the analysis of rates using poisson regression models models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters estimates of the parameters can be obtained by means of iteratively reweighted least squares irls when the events of interest follow the poisson distribution the irls algorithm is equivalent to using the method of scoring to obtain maximum likelihood ml estimates the general poisson regression models include log linear quasilinear and intrinsically nonlinear models the approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model standard statistical packages that support irls can then be used to obtain ml estimates their asymptotic covariance matrix and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space applications of these methods to epidemiologic follow up studies with the data organized into a life table type of format are discussed the method is illustrated by using a nonlinear model derived from the multistage theory of carcinogenesis to analyze lung cancer death rates among british physicians who were regular cigarette smokers

sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution statistical inference based on correlated count measurements are frequently performed in biomedical studies most of existing sample size calculation methods for count outcomes are developed under the poisson model deviation from the poisson assumption equality of mean and variance has been widely documented in practice which indicates urgent needs of sample size methods with more realistic assumptions to ensure valid experimental design in this study we investigate sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution this approach is flexible to accommodate overdispersion and unequal measurement intervals as well as arbitrary randomization ratios missing data patterns and correlation structures importantly the derived sample size formulas have closed forms both for the comparison of slopes and for the comparison of time averaged responses which greatly reduces the burden of implementation in practice we conducted extensive simulation to demonstrate that the proposed method maintains the nominal levels of power and type i error over a wide range of design configurations we illustrate the application of this approach using a real epileptic trial

quantum stochastic calculus associated with quadratic quantum noises we first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non solvable lie algebra consisting of all linear combinations of the generalized gross laplacian and its adjoint annihilation operator creation operator conservation and time and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes and the quantum ito formula is revisited the existence and uniqueness of solution of a quantum stochastic differential equation is proved the unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined the quantum stochastic calculus extends the hudson parthasarathy quantum stochastic calculus

coping with extra poisson variability in the analysis of factors influencing vaginal ring expulsions the vaginal ring is one method of contraception currently under investigation and development by the human reproduction programme of who one factor that reduces its acceptability is that some women experience involuntary expulsions of the ring who have collected prospective data on 1005 women from 19 centres worldwide to investigate various aspects of ring use including factors that might affect expulsions for each subject the data include number of expulsions age parity ponderal index number of days of ring use and health care centre to model the factors influencing expulsion the number of expulsions was first considered as a poisson variate with mean directly proportional to the log of the duration of ring use such a model gave a poor description of the data and it appeared that the number of expulsions was considerably over dispersed for an assumed poisson variate this paper examines a variety of strategies for coping with the resulting lack of fit of the model it turns out that a truncated poisson model gives a better description of the expulsion data and that health care centre and parity influence the rates

autoregressive age period cohort models summary age period cohort analysis of vital data has received much attention recently and it is already well known that the exact linear relation of the three time factors creates a non identifiability problem previous studies have shown that the curvature terms of these factors are estimable but the linear trends are not however little attention has been paid to the possibility that the effects due to cohort and or period might change through time stochastically rather than deterministically and hence display a stochastic trend in this paper we model the cohort effects as an ar 1 process and use lung cancer mortality data from 1966 to 1990 for males in taiwan as an example the parameters are identifiable in the proposed model and the estimates are found to be stable however the assumption made in the model should be carefully considered before using our methodology

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

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

estimation of the mean function with panel count data using monotone polynomial splines we study nonparametric likelihood based estimators of the mean function of counting processes with panel count data using monotone polynomial splines the generalized rosen algorithm proposed by zhang jamshidian 2004 is used to compute the estimators we show that the proposed spline likelihood based estimators are consistent and that their rate of convergence can be faster than n 1 3 simulation studies with moderate samples show that the estimators have smaller variances and mean squared errors than their alternatives proposed by wellner zhang 2000 a real example from a bladder tumour clinical trial is used to illustrate this method

estimating latent distributions in recurrent choice data this paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data these choice models are derived by specifying elements of the choice process at the individual level probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior due to the explicit consideration of random effect sources the choice models are parsimonious and readily interpretable an easy to implement em algorithm is presented for parameter estimation two applications illustrate the proposed approach

