analysis of embryonic development with a model for under or overdispersion relative to binomial variation summary observations from a study of the development of ovulations into embryos for texel sheep are analysed with a model for count data that are under or overdispersed relative to binomial variation the analysis is based on maximum quasi likelihood mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall following an approach suggested by williams 1982 applied statistics 31 144 148 the dispersion parameter is developed as a combination of a variance component representing shared maternal effects and a correlation typically negative between ovulations within ewes the number of ovulations the binomial denominator is included as an explanatory variable

an evaluation of some methods for fitting dose response models to quantal response developmental toxicology data the analysis of quantal response developmental toxicology data by dose response modeling is discussed with emphasis on methods that avoid exact distributional assumptions these methods quasi likelihood bootstrapping and jackknifing are contrasted with analyses based on the beta binomial distribution for the resampling procedures dose response models are fit under a binomial likelihood a justification for this choice of estimator in resampling plans is given based on an extension of the standard results for asymptotic normality and consistency of maximum likelihood estimators this justification depends only on the true distribution of the data having the usual binomial expectation a quasi likelihood approach is also considered in which simple assumptions about the intralitter correlation structure are made quasi likelihood methods are in theory asymptotically robust to misspecification of the intralitter correlation structure the practical implications of these asymptotic results are evaluated in a simulation study

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

robust tests for treatment effects based on censored recurrent event data observed over multiple periods summary we derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods these methods are based on estimating functions motivated by a working mixed poisson assumption under which conditioning can eliminate subject specific random effects robust pseudoscore test statistics are obtained via sandwich variance estimation the relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time homogeneous poisson model the robustness and empirical power of the semiparametric approach are assessed through simulation adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two period crossover trial of patients with bronchial asthma

small sample performance of the robust score test and its modifications in generalized estimating equations the sandwich variance estimator of generalized estimating equations gee may not perform well when the number of independent clusters is small this could jeopardize the validity of the robust wald test by causing inflated type i error and lower coverage probability of the corresponding confidence interval than the nominal level here we investigate the small sample performance of the robust score test for correlated data and propose several modifications to improve the performance in a simulation study we compare the robust score test to the robust wald test for correlated bernoulli and poisson data respectively it is confirmed that the robust wald test is too liberal whereas the robust score test is too conservative for small samples to explain this puzzling operating difference between the two tests we consider their applications to two special cases one sample and two sample comparisons thus motivating some modifications to the robust score test a modification based on a simple adjustment to the usual robust score statistic by a factor of j j 1 where j is the number of clusters reduces the conservativeness of the generalized score test simulation studies mimicking group randomized clinical trials with binary and count responses indicated that it may improve the small sample performance over that of the generalized score and wald tests with test size closer to the nominal level finally we demonstrate the utility of our proposal by applying it to a group randomized clinical trial trying alternative cafeteria options in schools tacos

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

the estimation of age period and cohort effects for vital rates in models for vital rates which include effects due to age period and cohort there is aliasing due to a linear dependence among these three factors this dependence arises both when age and period intervals are equal and when they are not one solution to the dependence is to set an arbitrary constraint on the parameters estimable functions of the parameters are invariant to the particular constraint applied for evenly spaced intervals deviations from linearity are estimable but only a linear function of the three slopes is estimable when age and period intervals have different widths further aliasing occurs it is assumed that the number of deaths in the numerator of the rate equation has a poisson distribution the calculations are illustrated with data on mortality from prostate cancer among nonwhites in the u s

working covariance model selection for generalized estimating equations we investigate methods for data based selection of working covariance models in the analysis of correlated data with generalized estimating equations we study two selection criteria gaussian pseudolikelihood and a geodesic distance based on discrepancy between model sensitive and model robust regression parameter covariance estimators the gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean variance relations for longitudinal data application is also made to a clinical dataset assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications and we describe open source software supporting this practice

nonparametric interval and point prediction using data trimmed by a grubbs type outlier rule for a fixed probability 0 y 1 the most outlying 100 1 y subset of the data from a location model may be located with a grubbs outlier subset test statistic this subset is essentially located in terms of its complement which is the connected looy span of the data which supports the smallest sample variance we show that this range of the data may be characterized approximately as the looy span such that its midpoint is equal to the trimmed mean averaged over the span such a range forms a tolerance interval for predicting a future observation from the location mqdel and the asymptotic laws for its location coverage and center are presented

