discharge rates of medicare stroke patients to skilled nursing facilities bayesian logistic regression with unobserved heterogeneity abstract we determine factors both hospital specific and market area specific associated with hospitals propensities for discharging medicare stroke patients to skilled nursing facilities snf s in california and florida logistic regression is generalized to the case of a betabinomial hierarchical model in which covariate information is included in the hyperparameters of the second stage beta distribution it is found that the posterior mean of the proportion discharged to snf is approximately a weighted average i e shrinkage estimator of the logistic regression estimator and the observed rate we develop fully bayesian inference that takes into account uncertainty about the hyperparameters and we find that this also allows us to test for overdispersion in a natural way the number of observed zeros i e hospitals that sent no stroke patients to a snf is excessive compared to the number expected from a standard logistic regression model and is fit better by the hierarchical betabinomial mod

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

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

classification error rate estimators evaluated by unconditional mean squared error in this article the criterion of unconditional mean squared error is used to compare four commonly used estimators of error rates in discriminant analysis the leave one out estimator which has relatively small bias is found to perform well relative to the other estimators when a large number of explanatory variables are used in the discriminant function with a small number of explanatory variables the large variance of this estimator results in poor performance we also find the estimators that assume normally distributed explanatory variables to be nonrobust when the parent distributions are skewed or have large tails

maximum likelihood estimation of the parameters of the prior distributions of three variables that strongly influence reproductive performance in cows ovulation detection rate pregnancy rate and embryo loss rate greatly affect the reproductive performance of cows a previous model described the separate effects of these variables on the resulting calving patterns and assumed that the variables have the same value for all cows belonging to the same herd this is not a realistic biological assumption so the beta distribution is used to introduce between cow variation in the three variables two approaches are used to find maximum likelihood estimates of the parameters of these prior beta distributions the first considers sequences of ovulations artificial inseminations and pregnancies separately for both ovulation detection rate and pregnancy rate this approach considers the number of successes of each event for a particular cow e g in the case of an ovulation a success is a detection and conditions on the total number of occurrences of that event in the cow so that beta binomial distributions are considered however for embryo loss rate the number of pregnancies required until a particular cow calves is considered so that a beta geometric distribution results if the cow is removed before she calves a censored sequence will result the second approach considers the sequences of ovulations artificial inseminations pregnancies and embryo losses together which will stop only when the cow calves otherwise if she is removed before that time a censored sequence will result in this case a joint distribution with three independent prior beta distributions is considered the results of the analysis of data from 22 herds are discussed

phase field computations of single needle crystals crystal growth and motion by mean curvature the phase field model for free boundaries consists of a system of parabolic differential equations in which the variables represent a phase or order parameter and temperature respectively the parameters in the equations are related directly to the physical observables including the interfacial width epsilon which we can regard as a free parameter in computation the phase field equations can be used to compute a wide range of sharp interface problems including the classical stefan model its modification to incorporate surface tension and or surface kinetic terms the cahn allen motion by mean curvature the hele shaw model etc also included is anisotropy in the equilibrium and dynamical forms generally considered by materials scientists by adjusting the parameters the computations can be varied continuously from single needle dendritic to faceted crystals the computational method consists of smoothing a sharp interface problem within the scaling of distinguished limits of the phase field e

the impact of litter effects on dose response modeling in teratology the fitting of dose response models to teratology data involving littermates in order to generate estimates of teratogenic risk is receiving increasing attention as a potential alternative to the safety factor approach to risk estimation in this paper we utilize the beta binomial distribution to introduce varying degrees of intralitter correlation and for purposes of illustration consider a logistic dose response model that describes the logit of risk as a straight line function of ln dose the biases and exact and asymptotic variances of the maximum likelihood estimators of the intercept and slope are studied by simulation as a function of the intralitter correlation structure

a mixed boundary value problem for tft lcd analysis and numerical methods abstract we study mixed boundary value problems for lcd liquid crystal displays with chiral nematic for calculating the orientation of molecules and the light transmission existence results are established for mixed boundary value problem numerical methods for time independent and dependent problems are investigated some numerical results are also given