regression analysis of overdispersed correlated count data with subject specific covariates a robust likelihood approach for the analysis of overdispersed correlated count data that takes into account cluster varying covariates is proposed we emphasise two characteristics of the proposed method that the correlation structure satisfies the constraints on the second moments and that the estimation of the correlation structure guarantees consistent estimates of the regression coefficients in addition we extend the mean specification to include within and between cluster effects the method is illustrated through the analysis of data from two studies in the first study cross sectional count data from a randomised controlled trial are analysed to evaluate the efficacy of a communication skills training programme the second study involves longitudinal count data which represent counts of damaged hand joints in patients with psoriatic arthritis motivated by this study we generalize our model to accommodate for a subpopulation of patients who are not susceptible to the development of damaged hand joints

bayesian modeling of multiple lesion onset and growth from interval censored data summary in studying rates of occurrence and progression of lesions or tumors it is typically not possible to obtain exact onset times for each lesion instead data consist of the number of lesions that reach a detectable size between screening examinations along with measures of the size severity of individual lesions at each exam time this interval censored data structure makes it difficult to properly adjust for the onset time distribution in assessing covariate effects on rates of lesion progression this article proposes a joint model for the multiple lesion onset and progression process motivated by cross sectional data from a study of uterine leiomyoma tumors by using a joint model one can potentially obtain more precise inferences on rates of onset while also performing onset time adjusted inferences on lesion severity following a bayesian approach we propose a data augmentation markov chain monte carlo algorithm for posterior computation

empirical comparisons of proportional hazards and logistic regression models we compare parameter estimates from the proportional hazards model the cumulative logistic model and a new modified logistic model referred to as the person time logistic model with the use of simulated data sets and with the following quantities varied disease incidence risk factor strength length of follow up the proportion censored non proportional hazards and sample size parameter estimates from the person time logistic regression model closely approximated those from the cox model when the survival time distribution was close to exponential but could differ substantially in other situations we found parameter estimates from the cumulative logistic model similar to those from the cox and person time logistic models when the disease was rare the risk factor moderate and censoring rates similar across the covariates we also compare the models with analysis of a real data set that involves the relationship of age race sex blood pressure and smoking to subsequent mortality in this example the length of follow up among survivors varied from 5 to 14 years and the cox and person time logistic approaches gave nearly identical results the cumulative logistic results had somewhat larger p values but were substantively similar for all but one coefficient the age race interaction the latter difference reflects differential censoring rates by age race and sex

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

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

semiparametric bayesian analysis of survival data abstract this review article investigates the potential of bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function the nonparametric part of every model is assumed to be a realization of a stochastic process the parametric part which may include a regression parameter or a parameter quantifying the heterogeneity of a population is assumed to have a prior distribution with possibly unknown hyperparameters careful applications of some recently popular computational tools including sampling based algorithms are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures the methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies here we focus on univariate survival data in the presence of fixed and time dependent covariates multiple event time data for repeated nonfatal events

power analyses for longitudinal study designs with missing data existing methods for power analysis for longitudinal study designs are limited in that they do not adequately address random missing data patterns although the pattern of missing data can be assessed during data analysis it is unknown during the design phase of a study the random nature of the missing data pattern adds another layer of complexity in addressing missing data for power analysis in this paper we model the occurrence of missing data with a two state first order markov process and integrate the modelling information into the power function to account for random missing data patterns the markov model is easily specified to accommodate different anticipated missing data processes we develop this approach for the two most popular longitudinal models the generalized estimating equations gee and the linear mixed effects model under the missing completely at random mcar assumption for gee we also limit our consideration to the working independence correlation model the proposed methodology is illustrated with numerous examples that are motivated by real study designs