clustered mixed nonhomogeneous poisson process spline models for the analysis of recurrent event panel data summary a flexible semiparametric model for analyzing longitudinal panel count data arising from mixtures is presented panel count data refers here to count data on recurrent events collected as the number of events that have occurred within specific follow up periods the model assumes that the counts for each subject are generated by mixtures of nonhomogeneous poisson processes with smooth intensity functions modeled with penalized splines time dependent covariate effects are also incorporated into the process intensity using splines discrete mixtures of these nonhomogeneous poisson process spline models extract functional information from underlying clusters representing hidden subpopulations the motivating application is an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth mature moths arise from hidden but distinct subpopulations and monitoring the subpopulation responses was of interest within cluster random effects are used to account for correlation structures and heterogeneity common to this type of data an estimating equation approach to inference requiring only low moment assumptions is developed and the finite sample properties of the proposed estimating functions are investigated empirically by simulation

content corrected tolerance limits based on the bootstrap this article considers k factor tolerance limits in which the p content is data dependent the proposed content corrected method is based on a bootstrap estimate of the given content and is shown to be robust in the sense of preserving the confidence coefficient for a variety of distributions for small or moderate sample sizes to all large samples we develop the theoretical basis for the asymptotic results and prove both asymptotic normality and weak consistency of the corresponding bootstrap statistic the method is shown to be asymptotically accurate with respect to the confidence coefficient for a wide class of distributions several simulations and two examples show the advantage of this method when the normality of the data cannot be assumed

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

using the overdispersed exponential family to estimate the distribution of usual daily intakes of people aged between 18 and 28 in taiwan assessment of usual dietary intake of a population is essential to understand the nutrition status of the population methods like 24 hour dietary recall and food records are commonly used for this task however within individual variation exists in the food record data methods considering measurement errors have been used to evaluate the association between nutrient intakes and diseases few have been devoted to estimating the distribution of usual daily intakes this paper proposes applying the formulation of the overdispersed exponential family to estimate the distribution of usual nutrient intake and applies the adjustments developed by liu to reduce the variance of the distribution the proposed method has the advantages of working on the original scale of data and implementation convenience the adjustment of the variance is carried out by dividing the variance into within individual variance and among individual variance the adjusted variance then is used to estimate the distribution of the usual daily intake sampling weights are considered in all the steps except the estimation of the ratio of within to among variance the data for this study are from the nutritional and health survey in taiwan conducted between 1993 and 1996 nahsit 1993 1996 an independent external set of data for people aged between 18 and 28 years 49 males and 20 females is used to estimate the ratio of within to among individual variance due to the availability of data in estimating the ratio of within to among individual variance 430 males and 422 females in the nahsit sample are used to estimate the distribution of usual daily intakes for people aged between 18 and 28 in taiwan the distribution also allows us to estimate the proportion of people who do not meet the recommended daily nutrient allowance rdna the results show that the intakes of calcium and vitamin e of this group of people fall far below rdna

chiral coefficient a measure of the amount of structural chirality a new concept of quantitative measurement of chiral structure is introduced and labelled as chiral coefficient chi a distinction is made between geometric and physical chiralities and chi is defined for various physical cases few general geometrical features are discussed and it is shown that for every chiral body there exists a natural z direction depending on the physical property treated possible practical applications of this concept are discussed a few simple examples of the chiral coefficient of mass chi m for chiral molecules are treated

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

a simple method for analysing overdispersion in clustered poisson data a simple method is proposed for analysing grouped count data exhibiting overdispersion relative to a poisson model the method is similar to the approach suggested for the analysis of clustered binary data in rao and scott 1992 it requires no specific model for the overdispersion and it can be implemented easily using standard programs designed to handle independent poisson counts after a small amount of preprocessing

chirality measures and graph representations abstract chirality handedness is a geometrical topological property of many physical systems a fundamentally important aspect of chemistry in particular of molecular shape and a fascinating feature of mathematical objects such as knots and graphs in this contribution some aspects of the quantification problem of chirality are discussed with special emphasis on chirality measures and their graph representations