the incorporation of historical control information in tests of proportions simulation study of tarone s procedure empirical bayes procedures for incorporating historical control information in bioassay carcinogenesis studies are receiving attention in the literature in general the empirical bayes methods fail to take into account the error in estimating the parameters of a prior distribution the implications of this are studied for the beta prior of tarone 1982 biometrics 38 215 220 using simulations we show that the skewness in the maximum likelihood estimators for the parameters of the beta prior increases the false positive rate in the test of dose related trend

estimation bias using the beta binomial distribution in teratology kupper et al 1986 biometrics 42 85 98 considered the fitting of dose response regressions to litter proportions in teratology experiments they found that the estimators which maximise the beta binomial likelihood become biased when the intralitter correlation is incorrectly assumed to be homogeneous this paper considers the nature of this bias and its implications for the analysis of litter proportions in toxicology

profile likelihood based confidence interval of the intraclass correlation for binary outcome data sampled from clusters the intraclass correlation in binary outcome data sampled from clusters is an important and versatile measure in many biological and biomedical investigations properties of the different estimators of the intraclass correlation based on the parametric semi parametric and nonparametric approaches have been studied extensively mainly in terms of bias and efficiency see for example ridout et al biometrics 1999 55 137 148 paul et al journal of statistical computation and simulation 2003 73 507 523 and lee statistical modelling 2004 4 113 126 but little attention has been paid to extending these results to the problem of the confidence intervals in this article we generalize the results of the four point estimators by constructing asymptotic confidence intervals obtaining closed form asymptotic and sandwich variance expressions of those four point estimators it appears from simulation results that the asymptotic confidence intervals based on these four estimators have serious under coverage to remedy this we introduce the fisher s z transformation approach on the intraclass correlation coefficient the profile likelihood approach based on the beta binomial model and the hybrid profile variance approach based on the quadratic estimating equation for constructing the confidence intervals of the intraclass correlation for binary outcome data as assessed by monte carlo simulations these confidence interval approaches show significant improvement in the coverage probabilities moreover the profile likelihood approach performs quite well by providing coverage levels close to nominal over a wide range of parameter combinations we provide applications to biological data to illustrate the methods copyright 2012 john wiley sons ltd

combining historical and randomized controls for assessing trends in proportions abstract a statistical method for incorporating historical control data in the analysis of proportions is proposed and illustrated the method has as its extremes logistic regressions completely pooling and completely ignoring historical controls the degree of pooling used is determined by the variability from experiment to experiment in the control incidences the fit of historical control groups to an assumed normal logistic model is assessed using probability plotting techniques monte carlo studies evaluate the adequacy of the asymptotic approximation used sensitivity analyses show that results are insensitive to alternative priors the method is applied to several sets of tumor data from animal experiments

a general goodness of fit approach for inference procedures concerning the kappa statistic the kappa statistic is frequently used as a measure of agreement among two or more raters although considerable research on statistical inferences for this statistic has been published for the case of two raters and a binary outcome relatively little work has appeared on inference problems for the case of multiple raters and or polytomous nominal outcome categories in this paper we propose a new procedure for constructing inferences for the kappa statistic that may be applied to this general case the procedure is based on a chi square goodness of fit test as applied to the dirichlet multinomial model and is a natural extension of previously proposed procedures that apply to more restricted cases a simulation study shows that the new procedure provides confidence interval coverage levels and type i error rates close to nominal over a wide range of parameter combinations we also present a sample size formula which may be used to determine the required number of subjects and raters for a given number of outcome categories

second variation of liquid crystal energy at x x dagger a new and simplified proof of the sign of the second variation of the oseen frank energy in terms of the elastic constants is given the proof relies on the frame indifference of the energy and a new expression for the second invariant null lagrangian as a surface integral