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

maximum likelihood estimation for cytogenetic dose response curves in vitro dose response curves are used to describe the relation between chromosome aberrations and radiation dose for human lymphocytes the lymphocytes are exposed to low let radiation and the resulting dicentric chromosome aberrations follow the poisson distribution the expected yield depends on both the magnitude and the temporal distribution of the dose a general dose response model that describes this relation has been presented by kellerer and rossi 1972 current topics on radiation research quarterly 8 85 158 1978 radiation research 75 471 488 using the theory of dual radiation action two special cases of practical interest are split dose and continuous exposure experiments and the resulting dose time response models are intrinsically nonlinear in the parameters a general purpose maximum likelihood estimation procedure is described and estimation for the nonlinear models is illustrated with numerical examples from both experimental designs poisson regression analysis is used for estimation hypothesis testing and regression diagnostics results are discussed in the context of exposure assessment procedures for both acute and chronic human radiation exposure

mixed model analysis of a censored normal distribution with reference to animal breeding a mixed model procedure for analysis of censored data assuming a multivariate normal distribution is described a bayesian framework is adopted which allows for estimation of fixed effects and variance components and prediction of random effects when records are left censored the procedure can be extended to right and two tailed censoring the model employed is a generalized linear model and the estimation equations resemble those arising in analysis of multivariate normal or categorical data with threshold models estimates of variance components are obtained using expressions similar to those employed in the em algorithm for restricted maximum likelihood reml estimation under normality

application of sample survey methods for modelling ratios to incidence densities we describe ratio estimation methods for multivariately analysing incidence densities from prospective epidemiologic studies commonly used in survey data analysis these ratio methods require minimal distributional assumptions and take into account the random variability in the at risk periods we illustrate their application with data from a study of lower respiratory illness lri in children during the first year of life one question of interest is whether children with passive exposure to tobacco smoke have a higher rate of lri on average than those with no exposure and in a setting where age of child and season are taken into account a second question is whether the relationship persists after adjusting for background variables such as family s socioeconomic status crowding in the home race and type of feeding the basic strategy consists of a two step process in which we first estimate subgroup specific incidence densities and their covariance matrix via a first order taylor series approximation these estimates are used to test for differences in marginal rates of lri between children exposed to tobacco smoke and those not exposed we then fit a log linear model to the estimated ratios in order to test for significant covariate effects the ability to produce direct estimates of adjusted incidence density ratios for risk factors of interest is an important advantage of this approach for comparison purposes and to address the limitations of the ratio method with respect to the number of covariates that can be controlled simultaneously we consider survey logistic regression methods for the example data as well as logistic and poisson regression models fitted via generalized estimating equation methods although the analysis strategy is illustrated with illness data from an epidemiologic study the context of application is broader and includes for example data on adverse events from a clinical trial

a serially correlated gamma frailty model for longitudinal count data a poisson gamma model is introduced to account for between subjects heterogeneity and within subjects serial correlation occurring in longitudinal count data the model extends the usual time constant shared frailty approach to allow time varying serially correlated gamma frailty whilst retaining standard marginal assumptions a composite likelihood approach to estimation and testing for serial correlation is proposed the work is motivated by a clinical trial on patient controlled analgesia where the number of analgesic doses taken by hospital patients in successive time intervals following abdominal surgery is recorded

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 semiparametric pseudolikelihood estimation method for panel count data in this paper we study panel count data with covariates a semiparametric pseudolikelihood estimation method is proposed based on the assumption that given a covariate vector z the underlying counting process is a nonhomogeneous poisson process with the conditional mean function given by e n t z 0 t exp 0 z the proposed estimation method is shown to be robust in the sense that the estimator converges to its true value regardless of whether or not n t is a conditional poisson process given z an iterative numerical algorithm is devised to compute the semiparametric maximum pseudolikelihood estimator of 0 0 the algorithm appears to be attractive especially when 0 is a high dimensional regression parameter some simulation studies are conducted to validate the method finally the method is applied to a real dataset from a bladder tumour study

dual wdvv equations in n 2 supersymmetric yang mills theory this paper studies the dual form of witten dijkgraaf verlinde verlinde wdvv equations in n 2 supersymmetric yang mills theory by applying a duality transformation to wdvv equations the dual wdvv equations called in this paper are nonlinear differential equations satisfied by dual prepotential and are found to have the same form with the original wdvv equations however in contrast with the case of weak coupling calculus the perturbative part of dual prepotential itself does not satisfy the dual wdvv equations nevertheless it is possible to show that the nonperturbative part of dual prepotential can be determined from dual wdvv equations provided the perturbative part is given as an example the su 4 case is presented the nonperturbative dual prepotential derived in this way is consistent to the dual prepotential obtained by d hoker and phong