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 detailed evaluation of adjustment methods for multiplicative measurement error in linear regression with applications in occupational epidemiology it is often appropriately assumed based on both theoretical and empirical considerations that airborne exposures in the workplace are lognormally distributed and that a worker s mean exposure over a reference time period is a key predictor of subsequent adverse health effects for that worker unfortunately it is generally impossible to accurately measure a worker s true mean exposure we begin by introducing a familiar model for exposure that views this true mean as well as logical surrogates for it as lognormal random variables in a more general context we then consider the linear regression of a continuous health outcome on a lognormal predictor measured with multiplicative error we discuss several candidate methods of adjusting for the measurement error to obtain consistent estimators of the true regression parameters these methods include a simple correction of the ordinary least squares estimator based on the surrogate regression the regression of the outcome on the covariates and on the conditional expectation of the true predictor given the observed surrogate and a quasi likelihood approach by means of a simulation study we compare the various methods for practical sample sizes and discuss important issues relevant to both estimation and inference finally we illustrate promising adjustment strategies using actual lung function and dust exposure data on workers in the dutch animal feed industry

interval estimation of the over dispersion parameter in the analysis of one way layout of count data the over dispersion parameter is an important and versatile measure in the analysis of one way layout of count data in biological studies for example it is commonly used as an inverse measure of aggregation in biological count data its estimation from finite data sets is a recognized challenge many simulation studies have examined the bias and efficiency of different estimators of the over dispersion parameter for finite data sets see for example clark and perry biometrics 1989 45 309 316 and piegorsch biometrics 1990 46 863 867 but little attention has been paid to the accuracy of the confidence intervals cis of it in this paper we first derive asymptotic procedures for the construction of confidence limits for the over dispersion parameter using four estimators that are specified by only the first two moments of the counts we also obtain closed form asymptotic variance formulae for these four estimators in addition we consider the asymptotic ci based on the maximum likelihood ml estimator using the negative binomial model it appears from the simulation results that the asymptotic cis based on these five estimators have coverage below the nominal coverage probability to remedy this we also study the properties of the asymptotic cis based on the restricted estimates of ml extended quasi likelihood and double extended quasi likelihood by eliminating the nuisance parameter effect using their adjusted profile likelihood and quasi likelihoods it is shown that these cis outperform the competitors by providing coverage levels close to nominal over a wide range of parameter combinations two examples to biological count data are presented copyright 2010 john wiley sons ltd

testing covariance structure in multivariate models application to family disease data abstract recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector the idea is to extend this distribution the null distribution to a more general distribution that depends on an additional scalar and a specific quadratic function of the response vector chosen to capture features of an alternative covariance structure when 0 the more general distribution reduces to the null one standard likelihood theory yields a score test for 0 that is a test of fit of the null distribution the score statistic is the standardized difference between observed and expected values of the quadratic function where the expectation is taken with respect to the null distribution with replaced by its maximum likelihood estimate applying the methods to case control data on familial cancers of the ovary and breast we illu

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

segregation analysis of case control data using generalized estimating equations generalized estimating equations gees liang and zeger 1986 biometrika 73 13 22 are used to fit genetic models to binary disease data for families of subjects in case control studies the gees include model specification of both the disease probabilities and the two way and possibly three way correlation coefficients of the family disease data these quantities are modelled as nonlinear functions of unobserved genotypes observed environmental covariates and the unknown parameters the functions reflect the method used to ascertain the family data goodness of fit is tested by allowing more flexible forms for the correlation coefficients regressing them against covariates specific to the relevant pair or triple of family members the approach is applied to family data obtained from simulated and real case control studies this semiparametric approach is less dependent on unverifiable assumptions and more computationally tractable than other methods for segregation analysis

the behavior of the stahel donoho robust multivariate estimator abstract the stahel donoho estimators t v of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w r where w is a weight function and r is a measure of outlyingness obtained by considering all univariate projections of the data it has a high breakdown point for all dimensions and order n consistency the asymptotic bias of v for point mass contamination for suitable weight functions is compared with that of rousseeuw s minimum volume ellipsoid mve estimator a simulation shows that for a suitable w t and v exhibit high efficiency for both normal and cauchy distributions and are better than their competitors for normal data with point mass contamination the performances of the estimators for detecting outliers are compared for both a real and a synthetic data set

principal component analysis based on robust estimators of the covariance or correlation matrix influence functions and efficiencies a robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix in this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors the behaviour of several of these estimators is investigated by a simulation study it turns out that the theoretical results and simulations favour the use of s estimators since they combine a high efficiency with appealing robustness properties 2000 biometrika trust