extended generalized estimating equations for clustered data abstract typically analysis of data consisting of multiple observations on a cluster is complicated by within cluster correlation estimating equations for generalized linear modeling of clustered data have recently received much attention this article proposes an extension to the generalized estimating equation method proposed by liang and zeger which treats within cluster correlations as nuisance parameters using ideas from extended quasi likelihood estimating equations for regression and association parameters are provided simultaneously the resulting estimators are proven to be asymptotically normal and consistent under certain conditions the consistency of regression estimators allows incorrect modeling of the correlation among repeated responses the method is illustrated with an analysis of data from a developmental toxicity study

general lemmas for stability analysis of linear continuous time systems with slowly time varying parameters this note investigates stability conditions for some dynamic systems with slowly time varying parameters or with unknown internal or external disturbances the models and conditions are motivated by adaptive control problems the results presented here provide some sufficient conditions for the exponential convergence of the state sequence of systems without system disturbance and for the uniform boundedness of the state sequence of such systems when they are subject to uniformly bounded system disturbances

two random effects models for multivariate binary data we consider two regression models for multivariate binary data in the case that the marginal success probabilities are unequal the first model is based on an additive random effect operating on the probability scale the second model assumes a discrete random effect operates on the logit scale consequently the interpretation of the regression parameters differs for the two models their use is illustrated by application to some dental data

the performance of the o brien fleming multiple testing procedure in the presence of intraclass correlation assuming that all subject responses were independent o brien and fleming 1979 biometrics 35 549 556 proposed a simple and useful multiple testing procedure for clinical trials for comparing two treatments with dichotomous data differences in the methods of evaluating subject responses at each evaluation time however may induce an intraclass correlation among these responses used in calculating the o brien fleming multiple testing procedure on the basis of monte carlo simulations we note that even a small intraclass correlation among subject responses in the same analysis can substantially inflate the type i error of the o brien fleming multiple testing procedure furthermore this inflation generally increases as either the number of analyses or the underlying response probability increases we also have demonstrated that if we were able to maintain a uniform medical test procedure between the two treatments for each analysis the actual type i error of the o brien fleming multiple testing procedure may conversely become conservative

interval estimation for the intraclass correlation in dirichlet multinomial data when the underlying distribution is discrete with a limited number of categories methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use on the basis of large sample theory this paper develops an asymptotic closed form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category this paper employs monte carlo simulation to demonstrate that when the underlying intraclass correlation is large the traditional interval estimator which assumes normality can be misleading we find that when the number of classes is 20 the interval estimator proposed here can generally perform reasonably well in a variety of situations this paper further notes that the proposed interval estimator is invariant with respect to a linear transformation when the data are on a nominal scale an extension of the proposed method to account for this case as well as a discussion on the relationship between the intraclass correlation and a kappa type measure defined here and on the limitation of the corresponding kappa type estimator are given

interval estimation of generalized odds ratio in data with repeated measurements when the underlying responses are on an ordinal scale the generalized odds ratio gor defined as the ratio of the proportions of concordant and discordant pairs is a useful index to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable we discuss interval estimation of the gor for ordinal data with repeated measurements on the basis of the dirichlet multinomial model we develop three asymptotic interval estimators of the gor using wald s test statistic a logarithmic transformation and a method analogous to fieller s theorem respectively to evaluate and compare the finite sample performance of these estimators we apply monte carlo simulation we find that when the number of subjects per group is not large the coverage probability of interval estimator using wald s test statistic is likely to be less than the desired confidence level by contrast the coverage probability of the other two estimators are approximately equal to or larger than the desired confidence level when the number of subjects per group is small and the intraclass correlation between repeated measurements within subjects is large we note that applying the interval estimator derived from a method analogous to fieller s theorem can lose efficiency we also note that the interval estimator using the logarithmic transformation is generally preferable to the other two estimators with respect to both the coverage probability and the average length finally on the basis of a few preliminary simulations we do find some robustness for all the estimators developed here we include an example comparing the inflammation grade after lung transplant between surgeries to illustrate the use of the proposed interval estimators

models for quantal response experiments over time response carter and hubert 1984 biometrics 40 699 706 propose and apply an approach based on multivariate growth curve theory to quantal bioassay over time their experimental data are reanalyzed using a fairly standard approach based on models for grouped response time data this alternate approach is considerably more direct and theoretically more satisfactory practical advantages include direct assessment of model adequacy and parsimonious modelling of extra multinomial variation