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 gamma frailty poisson model for the nonparametric estimation of panel count data summary in this article we study nonparametric estimation of the mean function of a counting process with panel observations we introduce the gamma frailty variable to account for the intracorrelation between the panel counts of the counting process and construct a maximum pseudo likelihood estimate with the frailty variable three simulated examples are given to show that this estimation procedure while preserving the robustness and simplicity of the computation improves the efficiency of the nonparametric maximum pseudo likelihood estimate studied in wellner and zhang 2000 annals of statistics28 779 814 a real example from a bladder tumor study is used to illustrate the method

two estimators of the mean of a counting process with panel count data we study two estimators of the mean function of a countingprocess based on panel count data the setting for panel count data is one in which n independent subjects each with a counting process with common mean function are observed at several possibly different times duringa study following a model proposed by schick and yu we allow the number of observation times and the observation times themselves to be random variables our goal is to estimate the mean function of the counting process we show that the estimator of the mean function proposed by sun and kalbfleisch can be viewed as a pseudo maximum likelihood estimator when a non homogeneous poisson process model is assumed for the counting process we establish consistency of both the nonparametric pseudo maximum likelihood estimator of sun and kalbfleisch and the full maximum likeli hood estimator even if the underlying counting process is not a poisson process we also derive the asymptotic distribution of both estimators at a fixed time t and compare the resulting theoretical relative efficiency with finite sample relative efficiency by way of a limited monte carlo study

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

implementation problem for the canonical commutation relation in terms of quantum white noise derivatives the implementation problem for the canonical commutation relation is reduced to a system of differential equations for fock space operators containing new type of derivatives we solve these differential equations systematically by means of quantum white noise calculus and obtain the solution to the implementation problem

a semiparametric model for the analysis of recurrent event panel data summary in many longitudinal studies interest focuses on the occurrence rate of some phenomenon for the subjects in the study when the phenomenon is nonterminating and possibly recurring the result is a recurrent event data set examples include epileptic seizures and recurrent cancers when the recurring event is detectable only by an expensive or invasive examination only the number of events occurring between follow up times may be available this article presents a semiparametric model for such data based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function a random subject specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data estimators are determined from quasi likelihood estimating functions because only first and second moment assumptions are required for quasi likelihood the method is more robust than those based on the specification of a full parametric likelihood consistency of the estimators depends only on the assumption of the proportional intensity model the semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators as with semiparametric methods in survival analysis the method provides useful diagnostics for specific parametric models including a quasi score statistic for testing specific baseline intensity functions the techniques are used to analyze cancer recurrences and a pheromone based mating disruption experiment in moths a simulation study confirms that for many practical situations the estimators possess appropriate small sample characteristics

nonparametric k sample tests with panel count data we study the nonparametric k sample test problem with panel count data the asymptotic normality of a smooth functional of the nonparametric maximum pseudolikelihood estimator wellner zhang 2000 is established under some mild conditions we construct a class of easy to implement nonparametric tests for comparing mean functions of k populations based on this asymptotic normality we conduct various simulations to validate and compare the tests the simulations show that the tests perform quite well and generally have good power to detect differences among the mean functions the method is illustrated with a real life example

bias reduction of approximate maximum likelihood estimates for heritability in threshold models approximate maximum likelihood estimates such as penalized quasi likelihood and iterated reweighted reml estimates for heritability or intraclass correlation in threshold models for binary data can be seriously biased two approaches to correct for this bias are studied with emphasis on animal breeding models for binary data scope for reduction of bias of heritability estimates is found to be slim because of the commonly large number of fixed effects in animal breeding models minimal dimensions for the data are identified such that bias and root mean squared error are of modest size and useful inference on heritability or intraclass correlation is feasible

