random copolymers and the morita approximation polymer adsorption and polymer localization we analyse directed walk models of random copolymer adsorption and localization ideally we would like t os olve thequenched problem but it appears to be intractable even for simple directed models the annealed approximation is solvable but is inadequate in the strong interaction regime fo rt he adsorption problem and gives a qualitatively incorrect phase diagram for the localization problem in this paper we treat these directed models using an approximation suggested by morita 1964 j math phys 5 1401 5 in which the proportion of each comonomer is fixed we find that the morita approximation leads to behaviour that is closer to that of the quenched average model and this is particularly interesting in the localization problem where the phase diagram is a tl east qualitatively very similar to that of the quenched average problem we also show that the phase boundaries in the morita approximation are bounds on the locations of the phase boundaries of the quenched model

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

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

a revised bound improvement sequence algorithm abstract in this paper we present a generalization and a computational improvement of the bound improvement sequence algorithm the main computational burden of this algorithm consists in determining whether there exists a feasible point on the objective hyperplane when the algorithm encounters a fixed point by generalizing the algorithm such that the objective function and constraints are treated alike the number of fixed points that are required can be reduced the computational results that we report allow us to conclude that the number of fixed points can generally be reduced for loosely constrained problems for this class of problems the new algorithm appears to be more efficient than a standard mip code such as fmps

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

on case control sampling of clustered data summary we derive the relationship between the population model and the sample model in the case of case control sampling of clustered responses the derived formulae provide insight into why methods that ignore the sampling scheme fail to provide consistent estimators in this case the differences between clustered and independent responses in the context of the case control design are discussed the case control design is known for its efficiency at a fixed sample size when the disease under study is rare it is also potentially useful in clustered data set ups where the interest is in covariate effects or in dependence within clusters neuhaus jewell 1990 showed that sampling clusters instead of individuals can bias the estimation of population parameters if standard logistic regression techniques are used even if the individuals within a cluster are independent they investigated the estimation problem under marginal conditional and random effect models for marginal models they presented expressions for the distribution of disease in the sampled observations in the case of within cluster independence we restrict attention to marginal also called population averaged models zeger liang albert 1988 for these models we extend the results of neuhaus jewell 1990 by presenting expressions for the sample mean and dependence structure in the general case allowing dependence among members of a cluster we envisage a population consisting of a large number of clusters observations within a cluster are dependent but clusters are independent of each other let yij be a binary random variable denoting the jth response in the ith cluster xij a p x 1 covariate vector i 1 2 k j 1 2 ni furthermore let y and xi be the response vector and covariate matrix for the ith cluster respectively suppose that the response is coded so that yj 1 indicates the presence of disease and yij 0 its absence we consider designs in which clusters rather than individual observations are the sampling units specifically let si 1 and si 0 indicate whether the ith cluster was sampled or not respectively the sampling probabilities are defined as oi pr si 1i1 y xi we consider only the case in which oi depends on yi only through t n i 1 and xi neuhaus jewell 1990 refer to this case as sampling with probability dependent on the number of responses in that case oi g t7 xi ni for a known function g we shall write gi ti for brevity a special case is one in which clusters with one or more affected members are sampled with probability rc and clusters with no affected member are sampled with probability co

a bivariate pseudolikelihood for incomplete longitudinal binary data with nonignorable nonmonotone missingness for analyzing longitudinal binary data with nonignorable and non monotone missing responses a full likelihood method is complicated algebraically and often requires intensive computation especially when there are many follow up times as an alternative a pseudo likelihood approach has been proposed in the literature under minimal parametric assumptions this formulation only requires specification of the marginal distributions of the responses and missing data mechanism and uses an independence working assumption however this estimator can be inefficient for estimating both time varying and time stationary effects under moderate to strong within subject associations among repeated responses in this article we propose an alternative estimator based on a bivariate pseudo likelihood and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudo likelihood obtained under the assumption of independence we illustrate the method using longitudinal data on cd4 counts from two clinical trials of hiv infected patients