brief adaptive control of input constrained type 1 plants stabilization and tracking we consider the problem of controlling non minimum phase type 1 plants in presence of model uncertainty and a saturation constraint imposed on the control input the control objectives are the following i robust global asymptotic stabilization of the controlled plant with respect to a multiplicative modeling error ii output regulation in presence of external perturbations and iii tracking of output reference trajectories the problem is dealt with using a saturated indirect adaptive regulator based on a specific pole placement of the closed loop poles the slower the reference trajectory and the perturbation sequence the better the tracking and regulation quality

on the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems this paper considers the asymptotic distribution of the likelihood ratio statistic t for testing a subset of parameter of interest h 0 0 based on the pseudolikelihood l where is a consistent estimator of the nuisance parameter we show that the asymptotic distribution of t under h 0 is a weighted sum of independent chi squared variables some sufficient conditions are provided for the limiting distribution to be a chi squared variable when the true value of the parameter of interest 0 or the true value of the nuisance parameter 0 lies on the boundary of parameter space the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix or from a mixture of multivariate normal distributions a variety of examples are provided for which the limiting distributions of t may be mixtures of chi squared variables we conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments

exponential dispersion models on etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d erreur de nelder et wedderburn 1972

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

an interval estimate for the interclass correlation in beta binomial sampling the beta binomial distribution has been frequently applied to model intraclass correlation among dichotomous responses in cluster sampling to avoid using sophisticated numerical procedures to calculate maximum likelihood estimates many authors have proposed different moment estimators most of them focused their discussion however on point estimation only in this paper we have developed a closed form interval estimate for the intraclass correlation and have shown it has asymptotically correct coverage we have further used a monte carlo simulation to evaluate the performance of the proposed interval estimation in a variety of situations we have found that when the number of clusters is moderate 50 the proposed interval estimation performs reasonably well except for the situation where the intraclass correlation is large and the underlying mean response probability is small even when the number of clusters is as small as 20 the proposed interval estimation may still be useful in the situation where the intraclass correlation is small we have also extended the proposed interval estimate to accommodate stratified sampling in which each stratum has a different mean response probability but has a common intraclass correlation

adaptive control of time varying linear systems the authors present a global bounded input bounded state stability theory for a class of continuously adapting controllers applied to time varying linear systems this gives theoretical support to the application of many of the algorithms used in practice a key feature of the analysis is that no persistence of excitation requirement is needed

general lemma for the stability analysis of discrete time adaptive control we present a general lemma to investigate the uniform b undedness of the solutions of a class of discrete time dynamic systems in practical terms this lemma allows a demonstration of the bounded input bounded output bibo robust stability of all the available discrete time adaptive linear control systems

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

a random effects model for ordered categorical data abstract this article presents a random effects model for multivariate and grouped univariate ordered categorical data the assumed family of distributions for the random effects adopts a wide variety of forms and shapes the model s likelihood has a closed expression and can be computed without recourse to numerical integration or gaussian quadrature a bivariate and a grouped univariate example are used to illustrate the proposed model

a note on the effect of the intraclass correlation in the multiple reading procedure with a unanimity rule the use of multiple reading procedures to improve the performance of a diagnostic test occurs often in practice evaluation of the utility of multiple reading procedures however usually ignores the effect of the intraclass correlation this paper provides a quantitative assessment of this effect in the multiple reading procedure with a unanimity rule with respect to sensitivity specificity positive and negative predictive values we have found that when the disease prevalence is rare or moderate less than or equal to 0 20 use of the multiple reading procedure with a unanimity rule is effective in increasing the positive predictive value of a single reading procedure for the situation in which the variation of responses among different subjects and the intraclass correlation among repeated tests are small this is however not true for the situation in which the disease is rare and the variation of responses among different subjects is large even when the intraclass correlation is small or 0 furthermore when the disease is rare and the variation of responses among subjects is small a small or moderate intraclass correlation can substantially decrease the positive predictive value that one calculates under the assumption that the intraclass correlation is equal to 0 in general when the disease is rare or moderate less than or equal to 0 20 the intraclass correlation between repeated tests and the variation of responses among subjects have little effect on the negative predictive value