the natural variability of vital rates and associated statistics the first concern of this work is the development of approximations to the distributions of crude mortality rates age specific mortality rates age standardized rates standardized mortality ratios and the like for the case of a closed population or period study it is found that assuming poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate poisson distribution it is suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories such a model is fit to mortality data for canadian females classified by age and year a dynamic variant of the model is further fit to the time series of total female deaths alone by year the models with extra poisson variation are found to lead to substantially improved fits excerpt

mirror symmetry and rational curves on quintic threefolds a guide for mathematicians we give a mathematical account of a recent string theory calcula tion which predicts the number of rational curves on the generic quintic three fold our account involves the interpretation of yukawa couplings in terms of variations of hodge structure a new q expansion principle for functions on the moduli space of calabi yau manifolds and the mirror symmetry phe nomenon recently observed by string theorists department of mathematics duke university durham north carolina 27706 e mail address drm math duke edu this content downloaded from 157 55 39 224 on wed 14 dec 2016 04 59 36 utc all use subject to http about jstor org terms

analyzing multiple emotions over time by autoregressive negative multinomial regression models abstract this article presents an autoregressive random coefficient model with overdispersed negative multinomial marginal distributions for the analysis of heterogeneity and serial dependencies in multivariate longitudinal count data the model structure consists of four components that take into account a individual difference effects b random time effects c multiple event categories and d autodependencies the last component is based on a stochastic integer valued autoregressive process proposed by mckenzie the model is applied to analyze count data from a panel diary study about the relationship between personality factors and emotion experiences it is shown that there are large and stable individual personality differences in the incidence and duration of self reported emotional experiences theoretical and clinical implications of this result are discussed

maximum likelihood estimation and large sample inference for generalized linear and nonlinear regression models summary the class of generalized linear models is extended to allow for correlated observations nonlinear models and error distributions not of the exponential family form the extended class of models include a number of important examples particularly of the composite transformational type large sample inference and maximum likelihood estimation for the extended class of generalized linear models are discussed and the analysis of deviance is generalized to the extended class of models calculation of the maximum likelihood estimate for a general likelihood by fisher s scoring method and a related method is considered and the relation with the gauss newton method is discussed

inference for means and covariances of point processes through estimating functions summary liang zeger 1986 introduced methodology for the analysis of longitudinal data that provides an alternative to likelihood based inference they considered modelling the marginal means of the response follow up measures and proposed the use of unbiased estimating functions to handle inference here we wish to do the same for point or jump processes we consider parametric models for the marginal means and possibly the covariance structures of processes that allow covariates inference is performed with unbiased estimating functions and robust variance estimates are provided the optimal linear estimating function is presented in general the special case of mixed poisson processes is discussed in further detail with an asymptotic efficiency study and simulations

goodness of fit in armitage doll poisson models summary we consider testing the adequacy of multistage models of cancer induction for poisson event rates depending on age and exposure to environmental agents the space of time and covariates is partitioned for comparison of observed and fitted event counts over regions of the partition a test of fit based on the quadratic score statistic is proposed to assess overall residual error between observed and fitted counts the limiting distribution of the test statistic is central chi squared under the null hypothesis and noncentral chi squared under local alternatives standardized residuals and tests of trend for individual regions of the partition are given the method is applied to lung cancer incidence rates among british physicians grouped by age by amount of smoking and by decile of estimated risk the relation of the proposed method to chi squared frequency tests and extensions to casecontrol studies are considered

annihilation derivative creation derivative and representation of quantum martingales on the basis of the quantum white noise theory we introduce the notion of creation and annihilation derivatives of fock space operators and study the differentiability of white noise operators we define the hitsuda skorohod quantum stochastic integrals by the adjoint actions of quantum stochastic gradients and show explicit formulas for their creation and annihilation derivatives as an application we derive direct formulas for the integrands in the quantum stochastic integral representation of a regular quantum martingale

an inar 1 negative multinomial regression model for longitudinal count data this paper discusses a regression model for the analysis of longitudinal count data observed in a panel study an integer valued first order autoregressive inar 1 poisson process is adapted to represent time dependent correlations among the counts by combining the inar 1 representation with a random effects approach a new negative multinomial distribution is derived that includes the bivariate negative binomial distribution proposed by edwards and gurland 1961 and subrahmaniam 1966 as a special case a detailed analysis of the relationship between personality factors and daily emotion experiences illustrates the approach