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

marginal analyses of longitudinal data with an informative pattern of observations we consider solutions to generalized estimating equations with singular working correlation matrices of which the estimator of diggle et al 2007 is a special case we give explicit conditions for consistent estimation when the pattern of observations may be informative in such cases simulations reveal reduced bias and reduced mean squared error compared with existing alternatives a study of peritoneal dialysis is used to illustrate the methodology

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

a shared response model for clustered binary data in developmental toxicity studies summary existing distributions for modeling fetal response data in developmental toxicology such as the beta binomial distribution have a tendency of inflating the probability of no malformed fetuses and hence understating the risk of having at least one malformed fetus within a litter as opposed to a shared probability extra binomial model we advocate a shared response model that allows a random number of fetuses within the same litter to share a common response an explicit formula is given for the probability function and graphical plots suggest that it does not suffer from the problem of assigning too much probability to the event of no malformed fetuses the em algorithm can be used to estimate the model parameters results of a simulation study show that the em estimates are nearly unbiased and the associated confidence intervals based on the usual standard error estimates have coverage close to the nominal level simulation results also suggest that the shared response model estimates of the marginal malformation probabilities are robust to misspecification of the distributional form but not so for the estimates of intralitter correlation and the litter level probability of having at least one malformed fetus the proposed model is fitted to a set of data from the u s national toxicology program for the same dose response relationship the fit based on the shared response distribution is superior to that based on the beta binomial and comparable to that based on the recently proposed q power distribution kuk 2004 applied statistics53 369 386 an advantage of the shared response model over the q power distribution is that it is more interpretable and can be extended more easily to the multivariate case to illustrate this a bivariate shared response model is fitted to fetal response data involving visceral and skeletal malformation

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

analysis of data with multiple sources of correlation in the framework of generalized estimating equations this paper is motivated by a study of physical activity participation habits in african american women with three potential sources of correlation among study outcomes according to method of assessment timing of measurement and intensity of physical activity to adjust for the multiple sources of correlation in this study we implement an approach based on generalized estimating equations that models association via a patterned correlation matrix we present a general algorithm that is relatively straightforward to program an analysis of our physical activity study and some asymptotic relative efficiency comparisons between correctly specifying the correlation structure vs ignoring two sources of correlation in the analysis of data from this study the efficiency comparisons demonstrate that correctly modeling the correlation structure can prevent substantial losses in efficiency in estimation of the regression parameter

improved lagrangean decomposition an application to the generalized assignment problem abstract recently two new ways of obtaining improved lagrangean bounds have been suggested lagrangean decomposition and bound improving sequences in this work we will obtain a lagrangean approach combining the two ideas mentioned above theoretical results are provided about the sharpness of the bounds obtained by the combined approach for the general case as well as an application to the generalized assignment problem computational experience is reported

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

on the localization transition of random copolymers near selective interfaces in this note we consider the de localization transition for random directed 1 1 dimensional copolymers in the proximity of an interface separating selective solvents we derive a rigorous lower bound on the free energy this yields a substantial improvement on the bounds from below on the critical line that were known so far our result implies that the critical curve does not lie below the critical curve set forth by monthus eur phys j b 13 111 130 2000 on the base of a renormalization group analysis we discuss this result in the light of the rigorous and non rigorous approaches present in the literature and by making an analogy with a particular asymptotics of a disordered wetting model we propose a simplified framework in which the question of identifying the critical curve as well as understanding the nature of the transition may be approached

estimating efficacy in clinical trials with clustered binary responses when non compliance occurs in a clinical trial it may be of interest to supplement the intent to treat analysis with an analysis of the efficacy or biological effect of therapy sommer and zeger 1991 developed a method for estimating efficacy applicable to the case of a binary response variable and all or none compliance that assumes independent subject responses we extend this approach to accommodate within cluster correlations as may be expected in a cluster randomized design the method is illustrated using data from a controlled village randomized clinical trial conducted in indonesia to investigate the effect of vitamin a supplementation on mortality in children we find that within cluster correlations for these data are very small and that taking into account the clustering does not substantially affect inferences in this case additional calculations show that small within cluster correlations though larger than those found in the vitamin a data may have a large impact on efficacy inferences we also present the results of a simulation study that demonstrates the validness of the proposed approach for finite sample sizes

