis goal is to identify important covariates and to explain their effect on the marginal mean of the outcome variable while also accounting for the correlation among observations on each subject accomplishing this research objective may be difficult due to certain conditions that are typical in longitudinal studies the timing and total number of measurements taken may vary from subject to subject so that the data may be unbalanced and unequally spaced the outcome variable may not be normally distributed the intrasubject correlation may be described using a time dependent pattern for example the correlation between two measurements may decrease as they become more

use of quasi least squares to adjust for two levels of correlation this article considers data with two levels of association our motivating example is an international intervention trial with repeated observations on subjects who reside within geographically defined clusters to account for the potential correlation within clusters and within the repeated measurements that pertain to each subject we apply a method based on generalized estimating equations for a correlation structure proposed by lefkopoulou moore and ryan 1989 journal of the american statistical association 84 810 815

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

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

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

exact observability of a 1 dimensional wave equation on a noncylindrical domain we discuss admissibility and exact observability estimates of boundary observation and interior point observation of a 1 dimensional wave equation on a time dependent domain for sufficiently regular boundary functions we also discuss moving observers inside the noncylindrical domain and simultaneous observability results

on the use of historical control data to estimate dose response trends in quantal bioassay new tests for trend in proportions in the presence of historical control data are proposed one such test is a simple score statistic based on a binomial likelihood for the current study and beta binomial likelihoods for each historical control series a closely related trend statistic based on estimating equations is also proposed trend statistics that allow overdispersed proportions in the current study are also developed including a version of tarone s 1982 biometrics 38 215 220 test that acknowledges sampling variation in the beta distribution parameters and a trend statistic based on estimating equations each such trend test is evaluated with respect to size and power under both binomial and beta binomial sampling conditions for the current study and illustrations are provided

ullrich conditions and smoothness of reachable states of a rotating beam we consider a timoshenko beam slowly rotating in a horizontal plane for this model we study the problem of description of all states reachable from a position of rest this problem is equivalent to a non fourier trigonometric problem with respect to a system with two asymptotically close families of exponentials technically such a problem can be analyzed in terms of divided differences of the moment sequences it turns out however that the set of reachable states admits an essentially more convenient analytical description in terms of smoothness of final states

the hilbert schmidt cohomology for the poincare group we consider cocycles for the poincart group pi satisfying gk v k v g where v is an irreducible strongly continuous representation of pi and g e b y the hilbert schmidt operators on the representation space 3 of v it is shown that i ii must be of the form g v av a with a e b x the method can be extended to analyse the cocycles of products of arbitrary irreducible representations of pi providing neither representation belongs to the little group of vanishing four momentum

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

marginal models for longitudinal continuous proportional data continuous proportional data arise when the response of interest is a percentage between zero and one e g the percentage of decrease in renal function at different follow up times from the baseline in this paper we propose methods to directly model the marginal means of the longitudinal proportional responses using the simplex distribution of barndorff nielsen and jorgensen that takes into account the fact that such responses are percentages restricted between zero and one and may as well have large dispersion parameters in such a marginal model are estimated using an extended version of the generalized estimating equations where the score vector is a nonlinear function of the observed response the method is illustrated with an ophthalmology study on the use of intraocular gas in retinal repair surgeries

the intraclass correlation coefficient distribution free definition and test a definition of the intraclass correlation coefficient is given on the basis of a general class of random effect model the conventional intraclass correlation coefficient and the intracluster correlation coefficient for binary data are both particular cases of the generalized coefficient we derive the score test for the hypothesis of null intraclass correlation in the exponential family the statistic does not depend on the particular distribution in this family and is related to the pairwise correlation coefficient the test can be adjusted for explanatory variables