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

the analysis of binomial data by a generalized linear mixed model summary methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution the method estimates the parameters directly on the underlying scale for a balanced one way random effects model the variance estimator simplifies to the usual analysis of variance one the estimation of variances and the prediction of random effects for binomial traits is required by animal breeders the predictors given are analogous to best linear unbiased predictors henderson 1973 but differ from those presented by harville mee 1984

two likelihood based semiparametric estimation methods for panel count data with covariates we consider estimation in a particular semiparametric regression model for the mean of a counting process with panel count data the basic model assumption is that the conditional mean function of the counting process is of the form efn t jzg exp fl t z 0 t where z is a vector of covariates and 0 is the baseline mean function the panel count observation scheme involves observation of the counting processn for an individual at a random number k of random time points both the number and the locations of these time points may difier across individuals we study semiparametric maximum pseudo likelihood and maximum likelihood estimators of the unknown parameters fl0 0 derived on the basis of a nonhomogeneous poisson process assumption the pseudo likelihood estimator is fairly easy to compute while the maximum likelihood estimator poses more challenges from the computational perspective we study asymptotic properties of both estimators assuming that the proportional mean model holds but dropping the poisson process assumption used to derive the estimators in particular we establish asymptotic normality for the estimators of the regression parameter fl0 under appropriate hypotheses the results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

ϕ derivations on operators on q fock space we study the q creation and q annihilation derivatives of operators on q fock space and then the derivatives are derivations with respect to the q wick product where is a homomorphism with respect to the q wick product which provide interesting non trivial examples of abstract derivation

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

improved likelihood inference for discrete data reference stat article 2006 001doi 10 1111 j 1467 9868 2006 00548 xview record in web of science record created on 2006 04 21 modified on 2017 05 12

regression analysis of panel count data with covariate dependent observation and censoring times panel count data often occur in a long term study where the primary end point is the time to a specific event and each subject may experience multiple recurrences of this event furthermore suppose that it is not feasible to keep subjects under observation continuously and the numbers of recurrences for each subject are only recorded at several distinct time points over the study period moreover the set of observation times may vary from subject to subject in this paper regression methods which are derived under simple semiparametric models are proposed for the analysis of such longitudinal count data especially we consider the situation when both observation and censoring times may depend on covariates the new procedures are illustrated with data from a well known cancer study

a mixed model procedure for analyzing ordered categorical data a mixed model procedure is developed for predicting the value of an ordered categorical response from knowledge of various predictor variables this procedure resembles the best linear unbiased procedure of henderson 1975 biometrics 31 423 447 for predicting the value of a quantitative response the approach is based on a mixed model version of the threshold model in which it is assumed that the observed category is determined by the value of an underlying unobservable continuous response that follows a mixed linear model the results are illustrated by an application to the problem of predicting the degree of difficulty that will be experienced by a dairy cow in the birth of her calf

one instanton prepotentials from wdvv equations in n 2 supersymmetric su 4 yang mills theory prepotentials in n 2 supersymmetric yang mills theories are known to obey nonlinear partial differential equations called witten dijkgraaf verlinde verlinde wdvv equations in this paper the prepotentials at the one instanton level in n 2 supersymmetric su 4 yang mills theory are studied from the standpoint of wdvv equations especially it is shown that the one instanton prepotentials are obtained from wdvv equations by assuming the perturbative prepotential and by using the scaling relation as a subsidiary condition but are determined without introducing the seiberg witten curve in this way various one instanton prepotentials which satisfy both wdvv equations and the scaling relation can be derived but it turns out that among them there exist one instanton prepotentials which coincide with the instanton calculus

estimation of variance in cox s regression model with shared gamma frailties the cox regression model with a shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times estimation in this model when the frailties are assumed to follow a gamma distribution is reviewed and we address the problem of obtaining variance estimates for regression coefficients frailty parameter and cumulative baseline hazards using the observed nonparametric information matrix a number of examples are given comparing this approach with fully parametric inference in models with piecewise constant baseline hazards