copolymers at selective interfaces new bounds on the phase diagram we investigate the phase diagram of disordered copolymers at the interface between two selective solvents and in particular its weak coupling behavior encoded in the slope mc of the critical line at the origin we focus on the directed walk case which has turned out to be in spite of the apparent simplicity extremely challenging in mathematical terms the partition function of such a model does not depend on all the details of the markov chain that models the polymer but only on the time elapsed between successive returns to zero and on whether the walk is in the upper or lower half plane between such returns this observation leads to a natural generalization of the model in terms of arbitrary laws of return times the most interesting case being the one of return times with power law tails with exponent 1 1 2 in the case of the symmetric random walk the main results we present here are

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

the order of the localization transition for a random copolymer we use monte carlo methods and a scaling analysis to estimate the crossover exponent for a model of the localization transition for a random copolymer at the interface between two immiscible liquids the model that we use is a directed walk in two dimensions we find evidence that the nature of the phase transition is different in different regions of the phase diagram this agrees with previous results for a self avoiding walk model we also use exact enumeration and series analysis methods to estimate the locations of the phase boundaries and compare our results to a rigorous bound obtained by partial annealing

tests of independence treatment heterogeneity dose related trend with exchangeable binary data abstract existing methods of testing for treatment effects for clustered binary data include the beta binomial quasilikelihood gee procedures all of these methods revolve around the mean response and the second order correlation however these two parameters alone do not fully determine the effect of treatment this article develops nonparametric likelihood ratio procedures to test for independence heterogeneity dose related trend in dose response studies involving exchangeable binary data the hypotheses of independence heterogeneity trend are expressed in terms of joint probabilities of similar responses among cluster mates constrained maximum likelihood estimates of these probabilities are computed and used to construct test statistics unlike the test statistics for independence and heterogeneity the asymptotic distribution of the likelihood ratio test for trend is not exactly a chi square however an upper bound of its p value is obtained by using a chi squared distribution a set of clustere

localization transition for a polymer near an interface consider the directed process i s i where the second component is simple random walk on mathbb z s 0 0 define a transformed path measure by weighting each n step path with a factor exp lambda sum 1 leq i leq n omega i h sign s i here omega i i geq 1 is an i i d sequence of random variables taking values pm 1 with probability 1 2 acting as a random medium while lambda in 0 infty and h in 0 1 are parameters the weight factor has a tendency to pull the path towards the horizontal because it favors the combinations s i 0 omega i 1 and s i 0 omega i 1 the transformed path measure describes a heteropolymer consisting of hydrophylic and hydrophobic monomers near an oil water interface we study the free energy of this model as n to infty and show that there is a critical curve lambda to h c lambda where a phase transition occurs between localized and delocalized behavior in the vertical direction we derive several properties of this curve in particular its behavior for lambda downarrow 0 to obtain this behavior we prove that as lambda h downarrow 0 the free energy scales to its brownian motion analogue

a saturated model for analyzing exchangeable binary data applications to clinical and developmental toxicity studies abstract correlated binary data occur very frequently in statistical practice in many applications it is reasonable to assume that data from the same cluster are exchangeable such data are commonly encountered in cluster sample surveys teratological experiments ophthalmologic and otolaryngologic studies and other clinical trials the standard methods of analyzing these data include the use of beta binomial models and generalized estimating equations with third and fourth moments specified by working matrices the focus of these procedures is an estimation of the mean and variance parameters more information can be obtained when data are exchangeable by expressing the joint distribution of a set of exchangeable binary random variables in terms of the probability of similar response within cluster this article introduces a procedure for obtaining maximum likelihood estimates of population parameters such as the marginal means moments and correlations of orders two and higher applications are m

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12