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

analysis of proportions in the presence of over under dispersion procedures for testing homogeneity of proportions in the presence of over dispersion or underdispersion occurring in several groups in toxicology teratology or mutagenicity or other similar fields are developed we consider c a neyman 1959 in probability and statistics the harold cramer volume pp 213 234 new york wiley or score type tests rao 1947 proceedings of the cambridge philosophical society 44 50 57 based on a parametric model namely the extended beta binomial model prentice 1986 journal of the american statistical association 81 321 327 and two semi parametric models using quasi likelihood wedderburn 1974 biornetrika 61 439447 and extended quasi likelihood nelder and pregibon 1987 biometrika 74 221 232 these procedures and a recent procedure by rao and scott 1992 biometrics 48 577 585 based on the concept of design effect and effective sample size are compared through simulation in terms of size power and robustness for departures from data distribution and dispersion homogeneity to study robustness in terms of departure from data distribution we simulate data from the betabinomial distribution the probit normal binomial distribution and the logit normal binomial distribution simulation shows evidence that for litter sizes and number of litters that may arise in practice a score test based on the quasi likelihood performs best in that it holds nominal level well in all data distribution situations considered here it shows some edge in power over some other statistics in some situations and also shows robustness in presence of moderate dispersion heterogeneity this statistic has a very simple form and it requires estimates of the parameters only under the null hypotheses

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

modelling overdispersion in toxicological mortality data grouped over time toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment both survival analysis and generalized linear models have been proposed for analyzing this type of data whatever the approach taken the model should allow for the presence of extra multinomial variation arising from the use of groups of animals rather than individuals as the experimental units we consider a number of models for overdispersion that can be incorporated into the generalized linear model framework for multinomial data these models are extensions of ones proposed for binomial data by williams 1982 applied statistics 31 144 148 and moore 1986 biometrika 73 583 588 1987 applied statistics 36 8 14 in addition we examine robust asymptotic covariance matrix estimators for regression parameters similar to those given in liang and zeger 1986 biometrika 73 13 22 and zeger and liang 1986 biometrics 42 121 130 and compare them to the model based asymptotic estimators recommendations for analysis are given

a variance components approach to categorical data models with heterogeneous cell populations analysis of spatial gradients in lung cancer mortality rates in north carolina counties a mixed categorical continuous variable model is proposed for the analysis of mortality rates this model differs from other available models such as weighted least squares and loglinear models in that the within cell populations are assumed to be heterogeneous in their levels of mortality risk heterogeneity implies that in addition to the sampling variance considered in other available models there will be a second component of variance due solely to within cell heterogeneity maximum likelihood procedures are presented for the estimation of the model parameters these procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function this assumption is shown to be equivalent to assuming a mixture of poisson processes with the differential risk levels among individuals within each cell being governed by a two parameter gamma distribution the model is applied to data on lung cancer mortality for 1970 1975 for the 100 counties of north carolina the analysis shows that though a gradient in lung cancer mortality rates exist in space the gradient is restricted to specific demographic categories identified by race age and sex

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

marginal analysis of panel counts through estimating functions we develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations using two types of self consistent estimating equations the first is derived from the likelihood studied in wellner zhang 2000 assuming a poisson counting process and gives a nondecreasing estimator which is the same as the nonparametric maximum likelihood estimator of wellner zhang and thus is consistent without the poisson assumption motivated by the construction of parametric generalized estimating equations the second type is a set of data adaptive quasi score functions which are likelihood estimating functions under a mixed poisson assumption we evaluate the procedures via simulation and illustrate them with the data from a bladder cancer study

testing trend for count data with extra poisson variability summary trend tests for monotone trend or umbrella trend monotone upward changing to monotone downward or vise versa in count data are proposed when the data exhibit extra poisson variability the proposed tests which are called the gs1 test and the gs2 test are constructed by applying an orthonormal score vector to a generalized score test under an rth order log linear model these tests are compared by simulation with the cochran armitage test and the quasi likelihood test of piegorsch and bailer 1997 statastics for enuiron mental biology and toxicology it is shown that the cochran armitage test should not be used under the existence of extra poisson variability that for detecting monotone trend the gs1 test is superior to the others and that the gs2 test has high power to detect an umbrella response