a parametric model for cluster correlated categorical data summary a fully parametric copula model for symmetric dependent clustered categorical data is discussed the model accommodates any marginal regression models of interest and admits a broad range of within cluster association the form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes the model contains an association parameter that is estimated from the data to give a measure of the strength of the within cluster association and also a test of independence two examples are given to illustrate the methods

the effect of retaining probability variation on sample size calculations for normal variates skalski 1992 biometrics 48 877 882 assumed a constant retaining probability p for all experimental units and found that the traditional ad hoc procedure of escalating sample size by the multiplicative factor ilp tends to underestimate the required sample size when p is small because this retaining probability p often depends on characteristics of different experimental units however p may vary from one unit to another in this report we have allowed p to vary among different experimental units we have noted that when the retaining probability p has a small mean but a large variance the underestimation of the required sample size for a desired precision by use of the traditional adjusted sample size formula can be even more serious than that demonstrated by skalski

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

empirical bayes confidence intervals for a series of related experiments when data from different studies are analyzed often one objective of the analysis is to obtain improved parameter estimates and confidence intervals for each individual study james stein or empirical bayes estimation is well suited to producing estimates this paper applies recent results on the construction of confidence intervals for the parameters of the individual studies a naive empirical bayes approach to confidence intervals assumes that the estimated posterior for each study can be used directly for inferences the naive approach generally leads to confidence intervals with less than the desired coverage morris 1983 journal of the american statistical association 78 47 59 suggested one approach to the construction of empirical bayes confidence intervals based on the use of a bayes hyperprior distribution laird and louis 1987 journal of the american statistical association 82 739 757 define the empirical bayes bootstrap for drawing bootstrap samples from the compound empirical bayes model and present a procedure for obtaining empirical bayes confidence intervals which uses the bootstrap samples to adjust for uncertainty in the estimate of the prior this paper compares the empirical performance of classical morris s and bootstrap intervals on a random sample of bioassays from the national cancer institute data base on potential chemical carcinogens

hypothesis testing for proportions with overdispersion summary the properties of likelihood ratio tests and simpler t tests are investigated by simulation under an assumed beta binomial model for parameter values typically found in toxicological studies it is found that likelihood ratio methods are at least as powerful as the simpler approaches and in certain situations can be significantly more powerful

the use of historical control information in testing for a trend in proportions a problem commonly faced in biometric applications is to test for a trend in proportions in a 2 x k contingency table in which the k columns have a natural ordering for example a test compound may be administered at increasing dose levels to groups of test animals to determine if the proportion of animals developing a tumor increases with increasing dose level cochran 1954 and armitage 1955 proposed a chi square statistic for testing for a trend in proportions for problems with a large amount of historical data a test for trend incorporating the historical data would be useful this paper develops such a test based on a statistic which is closely related to that of cochran and armitage this method for binomial proportions is analogous to the method derived by pocock 1976 for normallydistributed data the problem will be developed in the context of an animal carcinogenesis experiment consider an experiment involving r 1 groups of test animals one group serves as a control group and the remaining r groups are given a test compound at increasing dose levels dld2 dr the animals are followed for a fixed period of time and the number of animals which develop a tumor at a particular organ is recorded for each group let ni denote the number of animals in the ith group and let the number of these animals which develop a tumor during the course of the experiment be denoted by xi i 0 1 r the results of this experiment can be summarized in a 2 x r 1 table such as table 1 to test for ap increase in the proportions pi xjni with increasing dose level cochran and armitage suggested the test statistic