mixed poisson likelihood regression models for longitudinal interval count data summary in many longitudinal studies it is desired to estimate and test the rate over time of a particular recurrent event often only the event counts corresponding to the elapsed time intervals between each subject s successive observation times and baseline covariate data are available the intervals may vary substantially in length and number between subjects so that the corresponding vectors of counts are not directly comparable a family of poisson likelihood regression models incorporating a mixed random multiplicative component in the rate function of each subject is proposed for this longitudinal data structure a related empirical bayes estimate of random effect parameters is also described these methods are illustrated by an analysis of dyspepsia data from the national cooperative gallstone study

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

effects of exposure misclassification on regression analyses of epidemiologic follow up study data in epidemiologic studies subjects are often misclassified as to their level of exposure ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests for situations in which there is misclassification of exposure in a follow up study with categorical data we have developed a model that permits consideration of any number of exposure categories and any number of multiple category covariates when used with logistic and poisson regression procedures this model helps assess the potential for bias when misclassification is ignored when reliable ancillary information is available the model can be used to correct for misclassification bias in the estimates produced by these regression procedures

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

correspondence analysis applied to grouped cohort data in this paper we investigate application of generalized correspondence analysis gca to model a two way table of rates consisting of a cross classification of case numerators and person time denominators the gca reconstitution formula is proposed as a correlation model for analysing these data this provides two major advantages over the techniques usually applied the number of interaction parameters to be estimated is reduced and moreover they have useful interpretation the singular values and the scores are measures of row column modification interaction effects in addition the scores allow graphical display of these effects an asymmetrical plot is proposed for optimal representation of interaction parameters as distances finally two examples are presented to illustrate the method of analysing a two way table of covariate by exposure and a two way table derived from a cross classification of two exposure factors

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

a gee moving average analysis of the relationship between air pollution and mortality for asthma in barcelona spain several studies have assessed the association between air pollution and hospital admissions or emergency room visits for asthma because of both the presence of missing data and the small number of observations the relationship between air pollution and mortality for respiratory causes has been rarely analysed and when it has the results are very inconclusive or even inconsistent the objective of this study is to assess the relation between levels of air pollutants black smoke sulphur dioxide nitrogen dioxide and ozone meteorological variables 24th average temperature and relative humidity and daily mortality for asthma icd 9 493 2 to 45 years old in barcelona spain during the period 1986 1989 since the range of daily mortality for asthma 2 to 45 years old during the period 1986 1989 was 0 1 we have preferred to consider this variable as dichotomous first the relationship between air pollutants meteorological variables and daily mortality controlled for the occurrence of asthma epidemics was estimated using logistic regression models as was expected the residuals from this regression were autocorrelated showing a complex moving average ma structure if covariates were not time dependent the so called generalized linear mixed models could be applied in our case the covariates vary as a consequence the likelihood is numerically intractable because it involves the evaluation of n fold integral an alternative method that avoids these numerical problems is the generalized estimating equations method gee it is a multivariate analogue of quasilikelihood estimation in the absence of a likelihood function the parameters can be estimated by solving a multivariate analogue of the quasi score function we have modi ed the gee method in this paper allowing for a di erent structure in the error covariance matrix ma both air pollutants and meteorological variables are related with the occurrence of a death for asthma in this sense nitrogen dioxide no2 0 037 p 0 05 ozone o3 0 021 p 0 06 and high temperature the s were in the range 0 098 0 182 p 0 05 increased the probability of dying for asthma in barcelona during the period 1986 1989 copyright 1999 john wiley sons ltd

sample size calculations for comparative clinical trials with over dispersed poisson process data this paper develops a new formula for sample size calculations for comparative clinical trials with poisson or over dispersed poisson process data the criteria for sample size calculations is developed on the basis of asymptotic approximations for a two sample non parametric test to compare the empirical event rate function between treatment groups this formula can accommodate time heterogeneity inter patient heterogeneity in event rate and also time varying treatment effects an application of the formula to a trial for chronic granulomatous disease is provided