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

a comparison of methods for testing homogeneity of proportions in teratologic studies summary we consider teratologic studies in which the aim is to compare the survival rate of animals in a treatment group to the corresponding rate in a control group the design of such studies often involves the allocation of intact litters of animals to treatment invalidating the application of standard statistical methods we review the strengths and weaknesses of several approaches for dealing with this problem including methodology recently developed for the analysis of clustered binary data a simulation study is conducted in which litter sizes are generated from a distribution having specified mean and degree of imbalance it is recommended on the basis of this study and on theoretical considerations that the choice of method should depend on whether the comparison of interest is experimental or observational for experimental comparisons involving the random assignment of litters to different treatment groups methods based on the adjustment of standard chi square statistics are recommended unless the number of litters in each group is very large

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

likelihood quasi likelihood and pseudolikelihood some comparisons summary there is considerable interest in the fitting of models jointly to the mean and dispersion of a response for the mean parameter the wedderburn estimating equations are widely accepted however there is some controversy about estimating the dispersion parameters finite sampling properties of several dispersion estimators are investigated for three models by simulation we compare the maximum extended quasi likelihood estimator the maximum pseudolikelihood estimator and the maximum likelihood estimator if it exists of these estimators the maximum extended quasi likelihood estimator is usually superior in minimizing the mean squared error

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

a note on the efficiency of sandwich covariance matrix estimation the sandwich estimator also known as robust covariance matrix estimator heteroscedasticity consistent covariance matrix estimate or empirical covariance matrix estimator has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the fitted parametric model fails to hold or is not even specified surprisingly though there has been little discussion of properties of the sandwich method other than consistency we investigate the sandwich estimator in quasi likelihood models asymptotically and in the linear case analytically we show that under certain circumstances when the quasi likelihood model is correct the sandwich estimate is often far more variable than the usual parametric variance estimate the increased variance is a fixed feature of the method and the price that one pays to obtain consistency even when the p

using historical controls in the analysis of developmental toxicity data historical control data can often aid in the interpretation of the results from laboratory dose response experiments for example formal statistical methods for using historical data are well established for carcinogenicity studies in that case a score test derived from a beta binomial model yields a simple modification of the standard cochran armitage test for trend however this test cannot be used for developmental toxicity studies since it does not allow for the additional correlation structure induced by the presence of litter effects in this paper quasi likelihood methods are used to incorporate historical control information into a trend test for the types of correlated binary outcomes that typically arise in developmental toxicity studies the proposed test is asymptotically equivalent to the beta binomial score test in the special case when all the litter sizes are equal to 1 malformation data from a series of developmental toxicity studies illustrate the results

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

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

variances of mark recapture estimates when mark recapture data are analysed by log linear models as described by cormack 1989 biometrics 45 395 413 the analysis is in terms of parameters that are related nonlinearly to the parameters of biological interest for several models formulae are given expressing the variance of the interesting parameter estimates in terms of those provided by a computer log linear analysis a device is presented that allows such expressions to be computed simply

statistical methods for multivariate interval censored recurrent events multi type recurrent event data arise when two or more different kinds of events may occur repeatedly over a period of observation the scientific objectives in such settings are often to describe features of the marginal processes and to study the association between the different types of events interval censored multi type recurrent event data arise when the precise event times are unobserved but intervals are available during which the events are known to have occurred this type of data is common in studies of patients with advanced cancer for example where the events may represent the development of different types of metastatic lesions which are only detectable by conducting bone scans of the entire skeleton in this setting it is of interest to characterize the incidence of the various types of bone lesions to estimate the impact of treatment and other covariate effects on the development of new lesions and to understand the relationship between the processes generating the bone lesions we develop joint models for multi type interval censored recurrent events which accommodate dependencies between different types of events and enable one to examine the covariate effects via regression however since the marginal likelihood resulting from the multivariate random effect model is intractable we describe a gibbs sampling algorithm to facilitate model fitting and inference we use generalized estimating equations for estimation and inference based on marginal models the finite sample properties of the marginal approach are studied via simulation the estimates of both the regression coefficients and the variance covariance parameters are shown to have negligible bias and 95 per cent confidence intervals based on the asymptotic variance formula are shown to have excellent empirical coverage probabilities in all of the settings considered the application of these methods to data from a trial of women with advanced breast cancer provides insight into the clinical course of bone metastases in this population

robust multivariate tolerance regions influence function and monte carlo study in this article we define a class of multivariate tolerance regions that turn out to be more resistant than the classical ones to outliers the tolerance factors are numerically evaluated under the central model and the sensitivity to deviations from the normal distribution for moderate samples is studied through a monte carlo study moreover the influence function of the coverage probability allows us to compare the sensitivity of different proposals to anomalous data finally real data examples are discussed

mixed poisson regression models with covariate dependent rates this paper studies a class of poisson mixture models that includes covariates in rates this model contains poisson regression and independent poisson mixtures as special cases estimation methods based on the em and quasi newton algorithms properties of these estimates a model selection procedure residual analysis and goodness of fit test are discussed a monte carlo study investigates implementation and model choice issues this methodology is used to analyze seizure frequency and ames salmonella assay data