using empirical bayes methods in biopharmaceutical research a compound sampling model where a unit specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter underlies a wide variety of biopharmaceutical data for example in a multi centre clinical trial the true treatment effect varies from centre to centre observed treatment effects deviate from these true effects through sampling variation knowledge of the prior distribution allows use of bayesian analysis to compute the posterior distribution of clinic specific treatment effects frequently summarized by the posterior mean and variance more commonly with the prior not completely specified observed data can be used to estimate the prior and use it to produce the posterior distribution an empirical bayes or variance component analysis in the empirical bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects in both the bayes and empirical bayes approaches estimated clinic effects are shrunken towards a common value from estimates based on single clinics this shrinkage produces more efficient estimates in addition the compound model helps structure approaches to ranking and selection provides adjustments for multiplicity allows estimation of the histogram of clinic specific effects and structures incorporation of external information this paper outlines the empirical bayes approach coverage will include development and comparison of approaches based on parametric priors for example a gaussian prior with unknown mean and variance and non parametric priors discussion of the importance of accounting for uncertainty in the estimated prior comparison of the output and interpretation of fixed and random effects approaches to estimating population values estimating histograms and identification of key considerations in the use and interpretation of empirical bayes methods

innovations in bayes and empirical bayes methods estimating parameters populations and ranks by formalizing the relation among components and borrowing information among them bayes and empirical bayes methods can produce more valid efficient and informative statistical evaluations than those based on traditional methods in addition bayesian structuring of complicated models and goals guides development of appropriate statistical approaches and generates summaries which properly account for sampling and modelling uncertainty computing innovations enable implementation of complex and relevant models thereby substantially increasing the role of bayes empirical bayes methods in important statistical assessments policy relevant statistical assessments involve synthesis of information from a set of related components such as medical clinics geographic regions or research studies typical assessments include inference for individual parameters synthesis over the collection of components for example the parameter histogram and comparisons among parameters for example ranks the relative importance of these goals depends on the context bayesian structuring provides a guide to valid inference for example while posterior means are the obvious and optimal estimates for individual components under squared error loss their empirical distribution function edf is underdispersed and never valid for estimating the edf of the true underlying parameters effective histogram estimates result from optimizing a loss function based in a distance between the histogram and its estimate similarly ranking observed data usually produces poor estimates and ranking posterior means can be inappropriate effective estimates should be based on a loss function that caters directly to ranks using examples of borrowing information shrinkage and the variance bias trade off we motivate bayes and empirical bayes analysis then we outline the formal approach and discuss triple goal estimates with values that when ranked produce optimal ranks for which the edf is an optimal estimate of the parameter edf and such that the values themselves are effective estimates of co ordinate specific parameters we use basic models and data analysis examples to highlight the conceptual and structural issues

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

cluster sampling techniques in quantal response teratology and developmental toxicity studies summary this paper presents a model free approach for evaluating teratology and developmental toxicity data involving clustered binary responses in teratology studies a major statistical problem arises from the effect of intralitter correlation or the potential for littermates to respond similarly some statistical methods impose strict distributional assumptions to account for extra binomial variation while others rely on nonparametric resampling and empirical variance estimation techniques quasi likelihood methods and generalized estimating equations gee which model the marginal mean variance relationship also avoid strict distributional assumptions the proposed approach often used to analyze complex sample survey data is based on a first order taylor series approximation and a between cluster variance estimation procedure yielding consistent variance estimates for binomial based proportions and regression coefficients from dose response models the cluster sample technique presented here in the context of a logistic dose response model incorporates many of the advantages of quasi likelihood methods are valid for any underlying nested correlation structure and are adaptable to a variety of analytical settings the results of a simulation study show the cluster sample technique to be a viable competitor to gee methods currently receiving attention

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

a stabilized moment estimator for the beta binomial distribution the beta binomial distribution has been proposed as a model for the incorporation of historical control data in the analysis of rodent carcinogenesis bioassays low spontaneous tumor incidences along with the small number and sizes of historical control groups combine to make the moment and maximum likelihood estimates of the beta binomial parameters deficient we therefore propose a stabilized moment estimator for one of the parameters the stabilized moment estimator is similar to the ridge regression estimator and introduces a shrinkage parameter computer simulations were run to examine the behavior of the stabilized moment estimator the effect of the stabilized moment estimator on the score test for dose related trend is considered both on simulated data and on an example from the literature