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

on the use of the quasi likelihood method in teratological experiments this paper concerns the impact of litter effects on the inference of dose response relationships in teratological experiments with binary response kupper et al 1986 biometrics 42 85 98 concluded that when intra litter correlations are dose dependent the use of a common intra litter correlation likelihood based on the beta binomial distribution could lead to severe bias in estimation of the parameter beta which characterizes the dose response relationship we show here that the problems of bias and coverage probability for beta could still be substantial when one uses the likelihood with heterogeneous intra litter correlations we then examine through a simulation study the performance of the quasi likelihood method wedderburn 1974 biometrika 61 439 447 and recommend that this method with a common intra litter correlation parameter be used when the number of litters is small or modest

multivariate outlier detection with high breakdown estimators in this paper we develop multivariate outlier tests based on the high breakdown minimum covariance determinant estimator the rules that we propose have good performance under the null hypothesis of no outliers in the data and also appreciable power properties for the purpose of individual outlier detection this achievement is made possible by two orders of improvement over the currently available methodology first we suggest an approximation to the exact distribution of robust distances from which cut off values can be obtained even in small samples our thresholds are accurate simple to implement and result in more powerful outlier identification rules than those obtained by calibrating the asymptotic distribution of distances the second power improvement comes from the addition of a new iteration step after one step reweighting of the estimator the proposed methodology is motivated by asymptotic distributional results its finite sample performance is evaluated through simulations and compared to

transform both sides approach for overdispersed binomial data when n is unobserved abstract a common complication in analyzing binomial data is overdispersion where the observed variation exceeds that predicted from the binomial distribution with parameters n and p we consider the situation where n is not observed and variable to estimate the regression parameters associated with covariates we apply the transform both sides method based on the first order asymptotic variance stabilizing transformation we develop the arcsine transformation family indexed by a single parameter this family includes the square root and the arcsine transformations as special cases asymptotic properties of the transformation methods are obtained simulation study indicates that the arcsine transformation family is more efficient than the square root and arcsine transformations when there is moderate overdispersion these approaches are applied to a data set from radiobiology

a quasi empirical bayes method for small area estimation abstract this article develops an empirical bayes type approach for small area estimation based only on the specification of a set of conditionally independent hierarchical mean and variance functions describing the first two moments of the process generating the data the objective of the analysis is to draw inference about the intermediate or the random means we combine the quasi likelihood functions to construct the quasi posterior density of the random means conditional on the data and the marginal parameters we describe a method for estimating the marginal parameters that are then substituted in the quasi posterior density of the random means the empirical quasi posterior density so derived is used to obtain the quasi empirical bayes estimates of the random parameters we apply the methodology to estimate the utilization rates of cancer chemotherapy for the selected counties in the state of washington

heterogeneity in mantel haenszel type models summary the mantel haenszel problem involves inferences about a common odds ratio in a set of 2 x 2 tables although it is a fairly standard practice to test whether the odds ratios are indeed constant there is remarkably little methodology available for proceeding when there is evidence of some heterogeneity our interest is in models where the log odds ratios ok for tables k 1 2 k are thought of as a sample from a population with mean 0 and standard deviation a and inferences are desired regarding the parameters 0 a by mantel haenszel type models we mean to include the generalization involving pairs of poisson observations rather than 2 x 2 tables where the ok are logarithms of ratios of the poisson means within pairs direct computation of the likelihood function for 0 a in these settings involves numerical integration and the main point here is a simple approximation to this likelihood the approximation is based on laplace s method and is very accurate for practical applications inference regarding the parameter 0 of primary interest may be made from the profile likelihood function an alternative approach to likelihood methods based on approximations to the marginal means and variances is also considered the methods explored here can be readily generalized to settings where the parameters ok depend on covariables as well

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